Abstract

Genetic algorithms, and other forms of evolutionary computation, are controlled by numerous parameters, such as crossover and mutation rates, population size, among others depending upon the specific form of evolutionary computation as well as which operators are employed. Setting the values for these parameters is no simple task. In this paper, we develop a genetic algorithm with adaptive control parameters for an NP-Hard scheduling problem known as weighted tardiness scheduling with sequence-dependent setups. Our genetic algorithm uses the permutation representation along with the non-wrapping order crossover and insertion mutation operators. We encode the control parameters within the members of the population and evolve these during search using Gaussian mutation. We demonstrate this approach out-performs a manually tuned genetic algorithm for the problem, and that it converges upon effective parameter values very early in the run.

Highlights

  • The Genetic Algorithm (GA) and other forms of evolutionary computation are typically controlled by several parameters

  • The simplest form of GA is controlled by a crossover rate, mutation rate, and population size; while more sophisticated forms have additional parameters such as elitism rate, scaling window, generation gap, or use parameterized operators such as uniform crossover or k-point crossover

  • We explore an approach to dynamically adapting GA control parameters for an NP-Hard singlemachine scheduling problem known as weighted tardiness scheduling with sequence-dependent setups

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Summary

Introduction

The Genetic Algorithm (GA) and other forms of evolutionary computation are typically controlled by several parameters. The positions of the elements within the permutation are most important, such as assignment problems where an optimal one-to-one mapping from the elements of one set to the elements of another is sought (e.g., largest common subgraph and other isomorphism related problems [36, 13]). For such problems, crossover must focus on retaining absolute positions of elements in the parent permutations when forming children. Crossover operators for relative position problems include Order Crossover (OX) [16], Non-Wrapping Order Crossover (NWOX) [7], and Uniform Order Based Crossover (UOBX) [33]. There are yet other crossover operators that introduce problem-dependent knowledge into crossover (e.g., [28, 37, 9])

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