DESC:RESERVATION OF RIGHTS
[001] A portion of the disclosure of this patent document contains material which is subject to intellectual property rights such as, but are not limited to, copyright, design, trademark, Integrated Circuit (IC) layout design, and/or trade dress protection, belonging to Jio Platforms Limited (JPL) or its affiliates (herein after referred as owner). The owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent files or records, but otherwise reserves all rights whatsoever. All rights to such intellectual property are fully reserved by the owner.

TECHNICAL FIELD
[002] The present disclosure relates to a field of artificial intelligence, and specifically to a system and a method for constrained optimization with constraints of a topologically ordered set of equipment of a process unit, where each equipment is associated with a corresponding neural network that is trained with data filtered with active sampling strategy to maximise a business objective function defined for the process unit.

BACKGROUND
[003] The following description of related art is intended to provide background information pertaining to the field of the disclosure. This section may include certain aspects of the art that may be related to various features of the present disclosure. However, it should be appreciated that this section be used only to enhance the understanding of the reader with respect to the present disclosure, and not as admissions of prior art.
[004] Automation has been the primary objective of the Fourth Industrial Revolution. Automation in industries such as manufacturing, refineries, warehousing, supply chain management, and telecommunication, among others, has allowed for improved efficiency and dynamic optimization of operations of one or more process units in the industries, thereby improving productivity and profitability. The process units may be provided with a set of tangible inputs to produce a set of tangible outputs. The process unit may be optimized for productivity, profitability, or any other business objective by adjusting one or more operational parameters of the process unit, and by adjusting the tangible inputs provided to the process unit.
[005] Prevalent solutions for improving productivity and profitability, among others, tend to optimize each of one or more equipment in the process units independently of the other, and hence suffer from various limitations. Such solutions often use linear optimization which may not optimize the operation of the process unit to an acceptable degree. Linear optimization techniques are incapable of accurately optimizing the tangible inputs and the operational parameters for maximizing profits when dealing with each of the equipment in the process unit that are interconnected and topologically ordered.
[006] Particularly, existing solutions cannot dynamically optimize the tangible inputs and operational parameters in response to changes in market forces. For instance, existing linear optimization solutions that independently optimize tangible inputs such as feed quality, flow rates, and operating parameters like temperature, pressure, the efficiency of the equipment etc., cannot factor market prices of the tangible outputs produced by the process units and the cost of tangible inputs in real time for maximizing the business objective.
[007] Therefore, there is a need in the art to provide a system and a method for non-linear optimization of input and control values of equipment in a process unit having topological ordering, to maximize the business objective.

OBJECTS OF THE PRESENT DISCLOSURE
[008] An object of the present disclosure is to provide a system and a method that optimizes the operation of a process unit having a plurality of equipment.
[009] Another object of the present disclosure is to provide a system and a method that uses constrained optimization with constraints for the plurality of equipment of the process unit, where the plurality of equipment has a topological ordering.
[0010] Another object of the present disclosure is to provide a system and a method that optimizes the operation of the plurality of equipment that are connected in a Directed Acyclic Graph (DAG).
[0011] Another object of the present disclosure is to provide a system and a method that back-propagates a predetermined loss value through an entire chain of equipment to optimize the entire joint distribution of the equipment for maximizing a business objective value.
[0012] Another objective of the present disclosure is to provide a system and a method that updates one or more control values during back-propagation.
[0013] Another object of the present disclosure is to provide a system and a method that uses an active sampling strategy for selecting training data for a set of neural networks associated with the plurality of equipment.
[0014] Another object of the present disclosure is to provide a system and a method that has a business objective function of the process unit that uses a Lagrange multiplier for providing linear constraints.

SUMMARY
[0015] The present disclosure relates to a field of artificial intelligence, and specifically to a system and a method for constrained optimization with constraints of a topologically ordered set of equipment of a process unit where each of the equipment is associated with a corresponding neural network that is trained with data filtered with active sampling strategy to maximize a business objective function defined for the process unit.
[0016] In an aspect, a system for constrained optimization of a set of equipment of a process unit includes one or more processors and a memory operatively coupled to the one or more processors, the memory having one or more processor-executable instructions. Execution of the one or more processor-executable instructions cause the one or more processors to determine one or more output values based on one or more input values and one or more control values using a set of neural networks, where each neural network in the set of neural networks corresponds to at least one equipment from the set of equipment. The one or more processors determine a business objective value based on the one or more output values, the one or more input values, and the one or more control values. The one or more processors back-propagate a beta value through the set of neural networks to update the one or more control values, wherein at least one tangible input corresponding to the one or more updated control values and the one or more input values is provided to the process unit for producing at least one tangible output.
[0017] In an embodiment, the one or more processors may be configured to iteratively determine the one or more output values, determine the business objective value, and back-propagate the beta value for updating the one or more control values until a stopping criterion may be met.
[0018] In an embodiment, the set of neural networks may be topologically ordered corresponding to the set of equipment, wherein the one or more output values determined by a preceding neural network may be provided as the one or more input values for a succeeding neural network from the set of neural networks based on the topological ordering.
[0019] In an embodiment, the one or more processors may be configured to train the set of neural networks to map the one or more input values and the one or more control values to the one or more output values associated with the corresponding equipment in the set of equipment, each neural network from the set of neural networks being trained with any one or a combination of a set of historical data or a set of simulated data.
[0020] In an embodiment, the set of simulated data may be generated, using a simulation engine, for each combination of values within a predetermined operating range, the simulation engine filtering the set of simulated data with active complexity sampling such that the corresponding neural network learns regions of error in a parameter hyperspace associated with the neural network.
[0021] In an embodiment, to determine the business objective value, the one or more processors may be configured to retrieve a market cost value associated with each of the one or more input values and each of the one or more control values, and a market price value associated with the one or more output values, retrieve one or more constraints associated with the one or more input values and the one or more control values, and compute the business objective value based on the one or more input values and the one or more control values with the corresponding market cost values, and the one or more output values with the corresponding market price value, subject to the one or more constraints.
[0022] In an embodiment, the one or more constraints may include one or more linear constraints and one or more boundary constraints associated with each of the one or more input values and the one or more control values.
[0023] In an aspect, a method for constrained optimization of a set of equipment of a process unit includes determining, by one or more processors, one or more output values based on one or more input values and one or more control values using a set of neural networks, where each neural network in the set of neural networks corresponds to at least one equipment from the set of equipment. The method includes determining, by the one or more processors, a business objective value based on the one or more output values, the one or more input values, and the one or more control values. The method includes back-propagating, by the one or more processors, a beta value through the set of neural networks to update the one or more control values, where at least one tangible input corresponding to the one or more updated control values and the one or more input values is provided to the process unit for producing at least one tangible output.
