An analysis on recombination in multi-objective evolutionary optimization

Abstract

Evolutionary algorithms (EAs) are increasingly popular approaches to multi-objective optimization.One of their significant advantages is that they can directly optimize the Pareto front by evolving a population of solutions, where the recombination (also called crossover) operators are usually employed to reproduce new and potentially better solutions by mixing up solutions in the population.Recombination in multi-objective evolutionary algorithms is, however, mostly applied heuristically.In this paper, we investigate how from a theoretical viewpoint a recombination operator will affect a multi-objective EA. First, we employ artificial benchmark problems: the Weighted LPTNO problem (a generalization of the well-studied LOTZ problem), and the well-studied COCZ problem, for studying the effect of recombination. Our analysis discloses that recombination may accelerate the filling of the Pareto front by recombining diverse solutions and thus help solve multi-objective optimization. Because of this, for these two problems, we find that a multi-objective EA with recombination enabled achieves a better expected running time than any known EAs with recombination disabled.We further examine the effect of recombination on solving the multi-objective minimum spanning tree problem, which is an NP-Hard problem. Following our finding on the artificial problems, our analysis shows that recombination also helps accelerate filling the Pareto front and thus helps find approximate solutions faster.

MOEA/D-ARA+SBX: A new multi-objective evolutionary algorithm based on decomposition with artificial raindrop algorithm and simulated binary crossover

“…Crossover, which is sometimes also called recombination, operators, however, been widely applied in MOEAs in the last thirty years. Many studies have confirmed that the crossover operator is responsible for the search effort and can be useful in the interplay with the mutation operator, such that good solutions can be evolved efficiently [24]. Inspired by these aspects, SBX is integrated into the raindrop flowing operator with a certain probability σ.…”

“…First, a type of MOP with a sharp peak and low tail was constructed in Eq. (24), which is based on the modified ZDT1 formula.…”

Multi-objective approach based on grammar-guided genetic programming for solving multiple instance problems

“…In this section, we briefly describe their functioning. A interesting work about genetic operators in multi-objective evolutionary optimization can be consulted in Qian et al (2011).…”

Hybridizing the dynamic mutation approach with local searches to overcome local optima

“…The term (1+1) represents that, a) the population size of parents and children are both one, and b) an elitist selection is used, where the next generation will be chosen from both parents and children. Since MAs combine EAs and local searches, it is generally believed that many theoretical findings of EAs are also capable with MAs, for example, some studies show that the population-based EAs are useful [20], [12], [6], [4], and the crossover operation is essential [7], [9], [13]. There are also some theoretical studies that are specific for MAs.…”