Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives

TL;DR

This paper explores the properties of Pareto local optimal sets in multi-objective NK-landscapes with correlated objectives, analyzing how problem characteristics affect PLO-set size and the impact of bounded archiving on search efficiency and solution quality.

Contribution

It provides empirical insights into how the number of objectives and objective correlation influence PLO-set size and evaluates the effectiveness of bounded archiving methods in multi-objective local search.

Findings

Increasing objectives or decreasing correlation exponentially increases PLO-set size.

Variable correlation has a minor effect on PLO-set size.

Bounded archiving impacts running time and solution quality.

Abstract

The properties of local optimal solutions in multi-objective combinatorial optimization problems are crucial for the effectiveness of local search algorithms, particularly when these algorithms are based on Pareto dominance. Such local search algorithms typically return a set of mutually nondominated Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper investigates two aspects of PLO-sets by means of experiments with Pareto local search (PLS). First, we examine the impact of several problem characteristics on the properties of PLO-sets for multi-objective NK-landscapes with correlated objectives. In particular, we report that either increasing the number of objectives or decreasing the correlation between objectives leads to an exponential increment on the size of PLO-sets, whereas the variable correlation has only a minor effect. Second, we study the running time and the quality reached when using bounding archiving methods to limit the size of the archive handled by PLS, and thus, the maximum size of the PLO-set found. We argue that there is a clear relationship between the running time of PLS and the difficulty of a problem instance.