[0024] Various objects, features, aspects, and advantages of the inventive subject matter will become more apparent from the following detailed description of preferred embodiments, along with the accompanying drawing figures in which like numerals represent like components.

BRIEF DESCRIPTION OF THE DRAWINGS
[0025] In the figures, similar components and/or features may have the same reference label. Further, various components of the same type may be distinguished by following the reference label with a second label that distinguishes among the similar components. If only the first reference label is used in the specification, the description is applicable to any one of the similar components having the same first reference label irrespective of the second reference label.
[0026] The diagrams are for illustration only, which thus is not a limitation of the present disclosure, and wherein:
[0027] FIG. 1 illustrates an exemplary block diagram 100 of a proposed system 108, in accordance with embodiments of the present disclosure.
[0028] FIGs. 2A-2B illustrate exemplary block representations 200A and 200B of a business objective function, in accordance with embodiments of the present disclosure.
[0029] FIG. 2C illustrates an exemplary model 200C for the business objective function, in accordance with embodiments of the present disclosure.
[0030] FIG. 3 illustrates an exemplary block representation 300 for training neural networks 106 to approximating a simulation function, in accordance with embodiments of the present disclosure.
[0031] FIG. 4 illustrates an exemplary representation 400 of one or more constraints associated with the business objective function, in accordance with embodiments of the present disclosure.
[0032] FIGs. 5A-5B illustrate exemplary Lagrangian functions 500A and 500B indicating the boundary constraints of input values and control values respectively, in accordance with embodiments of the present disclosure.
[0033] FIGs. 5C-5D illustrate exemplary Lagrangian functions 500C and 500D indicating linear constraints of the input values and the control values respectively, in accordance with embodiments of the present disclosure.
[0034] FIGs. 6A-6B illustrate an exemplary flowchart 600A of a forward propagation function and an exemplary flowchart 600B of a back-propagation function, in accordance with embodiments of the present disclosure.
[0035] FIG. 7 illustrates an exemplary implementation 700 of the system 108, in accordance with embodiments of the present disclosure.
[0036] FIG. 8 illustrates an exemplary schematic block diagram 800 of the system 108 for optimizing a process unit 102, in accordance with embodiments of the present disclosure.
[0037] FIG. 9 illustrates exemplary graphical plots 902, 904, and 906 showing changes in boundary constraints, linear constraints, and profitability, respectively, over a plurality of epochs, in accordance with embodiments of the present disclosure.
[0038] FIG. 10 illustrates an exemplary flowchart of a method 1000 for constrained optimization of process units 102, in accordance with embodiments of the present disclosure.
[0039] FIG. 11 illustrates an exemplary computer system 1100 in which or with which embodiments of the present disclosure may be utilized in accordance with embodiments of the present disclosure.

DETAILED DESCRIPTION
[0040] In the following description, for the purposes of explanation, various specific details are set forth in order to provide a thorough understanding of embodiments of the present disclosure. It will be apparent, however, that embodiments of the present disclosure may be practiced without these specific details. Several features described hereafter can each be used independently of one another or with any combination of other features. An individual feature may not address all of the problems discussed above or might address only some of the problems discussed above. Some of the problems discussed above might not be fully addressed by any of the features described herein.
[0041] The ensuing description provides exemplary embodiments only, and is not intended to limit the scope, applicability, or configuration of the disclosure. Rather, the ensuing description of the exemplary embodiments will provide those skilled in the art with an enabling description for implementing an exemplary embodiment. It should be understood that various changes may be made in the function and arrangement of elements without departing from the scope of the invention as set forth.
[0042] Specific details are given in the following description to provide a thorough understanding of the embodiments. However, it will be understood by one of ordinary skill in the art that the embodiments may be practiced without these specific details. For example, circuits, systems, networks, processes, and other components may be shown as components in block diagram form in order not to obscure the embodiments in unnecessary detail. In other instances, well-known circuits, processes, algorithms, structures, and techniques may be shown without unnecessary detail in order to avoid obscuring the embodiments.
[0043] In an aspect, a system for constrained optimization of a set of equipment of a process unit may include one or more processors coupled to a memory, the memory having one or more processor-executable instructions. Execution of the one or more processor-executable instructions may cause the one or more processors to determine one or more output values based on one or more input values and one or more control values using a set of neural networks, where each neural network in the set of neural networks corresponds to at least one equipment from the set of equipment. The one or more processors may determine a business objective value based on the one or more output values, the one or more input values, and the one or more control values. The one or more processors may back-propagate a beta value through the set of neural networks to update the one or more control values, wherein at least one tangible input corresponding to the one or more updated control values and the one or more input values may be provided to the process unit for producing at least one tangible output.
[0044] Various embodiments of the present disclosure will be explained in detail with respect to FIGs. 1-11.
[0045] FIG. 1 illustrates an exemplary system architecture 100 of a proposed system 108, in accordance with an embodiment of the present disclosure. In some embodiments, the system 108 may be configured to optimize the operation or functioning of a process unit 102. In some embodiments, the process unit 102 may include a set of equipment 104, such as a first equipment 104-1 and a second equipment 104-2.
[0046] In some embodiments, the process unit 102 may be associated with an industry, including, but not limited to, manufacturing, refineries, warehousing, logistics, or the like. The process unit 102 may be designed to perform an operation such as including, but not limited to, manufacturing, processing, refining, packaging, or the like. In an example, the process unit 102 may be associated with a refinery. In such examples, the process unit 102 may be indicative of a petrochemical refinement unit having a set of equipment 104 for refining petrochemicals.
[0047] In some embodiments, the set of equipment 104 may be provided with a tangible input to produce a tangible output. The tangible input may be raw materials and resources provided to the set of equipment 104. In some embodiments, the tangible inputs provided to the set of equipment 104 may be quantified by one or more input values and one or more control values. The tangible output may include, but not be limited to, materials, compositions, articles, flows, products, or the like. In some embodiments, the tangible outputs produced by the set of equipment 104 may be quantified by one or more output values. The process unit 102, by the set of equipment 104, may be operated to convert the tangible input into the tangible output.
