Systems for solving general and user preference-based constrained multi-objective optimization problems
Gespeichert in:
| Titel: | Systems for solving general and user preference-based constrained multi-objective optimization problems |
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| Patent Number: | 10733,332 |
| Publikationsdatum: | August 04, 2020 |
| Appl. No: | 15/616959 |
| Application Filed: | June 08, 2017 |
| Abstract: | A user-preference-enabling (UPE) method optimizes operations of a system based on user preferences. The operations of the system are modeled as a user-preference-based multi-objective optimization (MOO) problem having multiple object functions subject to a set of constraints. The set of constraints include system constraints and a wish list specifying a respective user-preferred range of values for one or more of the objective functions. The UPE method calculates a wish list feasible solution (WL-feasible solution) to the user-preference-based MOO problem. The UPE method can be performed iteratively to compute targeted Pareto-optimal solutions. The UPE method can be used in a hybrid method in combination with other numerical methods to reliably compute feasible solutions of both conventional MOO problems and user-preference-based MOO problems. |
| Inventors: | Bigwood Technology, Inc. (Ithaca, NY, US) |
| Assignees: | Bigwood Technology, Inc. (Ithaca, NY, US) |
| Claim: | 1. A computer-implemented user-preference-enabling (UPE) method that optimizes operations of a system based on user preferences, comprising: modeling the operations of the system as a user-preference-based multi-objective optimization (MOO) problem having multiple object functions subject to a set of constraints that include system constraints and a wish list specifying a respective user-preferred range of values for one or more of the objective functions; and calculating a wish list feasible solution (WL-feasible solution) to the user-preference-based MOO problem, wherein the WL-feasible solution optimizes electrical power output in a power system, and wherein calculating the WL-feasible solution further comprises: constructing a nonlinear non-hyperbolic dynamical system based on the set of constraints; integrating the nonlinear non-hyperbolic dynamical system starting from an initial point to obtain a corresponding ω-limit point of a system trajectory; evaluating an equality constraint set, which is formed from both equality constraints and inequality constraints in the set of constraints, over the corresponding ω-limit point; comparing a result of evaluating the equality constraint set with a predetermined tolerance value to determine whether the WL-feasible solution exists; and in response to a determination that the WL-feasible solution exists, solving the equality constraint set over the ω-limit point to obtain the WL-feasible solution. |
| Claim: | 2. The method of claim 1 , further comprising: updating the wish list by a user based on the calculated WL-feasible solution, to obtain an updated user-preference-based MOO problem; and iteratively calculating a sequence of WL-feasible solutions to a sequence of updated user-preference-based MOO problems. |
| Claim: | 3. The method of claim 2 , wherein iteratively calculating further comprises: obtaining a targeted Pareto-optimal solution to the user-preference-based MOO problem based on the sequence of WL-feasible solutions, wherein the targeted Pareto-optimal solution optimizes the multiple objective functions and satisfies the set of constraints. |
| Claim: | 4. A computer-implemented user-preference-enabling (UPE) method that optimizes operations of a system based on user preferences, comprising: modeling the operations of the system as a user-preference-based multi-objective optimization (MOO) problem having multiple object functions subject to a set of constraints that include system constraints and a wish list specifying a respective user-preferred range of values for one or more of the objective functions; calculating a wish list feasible solution (WL-feasible solution) to the user-preference-based MOO problem; and updating the wish list by a user based on the calculated WL-feasible solution, to obtain an updated user-preference-based MOO problem, wherein the WL-feasible solution optimizes electrical power output in a power system, and wherein updating the wish list further comprises: iteratively scaling down user-preferred ranges of values specified in the wish list until a degenerate stable equilibrium manifold (SEM) is found; and using the degenerate SEM solution to scale up the user-preferred ranges of values, which cause non-existence of the WL-feasible solution, until a terminal condition is satisfied. |
| Claim: | 5. The method of claim 1 , wherein calculating the WL-feasible solution further comprises: constructing the nonlinear non-hyperbolic dynamical system based on the set of constraints, wherein a stable equilibrium manifold (SEM) of the nonlinear non-hyperbolic dynamical system corresponds to a feasible component of the user-preference-based MOO problem; and locating the SEM of the nonlinear non-hyperbolic dynamical system to find the WL-feasible solution to the user-preference-based MOO problem. |
