Convergence Of Solution Set Research Articles

Novel PIO Algorithm with Multiple Selection Strategies for Many-Objective Optimization Problems

With the increase of problem dimensions, most solutions of existing many-objective optimization algorithms are non-dominant. Therefore, the selection of individuals and the retention of elite individuals are important. Existing algorithms cannot provide sufficient solution precision and guarantee the diversity and convergence of solution sets when solving practical many-objective industrial problems. Thus, this work proposes an improved many-objective pigeon-inspired optimization (ImMAPIO) algorithm with multiple selection strategies to solve many-objective optimization problems. Multiple selection strategies integrating hypervolume, knee point, and vector angles are utilized to increase selection pressure to the true Pareto Front. Thus, the accuracy, convergence, and diversity of solutions are improved. ImMAPIO is applied to the DTLZ and WFG test functions with four to fifteen objectives and compared against NSGA-III, GrEA, MOEA/D, RVEA, and many-objective Pigeon-inspired optimization algorithm. Experimental results indicate the superiority of ImMAPIO on these test functions.

A Comparative Study on Evolutionary Multi-objective Optimization Algorithms Estimating Surface Duct.

The problem of atmospheric duct inversion is usually solved as a single objective optimization problem. Based on ground-based Global Positioning System (GPS) phase delay and propagation loss, this paper develops a multi-objective method including the effect of source frequency and receiving antenna height. The diversity and convergence of solution sets are evaluated for seven multi-objective evolutionary algorithms with three performance metrics: Hypervolume (HV), Inverted Generational Distance (IGD), and the averaged Hausdorff distance (). The inversion results are compared with the simulation results, and the experimental comparison is conducted on three groups of test situations. The results demonstrate that the ranking of algorithm performance varies because of the different methods used to calculate performance metrics. Moreover, when the algorithms show overwhelming performance using performance metrics, the inversion result is not more close to the real value. In the comparison of computational experiments, it was found that, as the retrieved parameter dimension increases, the inversion result becomes more unstable. When the observed data are sufficient, the inversion result seems to be improved.

A characterization of nonemptiness and boundedness of the solution set for set-valued vector equilibrium problems via scalarization and stability results.

In this paper, the existence theorems of solutions for generalized weak vector equilibrium problems are developed in real reflexive Banach spaces. Based on recession method and scalarization technique, we derive a characterization of nonemptiness and boundedness of solution set for generalized weak vector equilibrium problems. Moreover, Painlevé–Kuratowski upper convergence of solution set is also discussed as an application, when both the objective mapping and the constraint set are perturbed by difference parameters.

Painlevé-Kuratowski Convergences of the solution sets to perturbed generalized systems

In this paper, we obtain the Painleve-Kuratowski Convergence of the efficient solution sets, the weak efficient solution sets and various proper efficient solution sets for the perturbed generalized system with a sequence of mappings converging in a real locally convex Hausdorff topological vector spaces.