[0048] In some embodiments, each equipment in the set of equipment 104 may be topologically ordered. In some embodiments, the second equipment 104-2 may be dependent on the first equipment 104-1. In such embodiments, the tangible output of the first equipment 104-1 may be provided as the tangible input to the second equipment 104-2. In some embodiments, the set of equipment 104 may be interconnected in a Directed Acyclic Graph (DAG). In an example, the DAG of the set of equipment 104 may correspond to the piping and instrumentation diagram (P&ID) of the set of equipment 104 of the process unit 102.
[0049] In some embodiments, each equipment from the set of equipment 104 may have a corresponding neural network 106 associated therewith. As shown, the first equipment 104-1 may have a first neural network 106-1 associated therewith, and the second equipment 104-2 may have a second neural network 106-2. The set of neural networks 106 corresponding to the set of equipment 104 may be trained to map the one or more input values and the one or more control values to the one or more output values. In some embodiments, each neural network 106 may have a set of weights arranged in a plurality of layers. The weights may be represented by float point numbers.
[0050] In some embodiments, the system 108 may be configured to optimize the process unit 102. In some embodiments, the system 108 may have access to the set of neural networks 106 associated with the set of equipment 104 of the process unit 102. The system 108 may use the set of neural networks 106 to determine the one or more output values based on the one or more input values and the one or more control values. The system 108 may simulate the process unit 102 to estimate the tangible output produced by the process unit 102 when a known tangible input is provided thereto.
[0051] Referring to FIG. 1, the system 108 may include one or more processors 112 coupled with a memory 114, where the memory 114 may store processor-executable instructions. Execution of the processor-executable instruction by the one or more processors 112 may cause the system 108 to optimize the process unit 102. The one or more processor(s) 112 may be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, logic circuitries, and/or any devices that process data based on operational instructions. The memory 114 may be configured to store one or more processor-readable instructions or routines in a non-transitory processor-readable storage medium. The memory 114 may include any non-transitory storage device including, for example, volatile memory such as Random Access Memory (RAM), or non-volatile memory such as Erasable Programmable Read-Only Memory (EPROM), flash memory, and the like.
[0052] In some embodiments, the system 108 may include an interface(s) 116. The interface(s) 116 may include a variety of interfaces, for example, interfaces for data input and output devices, referred to as I/O devices, storage devices, and the like. The interface(s) 116 may facilitate communication with the system 108. The interface(s) 116 may also provide a communication pathway for one or more components of the system 108. Examples of such components include, but are not limited to, processing engine(s) 118 and a database 140.
[0053] The processing engine(s) 118 may be implemented as a combination of hardware and programming (for example, programmable instructions) to implement one or more functionalities of the processing engine(s) 118. In examples described herein, such combinations of hardware and programming may be implemented in several different ways. For example, the programming for the processing engine(s) 118 may be processor-executable instructions stored on a non-transitory machine-readable storage medium, and the hardware for the processing engine(s) 118 may include a processing resource (for example, one or more processors), to execute such instructions. In the present examples, the machine-readable storage medium may store instructions that, when executed by the processing resource, implement the processing engine(s) 118. In other examples, the processing engine(s) 118 may be implemented by an electronic circuitry.
[0054] The processing engine 118 may include one or more engines including, but not limited to, a simulation engine 120, a training engine 122, an inference engine 124, a price and cost engine 126, a business objective engine 128, a back-propagation engine 130, and other engines 132.
[0055] In an embodiment, the simulation engine 120 may be configured to generate training data for training the set of neural networks 106. The training data may include any one or combination of, but not limited to, historical data or simulated data. In some embodiments, the historical data may be indicative of the data collected from the corresponding equipment 104 during its operation. In an example, the historical data may be collected by an Internet of Things (IoT) device on the corresponding equipment. The set of simulated data may be generated by the simulation engine 120. The set of simulated data may be generated using a simulation function, as described in reference to FIGs. 2A to 3. In some embodiments, the set of simulated data may be stored in the database 140.
[0056] In some embodiments, the training engine 122 may be configured to train the set of neural networks 106 using the training data. In some embodiments, the inference engine 124 may be configured to determine the one or more output values based on the one or more input values and the one or more control values. In such embodiments, the inference engine 124 may use the neural network 106 to determine the one or more output values.
[0057] In some embodiments, the price and cost engine 126 may be configured to receive one or more market cost values associated with the tangible inputs and one or more market price values associated with the tangible output. In some embodiments, the price and cost engine 126 may retrieve the market cost values and the market price values by querying an external application engine in real-time. In other embodiments, the price and cost engine 126 may receive the market cost value and the market price values from a human operator.
[0058] In some embodiments, the business objective engine 128 may be configured to determine a business objective value based on the one or more output values, the one or more input values, and the one or more control values. In some embodiments, the objective engine 128 may include a business objective function that determines the one or more output values based on one or more constraints associated with the one or more input values and the one or more control values, as described in reference to FIGs. 4 to 5D.
[0059] In some embodiments, the back-propagation engine 130 may be configured to back-propagate a predetermined beta value through the set of neural networks 106 to update the one or more control values. The beta value may be indicative of a loss propagated through each of the neural networks 106 to update the one or more control values. In some embodiments, the beta value may be selected such that the gradient of the beta value causes the business objective value to ascend or increase after each iteration of back-propagation. In some embodiments, the back-propagation engine 130 may update the one or more control values during back-propagation. In some embodiments, the back-propagation engine 130 may perform gradient ascent during the back-propagation.
[0060] In some embodiments, the inference engine 124, the price and cost engine 126, the business objective engine 128, and the back-propagation engine 130 may iterate execution thereof until a stopping criterion is met.
[0061] In some embodiments, the other engine(s) 132 may include the external application engine. In some embodiments, the set of neural networks 106 may be stored in the database 140.
[0062] FIGs. 2A-2B illustrates exemplary block representations 200A and 200B of the business objective function, in accordance with embodiments of the present disclosure. The business objective functions as shown in FIGs. 2A and 2B may include the set of neural networks 106 for mapping the one or more input values and the one or more control values to the one or more output values. The business objective function, as shown in FIG. 2A, may include the set of neural networks 106. The business objective function, as shown in FIG. 2B, may adapt the set of neural networks 106 to optimize the one or more control values for the given one or more input values and the generated one or more output values.
[0063] In an embodiment, the set of neural networks 106 may be trained for mapping the input values and the control values to the output values. The set of neural networks 106 may provide linear or non-linear mappings of the input values and the control values with the output values.
[0064] In some embodiments, the one or more input values may correspond to one or more tangible inputs provided to the corresponding equipment 104 of the process unit 102. The one or more tangible outputs may have a market-determined cost associated therewith.
