Can deterministic chaos improve differential evolution for the linear ordering problem?

Abstract

Linear ordering problem is a popular NP-hard combinatorial optimization problem attractive for its complexity, rich library of test data, and variety of real world applications. It has been solved by a number of heuristic as well as metaheuristic methods in the past. The implementation of nature-inspired metaheuristic optimization and search methods usually depends on streams of integer and floating point numbers generated in course of their execution. The pseudo-random numbers are utilized for an in-silico emulation of probability-driven natural processes such as arbitrary modification of genetic information (mutation, crossover), partner selection, and survival of the fittest (selection, migration) and environmental effects (small random changes in particle motion direction and velocity). Deterministic chaos is a well known mathematical concept that can be used to generate sequences of seemingly random real numbers within selected interval in a predictable and well controllable way. In the past, it has been used as a basis for various pseudo-random number generators with interesting properties. Recently, it has been shown that it can be successfully used as a source of stochasticity for nature-inspired algorithms solving a continuous optimization problem. In this work we compare effectiveness of the differential evolution with different pseudo-random number generators and chaotic systems as sources of stochasticity when solving the linear ordering problem.