Abstract.A new and very efficient parallel algorithm for the Fast Non-dominated Sorting of Pareto fronts is proposed. By decreasing its computational complexity, the application of the proposed method allows us to increase the speedup of the best up to now Fast and Elitist Multi-Objective Genetic Algorithm (NSGA-II) more than two orders of magnitude. Formal proofs of time complexities of basic as well as improved versions of the procedure are presented. The provided experimental results fully confirm theoretical findings.
In this paper the job shop scheduling problem (JSP) with minimizing two criteria simultaneously is considered. JSP is frequently used model in real world applications of combinatorial optimization. Multi-objective job shop problems (MOJSP) were rarely studied. We implement and compare two multi-agent nature-based methods, namely ant colony optimization (ACO) and genetic algorithm (GA) for MOJSP. Both of those methods employ certain technique, taken from the multicriteria decision analysis in order to establish ranking of solutions. ACO and GA differ in a method of keeping information about previously found solutions and their quality, which affects the course of the search. In result, new features of Pareto approximations provided by said algorithms are observed: aside from the slight superiority of the ACO method the Pareto frontier approximations provided by both methods are disjoint sets. Thus, both methods can be used to search mutually exclusive areas of the Pareto frontier.
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