| Claim: | 6. The method of claim 5 , wherein the nonlinear non-hyperbolic dynamical system belongs to a class of nonlinear non-hyperbolic dynamical systems satisfying a requirement that specifies: a set is a regular SEM of the nonlinear non-hyperbolic dynamical system if and only if the set is the feasible component of a feasible region of the user-preference-based MOO problem. |
| Claim: | 7. The method of claim 5 , wherein the nonlinear non-hyperbolic dynamical system is a quotient gradient system. |
| Claim: | 8. The method of claim 1 , wherein integrating the nonlinear non-hyperbolic dynamical system further comprises: determining whether the system trajectory of the nonlinear non-hyperbolic dynamical system converges to a non-degenerate SEM, wherein the non-degenerate SEM is the WL-feasible solution. |
| Claim: | 9. The method of claim 1 , further comprising: applying a population-based meta-heuristic MOO method with a population of candidate solutions to the user-preference-based MOO problem until groups of the population are formed; for each of selected candidate solutions from each group, applying the user-preference-enabling method to calculate a corresponding WL-feasible solution to the user-preference-based MOO problem with the selected candidate solution being an initial vector; and applying a deterministic solver to corresponding feasible solutions for the selected candidate solutions to obtain a Pareto optimal solution, wherein the Pareto-optimal solution optimizes the multiple objective functions and satisfies the set of constraints. |
| Claim: | 10. The method of claim 9 , wherein the population-based meta-heuristic MOO method is based on a multi-objective evolutionary algorithm. |
| Claim: | 11. The method of claim 9 , wherein the population-based meta-heuristic MOO method is based on a multiple objective particle swarm optimization (MOPSO) method. |
| Claim: | 12. The method of claim 9 , wherein the deterministic solver is the normalized normal constraint method. |
| Claim: | 13. The method of claim 9 , wherein the Pareto-optimal solution is a targeted Pareto-optimal solution, whose objective vectors lie within a user-preferred range. |
| Claim: | 14. The method of claim 9 , further comprising: calculating a WL-feasible solution for each selected candidate solution in the populations; applying one or more objective values of WL-feasible solutions to refine the wish list; calculating new solutions that satisfy the refined wish list based on the WL-feasible solutions; and for each new solution, applying a deterministic MOO method to compute a nearby targeted Pareto-optimal solution of the MOO problem. |
| Claim: | 15. A computer-implemented hybrid method that optimizes operations of a system, comprising: modeling the operations of the system as a multi-objective optimization (MOO) problem having multiple object functions subject to a set of constraints; applying a population-based meta-heuristic MOO method with a population of candidate solutions to the MOO problem until groups of the population are formed; for each of selected candidate solutions from each group, applying a feasible solution solver to calculate a corresponding feasible solution to the MOO problem with the selected candidate solution being an initial vector; and applying a deterministic solver to corresponding feasible solutions for the selected candidate solutions to obtain a Pareto optimal solution, wherein the Pareto-optimal solution optimizes the multiple objective functions and satisfies the set of constraints to thereby optimize electrical power output in a power system, wherein applying the feasible solution solver further comprises: constructing a nonlinear non-hyperbolic dynamical system based on the set of constraints; integrating the nonlinear non-hyperbolic dynamical system starting from an initial point to obtain a corresponding ω-limit point of a system trajectory; evaluating an equality constraint set, which is formed from both equality constraints and inequality constraints in the set of constraints, over the corresponding ω-limit point; comparing a result of evaluating the equality constraint set with a predetermined tolerance value to determine whether the corresponding feasible solution exists; and in response to a determination that the corresponding feasible solution exists, solving the equality constraint set over the ω-limit point to obtain the corresponding feasible solution. |
| Claim: | 16. The method of claim 15 , wherein the population-based meta-heuristic MOO method is based on an evolutionary algorithm. |
| Claim: | 17. The method of claim 15 , wherein the population-based meta-heuristic MOO method is based on a multiple objective particle swarm optimization (MOPSO) method. |
| Claim: | 18. The method of claim 15 , wherein the deterministic solver is the normalized normal constraint method. |
