Primal–Dual Type Evolutionary Multiobjective Optimization

A new, primal-dual type approach for derivation of Pareto front approximations with evolutionary computations is proposed.

At present, evolutionary multiobjective optimization algorithms derive a discrete approximation of the Pareto front (the set of objective maps of efficient solutions) by selecting feasible solutions such that their objective maps are close to the Pareto front. As, except of test problems, Pareto fronts are not known, the accuracy of such approximations is known neither.

Here we propose to exploit also elements outside feasible sets with the aim to derive pairs of Pareto front approximations such that for each approximation pair the corresponding Pareto front lies, in a certain sense, in-between. Accuracies of Pareto front approximations by such pairs can be measured and controlled with respect to distance between such approximations.

A rudimentary algorithm to derive pairs of Pareto front approximations is presented and the viability of the idea is verified on a limited number of test problems.