Performance Scaling of Multi-objective Evolutionary Algorithms

In real world problems, one is often faced with the problem of multiple, possibly competing, goals, which should be optimized simultaneously. These competing goals give rise to a set of compromise solutions, generally denoted as Pareto-optimal. If none of the objectives have preference over the other, none of these trade-off solutions can be said to be better than any other solution in the set. Multi-objective Evolutionary Algorithms (MOEAs) can find these optimal trade-offs in order to get a set of solutions that are optimal in an overall sense. MOEAs are getting immense popularity in the recent past, mainly because of their ability to find a wide spread of Pareto-optimal solutions in a single simulation run. Various evolutionary approaches to multi-objective optimization have been proposed since 1985. Some of fairly recent ones are NSGA-II, SPEA2, PESA (which are included in this study) and others. They all have been mainly applied to two to three objectives. In order to establish their superiority over classical methods and demonstrate their abilities for convergence and maintenance of diversity, they need to be tested on higher number of objectives. This project mainly investigates two issues (1) Scalability of these algorithms with respect to the number of objectives, (2) Comparing these algorithms on the basis of • How close do they get to Pareto-optimal front? • How well do they maintain diversity and provide a good spread of solutions on the converged front? • Their running time. Experiments were done for 2, 3, 4, 6, and 8 objectives for all three algorithms on four scalable test problems [DTLZ01] namely DLTZ1, DLTZ2, DLTZ3 and DLTZ6. These problems differ from each other in the type of Pareto-optimal front, number of local Pareto-optimal fronts and the degree of difficulty they provide, to an algorithm, in both converging to the true Pareto-optimal front and maintaining a widely distributed set of solutions.