Cover-Encodings of Fitness Landscapes

TL;DR

This paper introduces cover-encoding maps that combine local search and heuristic approximation to effectively navigate rugged fitness landscapes and find global optima in combinatorial problems.

Contribution

It proposes a novel method of using cover-encoding maps with heuristics to transform landscapes, reducing local minima trapping and improving global optimization.

Findings

Successfully finds global minima in TSP, partitioning, matching, and clique problems.

Demonstrates practical feasibility through simulations of adaptive walks.

Shows landscapes become more navigable with the encoding approach.

Abstract

The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a feature of the typically rugged landscapes encountered arrest the progress of the search process. Another way of tackling optimization problems is by the use of heuristic approximations to estimate a global cost minimum. Here we present a combination of these two approaches by using cover-encoding maps which map processes from a larger search space to subsets of the original search space. The key idea is to construct cover-encoding maps with the help of suitable heuristics that single out near-optimal solutions and result in landscapes on the larger search space that no longer exhibit trapping local minima. We present cover-encoding maps for the problems of the traveling salesman, number partitioning, maximum matching and maximum clique; the practical feasibility of our method is demonstrated by simulations of adaptive walks on the corresponding encoded landscapes which find the global minima for these problems.