Multi-Objective Hybrid Evolutionary Optimization with Automatic Switching

This work offers details of our recent research dealing with the development of a hybrid multi-objective optimization. Wolpert and Macready determined in single objective optimization that no single algorithm outperforms another over all possible classes of objective functions. This is the well known “No Free Lunch Theorem” (NFL) as it applies to searches and optimization problems. Koppen has shown how NFL can be extended to multiobjective optimization problems. NFL does not reject the possibility that there are classes of problems where one algorithm outperforms another. The problem faced by design engineers is that they may not know the class of problem, from an NFL point of view, they need to optimize beforehand. The objective function(s) form(s) as the design develops, and a robust optimization tool must be able to handle whatever class of objective functions any design renders. If an optimization tool provides multiple search algorithms which are automatically switched to, as the search demands, it may be possible to robustly optimize a large variety of objective function combinations. In single objective optimization the measure of a search algorithm’s progress can be easily calculated from its ability to improve the value of the objective function. The objective function value is the single quality factor that can be used to accurately compare the final results of different optimization routines. A common method to handle MultiObjective Optimization Problems (MOOP) is to optimize using the concepts of Pareto fronts and non-dominated sets. Zitzler et al., discussed how for MOOPs it is difficult to impossible to use one quality factor to determine which Pareto approximation set is superior among multiple approximations generated by multiple algorithms (when the true non-dominated set is unknown). In this work the question of robustness in light of NFL, as applied to MOOP, is addressed with the development of a multi-objective hybrid evolutionary computer program. An approach utilizing multiple switching criteria is developed and implemented. The switching criteria are a set of quality factors that the switching algorithm uses to switch between search algorithms automatically. The software developed for this work was tested on multiple standard test function suites. The software was also tested against some of its single algorithm components to determine what performance differences a multi-objective hybrid search software may possess with respect to single search algorithm software.