Relationship between problem characteristics and the optimal number of genetic algorithm generations

Abstract

Genetic Algorithms (GAs) have been successfully applied to a wide range of engineering optimization problems. The success of the GA is dependent on the parameter values used, and identifying suitable values to use is a difficult task. Typically, the GA parameters must be calibrated for each application, hence it might be expected that the optimal parameter values are related to the characteristics of each problem. To aid the calibration of GAs, it is proposed that there exists an optimal number of GA generations for a given problem, where from the number of generations, the population size can be determined from the total function evaluations that are available. A number of test functions have been considered with different problem characteristics, such as salience, correlation structure, and epistasis, and statistics are proposed to quantify each of these characteristics. A large-scale parametric study has been undertaken to determine the effect of these characteristics on the optimal number of GA generations necessary in order to solve the problem most efficiently. From these results, two function classes have been identified. The function classes have been tested on two instances of an engineering optimization problem and found to classify the most appropriate population size accurately for solving each problem. Hence, the classification method developed can be used to assist in the calibration of GAs for applications where long simulation times are expected.

Review of surrogate modeling in water resources

“…Since the level of complexity of the original response function (which is typically unknown a priori) plays a key role in the determination of an appropriate function approximation technique, future research may be directed at developing methods to preanalyze the original response landscapes with a very limited number of samples to measure their level of complexity. The study by Gibbs et al [2011] is an example of research efforts for the response landscape analysis in the optimization context (not involving surrogate modeling).…”

Improved genetic algorithm optimization of water distribution system design by incorporating domain knowledge

“…As part of the first approach, it is argued that for large, real problems, the focus should be on finding the best possible solution within a realistic computational budget, rather than on attempting to find the global optimal solution (e.g. Tolson and Shoemaker, 2007;Gibbs et al, 2008;Tolson et al, 2009;Gibbs et al, 2010Gibbs et al, , 2011. This is because for such large problems, the global optimal solution is unlikely to be found within a reasonable computational timeframe.…”

Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions

“…While it is logical that a link between the characteristics of a fitness function and the best algorithm to find optimal solutions should exist, such links have not yet been identified in a way that provides general information to the optimisation process. An example of linking the results from fitness landscape measures to optimisation algorithm parameters is provided by Gibbs et al (2011). The utilisation of the results of fitness landscape analysis for the identification of the best, or even a suitable, algorithm, still remains a significant research challenge, and is discussed in more detail from the perspective of algorithm search behaviour in Section 2.3.2.…”

“…Gibbs et al, 2008;Gibbs et al, 2010;Gopalakrishnan et al, 2003;Reed et al, 2007;Reed et al, 2000) or the properties of the fitness function (e.g. Gibbs et al, 2011).…”

“…Salience Measure (Gibbs et al, 2011) Deception A deceptive function has the global optimum located away from good local optima, making it more difficult to locate (e.g. needle in a haystack problems).…”