Sets of interacting scalarization functions in local search for multi-objective combinatorial optimization problems

Searching in multi-objective search spaces is considered a challenging problem. Pareto local search (PLS) searches directly into the multi-objective search space maintaining an archive of best non-dominated solutions found so far, the non-dominated archive. PLS´ advantage is the exploitation of relationships between solutions in the non-dominated archive at the cost of high maintenance costs of the archive. The scalarized local search (SLS) uses scalarization functions to transform the multi-objective search space into a single objective search space. SLS is faster because it is searching in a single objective search space but the independent scalarization functions do not systematic exploit the structure of the multi-objective search space. We improve the performance of SLS algorithms by allowing interactions between scalarization functions. The adaptive scalarization functions select frequently the scalarization function that generates well performing SLS. The genetic scalarization functions assume that the scalarization functions have commonalities that can be exploited using genetic like operators. We experimentally show that the proposed techniques can improve the performance of local search algorithms on correlated bi-objective QAP in-stances.