Multi-Objective Optimization via Decision Variable Perturbation
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Solution Overview
Problem
Large-scale value-based non-linear models with many decision variables and constraints pose challenges for heuristic systems like Multi-Objective Optimization Algorithms (MOOAs) in arriving at optimized solutions due to high constraint violations, leading to inefficient computation and potential inability to find feasible solutions.
Innovation Solution
The MOOA system employs decision variable perturbations and cascading modifications to genes in chromosomes, driven by prior knowledge or learned constraint topologies, to minimize constraint violations and generate feasible solutions by perturbing genes based on linkages between decision variables, using weight vectors for perturbation and constraint minimization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If heuristic systems like MOOAs are used to optimize problems with large numbers of decision variables and constraints, then the ability to handle complex optimization problems is improved, but the computation efficiency deteriorates due to high constraint violations
Solution Approach 1:
The patent applies preliminary action by performing constraint minimization before the main optimization process. A secondary optimization is executed beforehand to reduce constraint violations in the decision variables, so that when the main MOOA begins, fewer constraints need to be violated. This preliminary constraint handling improves computation efficiency during the main optimization while maintaining the ability to handle complex problems with many constraints
Solution Approach 2:
The patent introduces an intermediary mechanism - a secondary optimization process that acts as a mediator between the main MOOA and the constraints. This intermediary layer handles the constraint minimization separately, allowing the main optimization algorithm to focus on objective functions while the intermediary manages constraint compliance. This mediation improves computation efficiency by pre-resolving constraint conflicts
2Adaptability or versatility
If the number of constraints in an optimization problem is increased, then the realism and applicability of the model is improved, but the difficulty of arriving at an optimized solution worsens
Solution Approach 1:
The patent performs constraint minimization as a preliminary action before main optimization. By executing a secondary optimization process that specifically targets constraint violations beforehand, the system prepares the decision variables to satisfy constraints more easily during the main optimization. This allows models with many realistic constraints to be optimized without excessive difficulty
Solution Approach 2:
The patent extracts the constraint handling function from the main optimization process and separates it into a secondary optimization. This extraction allows constraints to be managed independently, reducing the complexity of finding optimized solutions in highly constrained problems while maintaining model realism
3Reliability
If decision variable perturbations are applied to reduce constraint violations, then the feasibility of solutions is improved, but the complexity of the optimization process worsens
Solution Approach 1:
The patent segments the optimization process into two distinct parts: a secondary optimization for constraint minimization and a main optimization for objective function optimization. This segmentation allows each part to focus on specific tasks - constraint handling in the secondary optimization and solution quality in the main optimization - thereby improving solution feasibility while managing process complexity through structured division of labor
Solution Approach 2:
The secondary optimization acts as an intermediary layer that handles constraint violations separately from the main optimization. This intermediary process applies decision variable perturbations specifically to reduce constraints, while the main MOOA focuses on optimizing objectives. The mediation structure improves feasibility without unnecessarily complicating the entire optimization process
Data Source
AI summary
Systems and methods are provided for providing an optimized solution to a multi-objective problem. Potential solutions may be generated from parent solutions to be evaluated according to multiple objectives of the multi-objective problem. If the potential solutions are infeasible, the potential solutions may be perturbed according to a perturbation model to bring the potential solution to feasibility, or at least a reduced level of constraints. The perturbation models may include a weight vector that indicates the amount of perturbation, such as in a forward and/or reverse direction, of decision variables of the potential solutions. In some cases, the perturbation models may be predetermined. In other cases, the perturbation models may be learned, such as based on training constraint data. Additionally, potential solutions may be generated in a secondary optimization where a constraint based optimization may be performed to drive to generating a feasible solution for further evaluation according to objective values.