[0065] In some embodiments, the one or more control values may be indicative of variables or factors that may be updated for the purposes of optimization of the process unit 102. In some examples, the one or more control values may be operating parameters of the process unit 102, including, but not be limited to, temperature, pressure, flow rate, and the like. In some embodiments, the business objective function may correspond to either one or a combination of maximizing productivity or profitability.
[0066] In some embodiments, the one or more output values may correspond to the tangible output generated by the corresponding equipment 104. The one or more output values may be dependent on the one or more input values and the one or more control values. In some embodiments, the one or more output values may have a non-linear relationship with the one or more input values and the one or more control values. In other embodiments, the relationship therebetween may be linear.
[0067] FIG. 2C illustrates an exemplary model 200C for the business objective function, in accordance with embodiments of the present disclosure. The business objective function may indicate the relationship between the input values and the control values, and the output values. As shown, the business objective function may be a non-linear mapping from input x(i) and its control parameters u(i) to its output, y(i). The business objective function may be given as .
[0068] FIG. 3 illustrates an exemplary block representation 300 for training the neural networks 106 to approximate the simulation function, in accordance with embodiments of the present disclosure. In some embodiments, the set of neural networks 106 may be trained on historical data that maps the input values and control values to the output values. In such embodiments, the set of neural networks 106 may learn to approximate the simulation function.
[0069] In some embodiments, the simulation engine 120 may generate the set of simulated data using the simulation function over an operating range 304 associated with the input values and the control values. The simulation engine 120 may generate one or more of the output values for each combination of the input values and the control values within the operating range 304. In some embodiments, the operating range 304 may be provided by an operator of the process unit 102. In other embodiments, the operating range 304 may be dynamically altered based on historical data collected for each equipment 104 in the process unit 102. In some embodiments, the simulation engine 120 may generate the set of simulated data for each combination of values within the operating range 304. In some embodiments, the simulation engine 120 may use active complexity-based sampling to obtain the set of simulated data across the (input, control) space. The set of simulated data may be stored in the database 140. The active sampling may filter the set of simulated data for training the set of neural networks 106 such that each of the neural networks learns regions of error in the parameter hyperspace associated with the neural network.
[0070] In an example, a chemical process simulator may be used for generating simulated data. In some embodiments, active sampling may be used for extracting the set of simulated data for training the set of neural networks 106. In such embodiments, a steady-state or dynamic simulation of the set of equipment 104 may be generated. In such examples, a mass balance of compositions may have one or more of the output values where there may be lesser degrees of freedom.
[0071] In some embodiments, the simulation engine 120 may generate a unique simulated data for each equipment in the set of equipment 104 using the simulation function corresponding to the process unit 102. In some embodiments, the neural network 102 corresponding to each equipment 104 may be trained with the corresponding simulated data. The set of neural networks 106 may be trained to approximate the linear or non-linear mapping from (Input values, Control values) ? Output values based on the simulation function. On training, the neural network 106 may learn to approximate the mapping between the input values and the control values, and the output values. The trained neural network 106 may be represented as y(i)= NN(X(i), u(i)).
[0072] In some embodiments, the set of equipment 104, and correspondingly the set of neural networks 106, may have a topological ordering. In such embodiments, the topological ordering of the set of neural networks 106 may be represented by a DAG. In some embodiments, the DAG may correspond to the P&ID of the process unit 102. In such embodiments, one or more of the output values of a first subset of neural networks may be provided as one or more of the input values of a second subset of neural networks. The control values of each equipment in the set of equipment 104 may be provided to the corresponding neural network 106 for inference. In some embodiments, the control values may be provided manually. In other embodiments, the control values may be dynamically updated during the optimization of the process unit 102. Once the system 108 updates the control values, the process unit 102 may be provided with the tangible inputs corresponding to the control values.
[0073] In some embodiments, the output values from the final neural network in the set of neural networks 106 with respect to the DAG, and the output values of the neural networks unused by subsequent neural networks with respect to the DAG may be used for determining the business objective value. In some embodiments, one or more of the output values may be provided as input for deriving the business objective value. The business objective value may indicate the profitability or productivity of the process unit 102.
[0074] In some embodiments, the one or more output values may indicate the tangible output produced by the process unit 102 for the given set of tangible inputs indicated by the input values and the control values. The business objective value may be determined therefrom by the business objective engine 128. The business objective engine 128 may determine the business objective value using the business objective function based on the one or more output values, the one or more input values, and the one or more control values.
[0075] In some embodiments, the business objective function may use the market cost value associated with the tangible inputs and the market price value associated with the tangible outputs. The market cost value may be indicative of the cost of the tangible inputs and the market price values may be indicative of the prices of the tangible outputs produced by the process unit 102 in an open market. The market cost values and the market price values may dynamically change based on market forces.
[0076] In some embodiments, the market cost values and the market price values may be provided to the business objective function by the operator manually, or by the price and cost engine 126 in real-time. The business objective function value may be the difference between a first aggregate of products of the market cost values and the corresponding input values and control values, and a second aggregate of products of the market price value of each of the output values produced by the process unit 102. In some embodiments, the first aggregate may include cost of operating the set of equipment 104, cost incurred in terms of using feed or raw materials, and opportunity cost of selling the output in the open market. In some embodiments, the business objective function may also determine the business objective value subject to one or more constraints associated with the input values and the output values.
[0077] FIG. 4 illustrates an exemplary representation 400 of the one or more constraints associated with the business objective function, in accordance with embodiments of the present disclosure. With respect to FIG. 4, the one or more constraints may include one or more boundary constraints and one or more linear constraints associated with each of the input values and the control values. The one or more constraints of the system 108 may allow the business objective function to be differentiated for determining one or more gradient values. The one or more control values may be updated by the corresponding gradient values. As shown, the input values may be represented by , where ranges from 1 to any positive integer . The business objective function may have the one or more boundary conditions associated with the one or more input values defined by a predetermined indicative of a minimum threshold value and a predetermined indicative of a maximum threshold value for the input values. Similarly, the control values may be represented by , where ranges from 1 to any positive integer . The business objection function may have the one or more boundary conditions associated with the one or more control values defined by a predetermined indicative of a minimum threshold value and a predetermined indicative of a maximum threshold value for the control values. Each of the and the may be between the corresponding minimum and the maximum threshold values.