| Claim: | 19. The method of claim 15 , wherein the feasible solution solver comprising: constructing the nonlinear non-hyperbolic dynamical system based on the set of constraints, wherein a stable equilibrium manifold (SEM) of the nonlinear non-hyperbolic dynamical system corresponds to a feasible component of the MOO problem; and locating the SEM of the nonlinear non-hyperbolic dynamical system to find the feasible solution to the MOO problem. |
| Claim: | 20. The method of claim 19 , wherein the nonlinear non-hyperbolic dynamical system belongs to a class of nonlinear non-hyperbolic dynamical systems satisfying a requirement that specifies: a set is a regular SEM of the nonlinear non-hyperbolic dynamical system if and only if the set is the feasible component of a feasible region of the MOO problem. |
| Claim: | 21. The method of claim 19 , wherein the nonlinear non-hyperbolic dynamical system is a quotient gradient system. |
| Claim: | 22. The method of claim 19 , wherein integrating the nonlinear non-hyperbolic dynamical system further comprises: determining whether the system trajectory of the nonlinear non-hyperbolic dynamical system converges to a non-degenerate SEM, wherein the non-degenerate SEM is a feasible solution. |
| Claim: | 23. A computer-implemented user-preference-enabling (UPE) method that optimizes operations of a system based on user preferences, comprising: modeling the operations of the system as a user-preference-based multi-objective optimization (MOO) problem having multiple object functions subject to a set of constraints that include system constraints and a wish list specifying a respective user-preferred range of values for one or more of the objective functions; and calculating a wish list feasible solution (WL-feasible solution) to the user-preference-based MOO problem, wherein the WL-feasible solution optimizes, in a machine learning system, one or more of: clustering, feature extraction, feature selection, model selection, and ensemble generation, and wherein calculating the WL-feasible solution further comprises: constructing a nonlinear non-hyperbolic dynamical system based on the set of constraints; integrating the nonlinear non-hyperbolic dynamical system starting from an initial point to obtain a corresponding ω-limit point of a system trajectory; evaluating an equality constraint set, which is formed from both equality constraints and inequality constraints in the set of constraints, over the corresponding ω-limit point; comparing a result of evaluating the equality constraint set with a predetermined tolerance value to determine whether the WL-feasible solution exists; and in response to a determination that the WL-feasible solution exists, solving the equality constraint set over the ω-limit point to obtain the WL-feasible solution. |
| Claim: | 24. The method of claim 23 , further comprising: updating the wish list by a user based on the calculated WL-feasible solution, to obtain an updated user-preference-based MOO problem; and iteratively calculating a sequence of WL-feasible solutions to a sequence of updated user-preference-based MOO problems. |
| Claim: | 25. The method of claim 24 , further comprising: obtaining a targeted Pareto-optimal solution to the user-preference-based MOO problem based on the sequence of WL-feasible solutions, wherein the targeted Pareto-optimal solution optimizes the multiple objective functions and satisfies the set of constraints. |
| Claim: | 26. The method of claim 23 , further comprising: constructing the nonlinear non-hyperbolic dynamical system based on the set of constraints, wherein a stable equilibrium manifold (SEM) of the nonlinear non-hyperbolic dynamical system corresponds to a feasible component of the user-preference-based MOO problem; and locating the SEM of the nonlinear non-hyperbolic dynamical system to find the WL-feasible solution to the user-preference-based MOO problem. |
| Claim: | 27. The method of claim 23 , further comprising: iteratively scaling down user-preferred ranges of values specified in the wish list until no feasible solution is found; and scaling up the user-preferred ranges of values until a terminal condition is satisfied. |
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| Assistant Examiner: | Wechselberger, Alfred H B |
| Primary Examiner: | Perveen, Rehana |
| Attorney, Agent or Firm: | Lee, Tong J. |
| Dokumentencode: | edspgr.10733332 |
| Datenbank: | USPTO Patent Grants |
| Abstract: | A user-preference-enabling (UPE) method optimizes operations of a system based on user preferences. The operations of the system are modeled as a user-preference-based multi-objective optimization (MOO) problem having multiple object functions subject to a set of constraints. The set of constraints include system constraints and a wish list specifying a respective user-preferred range of values for one or more of the objective functions. The UPE method calculates a wish list feasible solution (WL-feasible solution) to the user-preference-based MOO problem. The UPE method can be performed iteratively to compute targeted Pareto-optimal solutions. The UPE method can be used in a hybrid method in combination with other numerical methods to reliably compute feasible solutions of both conventional MOO problems and user-preference-based MOO problems. |
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