Section: New Results

Fitness Landscape Analysis for Multiobjective Optimization

Participant : Arnaud Liefooghe.

The properties of local optimal solutions in multi-objective combinatorial optimization problems are crucial for the effectiveness of local search algorithms, particularly when these algorithms are based on Pareto dominance. Such local search algorithms typically return a set of mutually non-dominated Pareto local optimal (PLO) solutions, that is, a PLO-set. In [34] , we investigate two aspects of PLO-sets by means of experiments with Pareto local search (PLS). First, we examine the impact of several problem characteristics on the properties of PLO-sets for multi-objective NK-landscapes with correlated objectives. In particular, we report that either increasing the number of objectives or decreasing the correlation between objectives leads to an exponential increment on the size of PLO-sets, whereas the variable correlation has only a minor effect. Second, we study the running time and the quality reached when using bounding archiving methods to limit the size of the archive handled by PLS, and thus, the maximum size of the PLO-set found. We argue that there is a clear relationship between the running time of PLS and the difficulty of a problem instance.

Complementarily, in [25] we study the behavior of three elitist multi- and many-objective evolutionary algorithms in generating a high-resolution approximation of the Pareto set. Several search-assessment indicators are defined to trace the dynamics of survival selection and measure the ability to simultaneously keep optimal solutions and discover new ones under different population sizes, set as a fraction of the Pareto set size. Our study clarifies the ability and efficiency of the algorithms assuming scenarios where it is relatively easy to hit the Pareto set, showing the importance to properly assess algorithm’s performance according to the task of the optimizer in many-objective optimization.