Keywords: genetic algorithms, multi-objective optimization, evolution strategies, Pareto front, compromise solution, connected and disconnected objective space.

Many different evolutionary algorithms are applicable to solve a Pareto multi-objective optimization problem, to find a set of optimal solutions that collectively form a Pareto front. These algorithms generally do not provide any guidance for selecting best-compromise solutions to the problem. To address this issue, the present paper proposes a genetic algorithm for which the computational process to establish the Pareto front is driven by the fitness of an evolving best-compromise solution that uniquely represents a mutually agreeable trade-off between all competing objectives for the problem.

For a multi-objective optimization problem, there are generally many optimal solutions that collectively define the Pareto front in the n-dimensional objective space for the problem, and it remains to select the best-compromise solution(s) from among them [1]. Most of the selection procedures proposed in the literature to identify such compromise solutions are somewhat informal, and all are applied after the Pareto front has been established.

An important aspect of the multi-objective evolutionary strategy for a genetic algorithm is the way in which fitness is assigned to individual solutions for the purpose of selecting candidates for future generations. In this regard, two well known methods for assigning fitness are "Pareto-front sorting" and "Euclidean distance". These established methods are first reviewed, and then they are modified to achieve two alternative fitness-assignment methods based on evolving Pareto-compromise solutions.

The proposed evolutionary strategy is here applied to a suite of benchmark test problems having from two to five objective criteria for which the decision variables are constrained such that the Pareto front is either connected or disconnected.

The proposed multi-objective evolutionary strategy is reminiscent of single-objective optimization, in that its fitness assignment and convergence criteria are both based on tracking a single evolving solution over the search history. The Pareto-compromise solution is a benchmark that provides for ready identification of best-balanced solutions from among the multitude of optimal solutions on the Pareto front. This is otherwise a difficult task for disconnected fronts in higher-dimension objective space.

1

D.E. Grierson, "Pareto Multi-Criteria Decision Making", Advanced Engineering Informatics, 22, 371-384, 2008. doi:10.1016/j.aei.2008.03.001

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