Pareto Adaptive Decomposition algorithm

Dealing with multi-objective combinatorial optimization and local search, this article proposes a new multi-objective meta-heuristic named Pareto Adaptive Decomposition algorithm (PAD). Combining ideas from decomposition methods, two phase algorithms and multi-armed bandit, PAD provides a 2-phase modular framework for finding an approximation of the Pareto front. The first phase decomposes the search into a number of scalarized problems by linear aggregation of the original multi-objective problem. Following a data perturbation step, the second phase conducts an iterative process: a number of scalarized problems are selected by a multi-armed bandit policy and optimized by a single-objective local search solver. Resulting solutions will serve as a starting point of a multiobjective local search procedure, called Pareto Local Search. Based on this framework, we conduct experiments on several instances of the bi-objective symmetric Traveling Salesman Problem. The experiments show that our proposed algorithm outperforms the best current method on this problem.