The Binary Dynamic Hybrid Evolutionary Algorithm For Solving Contradictory Weak-constrained Optimization Problems

There are many Contradictory Weak-Constrained Optimization Problems(CWCOPs) in the application fields and they are rarely researched. There are twoimportant steps for solving CWCOPs. The first step is finding the BestWeak-Constraints (BWCs). The second step is obtaining the optimal feasible solution.BWCs satisfies most weak-constraints and all strong-constraints, while there is afeasible region within the most weak-constraints and all strong-constraints. To solveCWCOPs, the research contents in this paper are as follow:1) One key of solving CWCOPs is finding the BWCs. If the weak-constraints areignored directly, the real optimal feasible solution cannot be obtained. If theweak-constraints are treated as strong-constraints, the solution may not be obtainedbecause there may be contradictions in weak-constraints. Therefore, the BDHEA wasproposed. BDHEA finds the BWCs firstly, and then obtains the optimal feasiblesolution;2) CWCOPs are rarely researched so that there is no well-known benchmark testfunction. CWCOPs cannot be tested by test functions of Constrained OptimizationProblems (COPs) because COPs has no weak-constraints. Therefore, this paper detailshow to construct the test functions of CWCOPs, one2-D and ten n-D (based on24well-known benchmark test functions) test functions of CWCOPs were constructed;3) Experiments of test functions and analysis of experiments are detailed.The experimental results show, compared with some other existing methods, theBDHEA reduces the test times while finding all of the BWCs, and it can obtain theoptimal feasible solution.