Reducing Local Optima in Single-Objective Problems by Multi-objectivization

One common characterization of how simple hill climbing optimization methods can fail is that they become trapped in local op tima a state where no small modi cation of the current best solution will produce a solution that is better This measure of better depends on the performance of the solution with respect to the single objective be ing optimized In contrast multi objective optimization MOO involves the simultaneous optimization of a number of objectives Accordingly the multi objective notion of better permits consideration of solutions that may be superior in one objective but not in another Intuitively we may say that this gives a hill climber in multi objective space more freedom to explore and less likelihood of becoming trapped In this pa per we investigate this intuition by comparing the performance of sim ple hill climber style algorithms on single objective problems and multi objective versions of those same problems Using an abstract building block problem we illustrate how multi objectivizing a single objective optimization SOO problem can remove local optima Then we investi gate small instances of the travelling salesman problem where additional objectives are de ned using arbitrary sub tours Results indicate that multi objectivization can reduce local optima and facilitate improved optimization in some cases These results enlighten our intuitions about the nature of search in multi objective optimization and sources of di culty in single objective optimization