Fitness inheritance in multiple objective evolutionary algorithms: A test bench and real-world evaluation

In many real-world applications of evolutionary algorithms, the fitness of an individual has to be derived using complex models and time-consuming computations. Especially in the case of multiple objective optimisation problems, the time needed to evaluate these individuals increases exponentially with the number of objectives due to the 'curse of dimensionality' [J. Chen, D.E. Goldberg, S. Ho, K. Sastry, Fitness inheritance in multi-objective optimization, in: W.B. Langdon et al. (Eds.), GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, July 9-13, Morgan Kaufmann Publishers, New York, 2002, pp. 319-326]. This in turn leads to a slower convergence of the evolutionary algorithms. It is not feasible to use time-consuming models with large population sizes unless the time to evaluate the objective functions is reduced. Fitness inheritance is an efficiency enhancement technique that was originally proposed by Smith et al. [R.E. Smith, B.A. Dike, S.A. Stegmann, Fitness inheritance in genetic algorithms, in: Proceedings of the 1995 ACM Symposium on Applied Computing, February 26-28, ACM, Nashville, TN, USA, 1995] to improve the performance of genetic algorithms. Sastry et al. [K. Sastry, D.E. Goldberg, M. Pelikan, Don't evaluate, inherit, in: L. Spector et al. (Eds.), GECCO 2001: Proceedings of the Genetic and Evolutionary Computation Conference, Morgan Kaufmann Publishers, San Francisco, 2001, pp. 551-558] and Chen et al. [J. Chen, D.E. Goldberg, S. Ho, K. Sastry, Fitness inheritance in multi-objective optimization, in: W.B. Langdon et al. (Eds.), GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, July 9-13, Morgan Kaufmann Publishers, New York, 2002, pp. 319-326] have developed analytical models for fitness inheritance. In this paper, the usefulness of fitness inheritance for a set of popular and separable multiple objective test functions as well as a non-separable real-world problem is evaluated based on unary performance measures testing closeness to the Pareto-optimal front, uniform distribution along and extent of the obtained Pareto front. A statistical evaluation of the performance of an NSGA-II like algorithm on the basis of these unary performance measures suggests that especially for non-convex or non-continuous problems the use of fitness inheritance negatively affects the closeness to the Pareto-optimal front.