Multi-Objective Evolutionary Algorithm with Soft Constraints

The patent segments constraints into two categories: hard constraints and soft constraints. Hard constraints are evaluated with strict feasibility checks, while soft constraints allow for gradual penalty applications. This segmentation reduces computational overhead by avoiding exhaustive evaluation of all constraints for every candidate solution, thereby resolving the contradiction between reliable feasibility determination and computational bandwidth consumption.

The patent introduces a penalty parameter that can be dynamically adjusted during the evolutionary process. Instead of binary feasible/infeasible classification, the system uses continuous penalty values that change based on the degree of constraint violation. This parameter change approach allows for more efficient computational evaluation while maintaining reliability in identifying viable solutions.

By dividing constraints into hard and soft categories, the patent applies strict validity checks only to hard constraints while using softer evaluation for soft constraints. This selective validation ensures solution validity where critical while reducing time-consuming checks for non-critical constraints, thereby improving convergence speed without sacrificing essential solution validity.

The patent applies partial feasibility checking by not evaluating all constraints with the same strictness level. Soft constraints are evaluated with partial enforcement, allowing the algorithm to make progress toward optimized solutions without waiting for complete validation of all constraints, thus reducing convergence time while maintaining necessary solution validity.

The patent introduces penalty functions as intermediaries between the search space and feasibility evaluation. These penalty functions guide the evolutionary algorithm through infeasible regions by providing gradient information that gradually steers solutions toward feasible areas. This intermediary mechanism makes navigation through vast infeasible spaces more manageable while maintaining comprehensive exploration capability.

The patent converts the harmful effect of infeasible solutions into a beneficial guidance mechanism. Instead of discarding infeasible solutions outright, the system uses their penalty values to guide the search direction. Infeasible regions thus become informative rather than obstructive, helping the algorithm navigate toward feasible optimized solutions more efficiently.