Many-Objective Optimization Using Taxi-Cab Surface Evolutionary Algorithm

Optimization of problems spanning more than three objectives, called many-objective optimization, is often hard to achieve using modern algorithm design and currently available computational resources. In this paper a multiobjective evolutionary algorithm, called the Surface Evolutionary Algorithm, is extended into many-objective optimization by utilizing, for the first time, the taxi-cab metric in the optimizer. The Surface Evolutionary Algorithm offers an alternative to multi-objective optimizers that rely on the principles of domination, hypervolume and so forth. The taxi-cab metric, or Manhattan distance, is introduced as the selection criterion and the basis for calculating attraction points in the Surface Evolutionary Algorithm. This allows for fast and efficient many-objective optimization previously not attainable using this method. The Taxi-Cab Surface Evolutionary Algorithm is evaluated on a set of well-known many-objective benchmark test problems. In problems of up to 20 dimensions, this new algorithm of low complexity is tested against several modern multi-objective evolutionary algorithms. The results reveal the Taxi- Cab Surface Evolutionary Algorithm as a conceptually simple, yet highly efficient many-objective optimizer.