[0078] Further, the business objective function may have the one or more linear constraints associated with each of the one or more input values. The one or more linear constraints may be associated with one or more linear equations corresponding to the input values and the control values. A first linear equation corresponding to the input values may be given by where is a coefficient corresponding to the input value . In some embodiments, a first linear constraint may be represented as , where is indicative of minimum threshold linear constraint and is indicative of maximum threshold linear constraint for the input values. In an example, one of the input values, such as , may correspond to quantity feedstock provided to the process unit 102 indicative of a petrochemical refinery. In such example, the coefficient may correspond to the market cost value of providing the feedstock to the process unit 102. In an embodiment, the price and cost engine 126 may determine the aggregate cost of one or more fixed tangible inputs based on the first linear equation.
[0079] A second linear equation corresponding to the control values may be given by where is a coefficient corresponding to the input variable . In some embodiments, a second linear constraints may be represented as , where is indicative of minimum threshold linear constraint and is indicative of maximum threshold linear constraint for the control values. The second linear equation may be used to derive the second aggregate associated with the one or more control values provided to the process units 102. In an example, one of the control values, such as , may correspond to temperature at which the feedstock in the process unit 102 indicative of a petrochemical refinery is maintained. In such example, the coefficient may correspond to the market cost value of operating the process unit 102 at the temperatures corresponding to the control value. In an embodiment, the price and cost engine 126 may determine an aggregate of one or more controlled tangible inputs based on the second linear equation.
[0080] In some embodiments, the business objective function may be an optimization function given by:
, where:
• correspond to the input values and the control values, respectively,
• corresponds to the business objective function,
• corresponds to the business objective value determined from the output values, which in-turn is generated based on the input values and the control values,
• corresponds to the input cost function,
• corresponds to the control cost function,
• corresponds to a first Lagrange multiplier associated with the control values,
• corresponds to the one or more constraints associated with the control values,
• corresponds to a second Lagrange multiplier associated with the input values, and
• corresponds to the one or more constraints associated with the input values.
[0081] In some embodiments, once the business objective engine 128 uses the set of neural networks 106 to determine the one or more output values based on the input values and the control values during forward propagation, the business objection engine 128 may determine the business objective value therewith. In an example, the business objective value may be indicative of the profit generated by selling the tangible outputs produced by the process unit 102 in the open market.
[0082] In such examples, the input values and the control values may be indicative of raw materials and operating parameters provided to the process unit 102, respectively. The inference engine 124 may generate the one or more output values therewith, which may correspond to the quantum of the tangible outputs produced by the process unit 102. The business objective engine 128 may multiply and aggregate the input values and the control values with the corresponding cost values to determine cost of production, based on the market cost values retrieved by the price and cost engine 126. The business objective engine 128 may also multiply the output values with corresponding market price values retrieved by the price and cost engine 126 to determine the revenue. The business objective engine 128 may use the business objective function to determine the business objective value, subject to the one or more constraints.
[0083] The business objective function may be an optimization function that maximizes the profit based on the one or more constraints. In such examples, the one or more constraints of the business objective function may have one or more parameters including, but not limited to, operating, design, thermodynamic constraints, and the market cost values, the market price values, the one or more input values, the one or more output values, and the one or more control values, where each of the aforementioned parameters have a maximum threshold value and a minimum threshold value associated therewith. Further, in such examples, the business objective engine 128 may determine the difference between the cost of production and the revenue to determine the profit.
[0084] In some embodiments, the back-propagation engine 130 may be configured to back-propagate the predetermined beta value for updating the one or more control values. In some embodiments, the beta value may be a predetermined constant value, such as 1 for example. In other embodiments, the beta value may be a function of the business objective value. In yet other embodiments, the beta value may be dynamically updated during each iteration of back-propagation. In some embodiments, each of the one or more control values may be updated by the corresponding gradient value. In some embodiments, the gradient value may be a partial derivative of the beta value with respect to the corresponding control value. In some embodiments, the system 108 may iteratively determine the one or more output values, calculate the business objective value, and back-propagate the beta value for updating the one or more control values until a stopping criterion is met.
[0085] In some embodiments, the stopping criterion may be indicative of a predetermined number of epochs for which the system 108 updates the one or more control values. In other embodiments, the system 108 may be configured to stop iterating when change in the business objective value between successive iterations is less than a predetermined threshold.
[0086] In some embodiments, a gradient ascent may be performed by the back-propagation engine 130 for updating the one or more control values. During gradient ascent, the one or more control values may be updated by determining a steepest ascent direction or steepest gradient in the positive direction, such that the one or more updated control values increase the business objective value at each iteration. The back-propagation engine 130 may update the one or more control values in a cascaded manner from the succeeding equipment to the preceding equipment in the DAG. Such constrained optimization with the one or more constraints may allow for transferring the gradient across the entire chain of equipment 104 and update the control values of each equipment 104 in the process unit 102.
[0087] FIGs. 5A-5B illustrate exemplary Lagrangian functions 500A and 500B indicating the boundary constraints of the input values and the control values respectively, in accordance with embodiments of the present disclosure. As illustrated, the functions 500A and 500B show the Lagrangian functions of the one or more input values and the control values. The Lagrangian functions may include a term indicative of a penalty term for violating the boundary constraints. FIGs. 5C-5D illustrate exemplary Lagrangian functions 500C and 500D indicating the linear constraints of the input values and the control values respectively, in accordance with embodiments of the present disclosure. As illustrated, the functions 500C and 500D show the Lagrangian functions of the one or more input values and the control values. The Lagrangian functions may include a term indicative of a penalty term for violating the linear constraints. It may be appreciated by those skilled in the art that the business objective function and the one or more constraints may be suitably adapted based on requirements, and the mathematical equations disclosed in the present disclosure are for illustration purpose only.
[0088] FIGs. 6A-6B illustrate an exemplary flowchart 600A of a forward propagation function and a flowchart 600B of a back-propagation function, in accordance with embodiments of the present disclosure. As shown in FIG. 6A, the system 108 may determine the one or more output values via the set of neural networks 106 trained on the historical data or the set of simulated data, or any combination thereof, of the corresponding set of equipment 104 during the forward propagation through the set of neural networks 106. In such embodiments, the set of neural networks 106 may receive the one or more input values and the one or more control values as input, and determine the one or more output values therewith.
[0089] As shown in FIG. 6B, the system 108 may determine the business objective value based on the output values, subject to the one or more constraints associated with the input values and the control values. During the back-propagation, the system 108 may update the one or more control values. The one or more control values may be updated by either the beta value or a function of the beta value. The beta value may be indicative of an error produced by the set of neural networks 106 on basis of which the one or more control values may be updated. In some embodiments, the beta value may be a predetermined positive constant on basis of which the gradient ascent may be performed. While FIGs. 6A and 6B show a single set of input values and a single set of control values, each neural network in the set of neural networks 106 may have one or more of the input values and one or more of the control values associated thereto. During back-propagation, the one or more control values of each of the neural networks 106 may be updated. The system 108 may iteratively perform the forward propagation and the back-propagation to continually update the one or more control values. In some embodiments, the system 108 may update the one or more control values such that the business objective value increases during each iteration. The system 108 may iterate the forward propagation and the back-propagation for updating the one or more control values until the stopping criterion is met. The stopping criterion may be selected so as to maximize the business objective value.
