Evolutionary Many-Objective Optimization

Over the past two decades, evolutionary algorithms have successfully been applied to single and multiobjective optimization problems having up to three objectives. Compared to traditional mathematical programming techniques, evolutionary multiobjective algorithms (MOEAs) are particularly powerful in achieving multiple nondominated solutions in a single run. However, the performance of most existing algorithms seriously degrades when the number of objectives is larger than three. Such optimization problems, often referred to as many-objective optimization problems (MaOPs) in the evolutionary computation community, are widely seen in the real-world and therefore it is of great practical importance to efficiently solve them. Challenges to evolutionary algorithms and other meta-heuristics in solving MaOPs include the inability of dominance-based MOEAs to converge to the Pareto frontier while maintaining good diversity, the prohibitively high computational complexity for MOEAs based on performance indicators, and the difficulty for human users or decision makers to clearly understand the relationship between objectives and articulate preferences. In addition, existing performance indicators for multiobjective optimization may become incapable of accurately assessing and comparing the quality of solution sets. Finally, visualization of the solutions of MaOPs also becomes a grand challenge. © 1997-2012 IEEE.