Non-Epsilon Dominated Evolutionary Algorithm for the Set of Approximate Solutions

Abstract

In this paper, we present a novel evolutionary algorithm for the computation of approximate solutions for multi-objective optimization problems. These solutions are of particular interest to the decision-maker as backup solutions since they can provide solutions with similar quality but in different regions of the decision space. The novel algorithm uses a subpopulation approach to put pressure towards the Pareto front while exploring promissory areas for approximate solutions. Furthermore, the algorithm uses an external archiver to maintain a suitable representation in both decision and objective space. The novel algorithm is capable of computing an approximation of the set of interest with good quality in terms of the averaged Hausdorff distance. We underline the statements on some academic problems from literature and an application in non-uniform beams.

A Comparison of Archiving Strategies for Characterization of Nearly Optimal Solutions under Multi-Objective Optimization

“…There are MMEAs and algorithms that consider nearly optimal solutions that offer these solutions: P Q, -NSGA-II [28], P Q, -MOEA [30], nevMOGA [29], N SGA [18], DIOP [10], 4D-Miner [40,41], MNCA [42].…”

“…Generalizing, it can be considered that multimodal solutions are included in nearly optimal solutions. Nearly optimal solutions have been studied by many authors in the bibliography [15][16][17][18][19], have similar performance to optimal solutions and can sometimes be more adequate according to DM preferences (for instance, more robust [14]). Therefore, an additional challenge then arises: to obtain a set of solutions that, in addition to good performance in the design objectives, offer the greatest possible diversity.…”

“…∆ p measures the diversity and convergence in the decision and objective spaces. In this work we use ∆ p with p = 2 (as in [18,38]) so that the influence of outliers is low.…”

“…Therefore, the purpose of the paper is: (1) to understand the properties of these archivers, (2) to provide an analysis for choosing one of these archivers and (3) to give ideas for designing new archivers. The design of these algorithms are currently open issues in this research area [18,20,27].…”

Pareto Explorer for Finding the Knee for Many Objective Optimization Problems

“…Such problems are also termed many objective optimization problems (MaOPs). Though MOPs and MaOPs are identical mathematically, the above described "curse of dimensionality" calls for different numerical procedures for their treatment: while it is, in many cases, possible to compute suitable finite-size approximations of the entire Pareto sets/fronts of MOPs (e.g., Reference [1,[6][7][8][9][10][11][12][13][14][15]), this becomes more challenging and even intractable with increasing number of objectives. There exist some evolutionary approaches that aim to compute finite size approximations of the entire solution sets for MaOPs.…”