[0090] FIG. 7 illustrates an exemplary implementation 700 of the system 108, in accordance with embodiments of the present disclosure. As shown, the system 108 may have the set of equipment 104 associated therewith. In the implementation 700, the set of equipment 104 may have one or more equipment with the corresponding set of neural networks 106. Further, each equipment in the set of equipment 104, and correspondingly each neural network in the set of neural networks 106, may have a topological ordering associated therewith. In the topological ordering shown in FIG. 7, a second neural network 106-2 may be dependent on a first neural network 106-1, whereby one or more of a first output value of the first neural network 106-1 may be provided as one or more of a second input value to the second neural network 106-2. Further, a third neural network 106-3 and a fourth neural network 106-4 may be dependent on the second neural network 106-2, whereby one or more of a second output value of the second neural network 106-2 may be provided as third input values and fourth input values to the third neural network 106-3 and the fourth neural network 106-4, respectively.
[0091] Further, the business objective engine 128 may be configured to receive the third output value and the fourth output value from the third and fourth neural networks 106-3, 106-4, respectively. In some embodiments, the business objective engine 128 may also receive the market cost values of one or more of the tangible inputs corresponding to the first, second, third, and fourth input values and the control values of each of the neural networks 106-1, 106-2, 106-3, and 106-4, respectively. Further, the business objective engine 128 may also receive the market price values associated with the third and fourth output values.
[0092] The business objective engine 128 may have the one or more constraints associated with each of the one or more input values, the one or more control values, and the one or more output values. In an example, the one or more constraints may include, but not limited to, thermodynamic, operational and design constraints of the process unit 102, and one or more boundary constraints and linear constraints associated with the one or more input values, the control values, and the output values, and the corresponding market cost values and the market price values thereof. The one or more constraints may be represented by corresponding Lagrange parameters. The business objective engine 128 may determine the business objective value therewith.
[0093] Thereafter, the system 108 may be configured to optimize the one or more control values associated with each of the neural networks 106-1 to 106-4. For optimization of the control values, the system 108 may be configured to back-propagate, by the back-propagation engine 130, a loss value of the predetermined beta value through each of the neural networks 106-1 to 106-4 in a cascaded manner such that the business objective value increases during each iteration of back-propagation. The business objective value may be increased in each iteration of the back-propagation by determining the steepest gradient ascent direction and updating the one or more control values therewith. In an example, the beta value may be +1. The system 108 may iterate the forward propagation and the back-propagation until the business objective value saturates over a predetermined number of iterations.
[0094] FIG. 8 illustrates an exemplary schematic block diagram 800 of the system 108 for optimizing the process unit 102, in accordance with embodiments of the present disclosure. As shown, the process unit 102 may include the set of equipment 104. In an embodiment, the set of equipment 104 may include a Naphtha Splitter (NSPL) 802-1 and a platformer 802-2. In some embodiments, the NSPL 802-1 may have the first neural network 106-1 associated therewith, and the platformer 802-2 may have the second neural network 106-2 associated therewith. The NSPL 802-1 may be a distillation column, and may produce an overhead flow and a bottom flow.
[0095] In some embodiments, the NSPL 802-1 may be provided withe or more of a first set of tangible input 804-1. The first set of tangible input 804-1 may include a first controlled input 804A-1 and a first fixed input 804B-1. In an example, the first fixed input 804B-1 may be any one or combination of including, but not limited to, a feed composition, a feed flow, a cost of feed flow, one or more components in the feed, and the like. The first controlled input 804A-1 may be indicative of a feed flow rate provided to the NSPL 802-1. The first fixed input 804B-1 may have a first cost 806-1 associated therewith, and the first controlled input 804A-1 may have a first constraint 808-1 associated therewith. The first constraint 808-1 may be a boundary constraint for the first controlled input 804A-1. In some embodiments, the one or more control values may quantify the first controlled input 804A-1 and the one or more input values may quantify the first fixed input 804B-1.
[0096] The first controlled input 804A-1 and the first fixed input 804B-1 may be provided to the NSPL 802-1. The NSPL 802-1 may produce a first set of tangible outputs 810-1 with the first controlled input 804A-1 and the first fixed input 804B-1. In some embodiments, the first set of tangible outputs 810-1 may include an overhead output 810A having an overhead flow and an overhead composition, and a bottom output 810B having a bottom flow and a bottom composition. The first set of tangible outputs 810-1 may be quantifiable via the one or more output values. In some embodiments, the first neural network 106-1 (shown in FIG. 1) associated with the NSPL 802-1 may determine the one or more output values based on the one or more control values and the one or more input values. In some embodiments, the overhead output 810A may have a second constraint 808-2 and a first market price 812-1 associated therewith. The second constraint 808-2 may be a linear constraint. The first market price 812-1 may be the market price value of the overhead output 810A if sold in the open market.
[0097] In some embodiments, the platformer 802-2 may be provided with a second set of tangible input 804-2 and the bottom output 810B of the NSPL 802-1. In some embodiments, the second set of tangible input 804-2 may include a second controlled input 804A-2, a third controlled input 804A-3, and a fourth controlled input 804A-4, and a second fixed input (not shown). In some embodiments, the platformer 802-2 may also be provided with a fifth controlled input 804A-5 having a fourth constraint 808-4 associated therewith. The fourth constraint 808-4 may be a boundary constraint.
[0098] The second controlled input 804A-2 may be indicative of Fluid Catalytic Cracking (FCC) composition and FCC flow. The third controlled input 804A-3 may be indicative of a Light Cycle Oil (LCO) composition and LCO flow. The fourth controlled input 804A-4 may be indicative of a coker composition and coker flow. In some embodiments, the platformer 802-2 may produce a second set of tangible outputs 810-2 based on the second controlled input 804A-2, the third controlled input 804A-3, the fourth controlled input 804A-4, the fifth controlled input 804A-5, and the bottom output 810B of the NSPL 802-1. The second set of tangible outputs 810-2 may be quantifiable via one or more of the corresponding output values. Each of the second, third, and fourth controlled inputs 804A-2, 804A-3, 804A-4 may be quantified via the one or more control values associated with the platformer 802-2. In some embodiments, the second, third, and fourth controlled inputs 804A-2, 804A-3, 804A-4 may include corresponding fixed inputs associated therewith. In some embodiments, the second, third, fourth controlled inputs 804A-2, 804A-3, and 804A-4 may have a second cost 806-2, and may include a third constraint 808-3 associated therewith. In some embodiments, the third constraint may be given by:-
, where
.
