Efficient Hill-Climber for Multi-Objective Pseudo-Boolean Optimization

TL;DR

This paper introduces an efficient hill-climbing method for multi-objective pseudo-Boolean optimization, leveraging constant-time identification of improving moves to enhance local search and evolutionary algorithms.

Contribution

It extends constant-time move identification to multi-objective pseudo-Boolean problems, enabling more efficient local search in complex landscapes.

Findings

Constant-time move identification for multi-objective problems.

Application to NK and Mk Landscapes.

Improved efficiency in local search algorithms.

Abstract

Local search algorithms and iterated local search algorithms are a basic technique. Local search can be a stand along search methods, but it can also be hybridized with evolutionary algorithms. Recently, it has been shown that it is possible to identify improving moves in Hamming neighborhoods for k-bounded pseudo-Boolean optimization problems in constant time. This means that local search does not need to enumerate neighborhoods to find improving moves. It also means that evolutionary algorithms do not need to use random mutation as a operator, except perhaps as a way to escape local optima. In this paper, we show how improving moves can be identified in constant time for multiobjective problems that are expressed as k-bounded pseudo-Boolean functions. In particular, multiobjective forms of NK Landscapes and Mk Landscapes are considered.