A preliminary study on distance selection in probabilistic memetic framework for capacitated arc routing problem

Memetic algorithms (MAs), which have materialized as a fusion of population based global search and individual lifetime learning (i.e., local search) in the literature, have been widely used in real world applications to solve complex optimization problems. The balance of global and local search in MA plays a key role in defining the performance of MA in problem solving. The probabilistic memetic framework (PMF) was thus introduced to model MA as a process involving the decision of embracing the separate actions of global or local search. PMF balances these two actions by governing the local search intensity of each individual based on a theoretical upper bound derived while the search progresses. To use PMF for solving combinatorial optimization problems, according to our previous study [1], we note that the appropriate selection of a distance metric for estimating the local search intensity is a critical role. Nevertheless, to the best of our knowledge, little or no research works in the literature has studied on suitable distance metric for PMF in the context of combinatorial optimization problems. In this paper, we attempt to fill this gap by presenting a preliminary study on the selection of distance metric in PMF for capacitated arc routing problem (CARP). In particular, we first analyze the suitability of 4 existing popular distance metrics used in combinatorial optimization for solving CARP. Subsequently a score based on closeness of neighborhood and fitness landscape correlation is proposed to quantify the suitability of a distance metric in estimating the local search intensity for PMF in the context of combinatorial optimization. Experimental study on 24 egl CARP benchmark instances highlighted the significance of choice of appropriate distance metric in PMF for solving combinatorial optimization problems, with 4 new best known CARP solutions established in the present study.