[0099] In some embodiments, the second neural network 106-2 (shown in FIG 1) associated with the platformer 802-2 may determine one or more of the corresponding output values based on the one or more control values and the one or more input values corresponding to the second set of tangible input 804-2 provided to the platformer 802-2. In some embodiments, the second set of tangible outputs 810-2 may include, but not limited to, a LTG 810C, a xylene 810D, a gasoline 810E, and a benzene 810F composition. In some embodiments, each tangible output in the second set of tangible outputs 810-2 may have a second market price 812-2 associated therewith.
[00100] In some embodiments, the business objective engine 128 may use the first cost 806-1 and the second cost 806-2 corresponding to the first set of tangible input 804-1 and the second set of tangible input 804-2, respectively, and the first market price 812-1 and the second market price 812-2 corresponding to the first set of tangible outputs 810-1 and the second tangible output 810-2, respectively, to determine the business objective value. In some embodiments, the business objective engine 128 may determine the business objective value subject to the first, second, third, and fourth constraints 808-1, 808-2, 808-3, 808-4.
[00101] In some embodiments, the system 108 may be configured to optimize the one or more control values associated with each of the neural networks 106-1, 106-2. For optimization of the control values, the system 108 may be configured to back-propagate the loss value indicative of the predetermined beta value through each of the neural networks 106-1 and 106-2 in a cascaded manner such that the business objective value increases in each iteration. The system 108 may iterate the forward propagation and the back-propagation until the change in the business objective value in each iteration saturates. In the example shown in FIG. 8, once the one or more control values are updated, the NSPL 802-1 may be provided with the first set of tangible input 804-1 and the platformer 802-2 may be provided with the second set of tangible input 804-2 corresponding to the updated one or more control values so as to maximize the business objective value.
[00102] FIG. 9 illustrates exemplary graphical plots 902, 904, and 906 showing changes in boundary constraints, linear constraints, and profitability, respectively, over a plurality of epochs, in accordance with embodiments of the present disclosure. As illustrated, in about 2000 epochs, a weight boundary loss associated with the one or more input values moves closer to 1 as shown in graphical plot 902. Further, after about 2000 epochs of back-propagation, the weight linear loss associated with the one or more input values may approach zero. Additionally, the business objective value indicative of profit may increase during the 2000 epochs of constrained optimization of the one or more control values.
[00103] FIG. 10 illustrates an exemplary flowchart of a method 1000 for constrained optimization of process units 102, according to the embodiments of present disclosure.
[00104] At step 1002, the method 1000 includes determining, by one or more processors such as the processors 112, one or more output values based on one or more input values and one or more control values using a set of neural networks 106, where each neural network in the set of neural networks 106 corresponds to at least one equipment from the set of equipment 104.
[00105] At step 1004, the method 1000 includes determining, by the one or more processors, a business objective value based on the one or more output values, the one or more input values, and the one or more control values.
[00106] At step 1006, the method 1000 includes back-propagating, by the one or more processors, a beta value through the set of neural networks to update the one or more control values, wherein at least one tangible input corresponding to the one or more updated control values and the one or more input values is provided to the process unit for producing at least one tangible output.
[00107] In an aspect, the present disclosure relates to a non-transitory computer-readable medium which may include processor-executable instructions that implement the system108 and the method 1000 of the present disclosure.
[00108] The system 108 and the method 1000 may be implemented in the industries including, but not limited to, manufacturing, refineries, warehousing, supply chain management, and telecommunication, among others. In applications related to refinery and in petro-chemical division, the system 108 may be used for real time optimization of the process unit 102. The real-time optimization may be performed by updating the one or more control values associated with each equipment in the process unit 102. The real-time optimization may maximize the business objective, such as productivity or profitability, dynamically based on the market price values of the tangible outputs produced by the process unit 102 and the cost of tangible inputs provided to the process unit 102. The system 108 optimizes the process unit 102 while factoring the topological ordering associated with each of the equipment associated with the process units 102.
[00109] FIG. 11 illustrates an exemplary computer system 1100 in which or with which embodiments of the present disclosure may be utilized in accordance with embodiments of the present disclosure. As shown in FIG. 11, computer system 1100 may include an external storage device 1110, a bus 1120, a main memory 1130, a read only memory 1140, a mass storage device 1150, a communication port 1160, and a processor 1170. A person skilled in the art will appreciate that the computer system 1100 may include more than one processor and communication ports. The processor 1170 may include various modules associated with embodiments of the present disclosure. The communication port 1160 may be any of an RS-232 port for use with a modem-based dialup connection, a 10/100 Ethernet port, a Gigabit or 10 Gigabit port using copper or fiber, a serial port, a parallel port, or other existing or future ports. The communication port 1160 may be chosen depending on a network, such a Local Area Network (LAN), Wide Area Network (WAN), or any network to which computer system 1100 connects. The memory 1130 may be Random Access Memory (RAM), or any other dynamic storage device commonly known in the art. The read-only memory 1140 may be any static storage device(s) e.g., but not limited to, a Programmable Read Only Memory (PROM) chips for storing static information. The mass storage 1150 may be any current or future mass storage solution, which can be used to store information and/or instructions. Exemplary mass storage solutions include, but are not limited to, Parallel Advanced Technology Attachment (PATA) or Serial Advanced Technology Attachment (SATA) hard disk drives or solid-state drives (internal or external, e.g., having Universal Serial Bus (USB) and/or Firewire interfaces) one or more optical discs, Redundant Array of Independent Disks (RAID) storage, e.g. an array of disks (e.g., SATA arrays).
[00110] The bus 1120 may communicatively couple the processor(s) 1170 with the other memory, storage and communication blocks. The bus 1120 can be, e.g. a Peripheral Component Interconnect (PCI) / PCI Extended (PCI-X) bus, Small Computer System Interface (SCSI), USB or the like, for connecting expansion cards, drives and other subsystems as well as other buses, such a front side bus (FSB), which connects processor 1170 to the computer system 1100.
