Improved selection in evolutionary multi–objective optimization of multi–skill resource–constrained project scheduling problem

Abstract

In this paper a modified selection operator is presented in combination with classical Non-dominated Sorting Genetic Algorithm II (NSGA-II). It is shown that various modifications can lead to increased convergence, spread or uniformity of achieved Pareto fronts. A clone prevention method is used to increase the spread of resulting sets. Furthermore a crowding operator is removed from the NSGA-II as it serves a similar purpose as the clone prevention, even though it achieves it in a different manner. The former enforces diversity in a phenotype, while the latter enforces diversity in a genotype. Combinations of multiple selection modifiers are researched and the best configurations are identified. Multiple absolute measures are selected and applied to verify quality of the results. Additionally a relative measure is used to compare the fronts. They indicate that used selection improves convergence and spread of the front at the cost of its uniformity, while at the same time increasing the efficiency of search. Results are compared to the fronts obtained by multiple runs of a single–objective hybrid Differential Evolution with Greedy Algorithm. All experiments are performed on Multi–Skill Resource–Constrained Project Scheduling Problem.