Abstract
In multi/many-objective evolutionary algorithms (MOEAs), to alleviate the degraded convergence pressure of Pareto dominance with the increase in the number of objectives, numerous modified dominance relationships were proposed. Recently, the strengthened dominance relation (SDR) has been proposed, where the dominance area of a solution is determined by convergence degree and niche size (θ¯). Later, in controlled SDR (CSDR), θ¯ and an additional parameter (k) associated with the convergence degree are dynamically adjusted depending on the iteration count. Depending on the problem characteristics and the distribution of the current population, different situations require different values of k, rendering the linear reduction of k based on the generation count ineffective. This is because a particular value of k is expected to bias the dominance relationship towards a particular region on the Pareto front (PF). In addition, due to the same reason, using SDR or CSDR in the environmental selection cannot preserve the diversity of solutions required to cover the entire PF. Therefore, we propose an MOEA, referred to as NSGA-III*, where (1) a modified SDR (MSDR)-based mating selection with an adaptive ensemble of parameter k would prioritize parents from specific sections of the PF depending on k, and (2) the traditional weight vector and non-dominated sorting-based environmental selection of NSGA-III would protect the solutions corresponding to the entire PF. The performance of NSGA-III* is favourably compared with state-of-the-art MOEAs on DTLZ and WFG test suites with up to 10 objectives.
Highlights
In literature [1], evolutionary algorithms (EAs) have demonstrated their ability to tackle a variety of optimization problems efficiently
Motivated by the observations that (1) by controlling the parameter k, different sections of the Pareto front (PF) can be emphasized, and (2) different stages of the evolutions require different parameter values of k depending on the status of the population, we propose a mating selection that employs modified strengthened dominance relation (SDR) with an adaptive ensemble of parameters where the probability of applying the parameter values in the ensemble depends on the success rate of the parameter values
Multi/many-objective evolutionary algorithm (MOEA) that employs mating selection based on modified SDR (MSDR) and environmental selection using weight vectors and Pareto dominance is proposed, referred to as NSGA-III*
Summary
In literature [1], evolutionary algorithms (EAs) have demonstrated their ability to tackle a variety of optimization problems efficiently. CSDR introduces two parameters k and a into convergence degree and niche size, to control the dominance area and to be adapted based on the generation count. The use of SDR or CSDR in the niching process of the oversized population during the environmental selection results in the loss of some promising solutions as k value stresses on some sections of the PF. Motivated by the observations that (1) by controlling the parameter k, different sections of the PF can be emphasized, and (2) different stages of the evolutions require different parameter values of k depending on the status of the population, we propose a mating selection that employs modified SDR with an adaptive ensemble of parameters where the probability of applying the parameter values in the ensemble depends on the success rate of the parameter values.
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