[00111] Optionally, operator and administrative interfaces, e.g. a display, keyboard, joystick and a cursor control device, may also be coupled to the bus 1120 to support direct operator interaction with a computer system 1100. Other operator and administrative interfaces can be provided through network connections connected through the communication port 1160. The external storage device 1110 can be any kind of external hard-drives, floppy drives, Compact Disc - Read Only Memory (CD-ROM), Compact Disc-Re-Writable (CD-RW), Digital Video Disk-Read Only Memory (DVD-ROM). Components described above are meant only to exemplify various possibilities. In no way should the aforementioned exemplary computer system 1100 limit the scope of the present disclosure.
[00112] While the foregoing describes various embodiments of the invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof. The scope of the invention is determined by the claims that follow. The invention is not limited to the described embodiments, versions or examples, which are included to enable a person having ordinary skill in the art to make and use the invention when combined with information and knowledge available to the person having ordinary skill in the art.

ADVANTAGES OF THE PRESENT DISCLOSURE
[00113] The present disclosure optimizes the operation of a process unit having a plurality of equipment.
[00114] The present disclosure provides a system and a method that use constrained optimization with constraints for the plurality of equipment of the process unit, where the set of equipment has a topological ordering.
[00115] The present disclosure optimizes the operation of the plurality of equipment that are connected in a Directed Acyclic Graph (DAG).
[00116] The present disclosure back-propagates a predetermined loss value through an entire chain of equipment to optimize the entire joint distribution of the equipment for maximizing a business objective value.
[00117] The present disclosure provides a system and a method that updates one or more control values during back-propagation.
[00118] The present disclosure provides a system and a method that uses an active sampling strategy for selecting training data for the set of neural networks associated with the set of equipment.
[00119] The present disclosure provides a system and a method having a business objective function of the process unit that uses a Lagrange multiplier for providing linear constraints.
,CLAIMS:1. A system (108) for constrained optimization of a set of equipment (104) of a process unit (102), the system (108) comprising:
one or more processors (112); and
a memory (114) operatively coupled to the one or more processors (112), the memory (114) having one or more processor-executable instructions, which when executed, cause the one or more processors (112) to:
determine one or more output values based on one or more input values and one or more control values using a set of neural networks (106), wherein each neural network in the set of neural networks (106) corresponds to at least one equipment from the set of equipment (104);
determine a business objective value based on the one or more output values, the one or more input values, and the one or more control values; and
back-propagate a beta value through the set of neural networks (106) to update the one or more control values, wherein at least one tangible input corresponding to the one or more updated control values and the one or more input values is provided to the process unit (102) for producing at least one tangible output.
2. The system (108) as claimed in claim 1, wherein the one or more processors (112) are configured to iteratively determine the one or more output values, determine the business objective value, and back-propagate the beta value for updating the one or more control values until a stopping criterion is met.
3. The system (108) as claimed in claim 1, wherein the set of neural networks (106) is topologically ordered corresponding to the set of equipment (104), wherein the one or more output values determined by a preceding neural network is provided as the one or more input values for a succeeding neural network from the set of neural networks (106) based on the topological ordering.
4. The system (108) as claimed in claim 1, wherein the one or more processors (112) are configured to train the set of neural networks (106) to map the one or more input values and the one or more control values to the one or more output values associated with the corresponding equipment in the set of equipment (104), each neural network from the set of neural networks (106) being trained with any one or a combination of a set of historical data or a set of simulated data.
5. The system (108) as claimed in claim 4, wherein the set of simulated data is generated, using a simulation engine (120), for each combination of values within a predetermined operating range (304), the simulation engine (120) filtering the set of simulated data with active complexity sampling such that the corresponding neural network learns regions of error in a parameter hyperspace associated with the neural network.
6. The system (108) as claimed in claim 1, wherein to determine the business objective value, the one or more processors (112) are configured to:
retrieve a market cost value associated with each of the one or more input values and each of the one or more control values, and a market price value associated with the one or more output values;
retrieve one or more constraints associated with the one or more input values and the one or more control values; and
compute the business objective value based on the one or more input values and the one or more control values with the corresponding cost values, and the one or more output values with the corresponding market price value, subject to the one or more constraints.
7. The system (108) as claimed in claim 6, wherein the one or more constraints comprise one or more linear constraints and one or more boundary constraints associated with each of the one or more input values and the one or more control values.
8. A method (1000) for constrained optimization of a set of equipment of a process unit, the method (1000) comprising:
determining, by one or more processors, one or more output values based on one or more input values and one or more control values using a set of neural networks, wherein each neural network in the set of neural networks corresponds to at least one equipment from the set of equipment;
determining, by the one or more processors, a business objective value based on the one or more output values, the one or more input values, and the one or more control values; and
back-propagating, by the one or more processors, a beta value through the set of neural networks to update the one or more control values, wherein at least one tangible input corresponding to the one or more updated control values and the one or more input values is provided to the process unit for producing at least one tangible output.
9. The method (1000) as claimed in claim 8, wherein the method (1000) comprises iteratively determining the one or more output values, determining the business objective value, and back-propagating the beta value for updating the one or more control values until a stopping criterion is met.
10. The method (1000) as claimed in claim 8, wherein the set of neural networks is topologically ordered correspondingly to the set of equipment, wherein the one or more output values determined by a preceding neural network is provided as the one or more input values for a succeeding neural network from the set of neural networks based on the topological ordering.
11. The method (1000) as claimed in claim 8, wherein the method (1000) comprises training, by the one or more processors, the set of neural networks to map one or more input values and one or more control values to one or more output values associated with the corresponding equipment in the set of equipment, each neural network from the set of neural networks being trained with any one or a combination of a set of historical data or a set of simulated data.
12. The method (1000) as claimed in claim 11, wherein the method (1000) comprises generating, by a simulation engine, the set of simulated data for each combination of values within a predetermined operating range, the simulation engine filtering the set of simulated data with active complexity sampling such that the corresponding neural network learns regions of error in a parameter hyperspace associated with the neural network.
13. The method (1000) as claimed in claim 8, wherein for determining the business objective value, the method (1000) comprises:
retrieving, by the one or more processors, a market cost value associated with each of the one or more input values and each of the one or more control values, and a market price value associated with the one or more output values;
retrieving, by the one or more processors, one or more constraints associated with the one or more input values and the one or more control values; and
computing, by the one or more processors, the business objective value based on the one or more input values and the one or more control values with the corresponding cost values, and the one or more output values with the corresponding market price value, subject to the one or more constraints.
14. The method (1000) as claimed in claim 8, wherein the one or more constraints comprise one or more linear constraints and one or more boundary constraints associated with each of the one or more input values and the one or more control values.