Hybridization of Decomposition and Local Search for Multiobjective Optimization

Combining ideas from evolutionary algorithms, decomposition approaches, and Pareto local search, this paper suggests a simple yet efficient memetic algorithm for combinatorial multiobjective optimization problems: memetic algorithm based on decomposition (MOMAD). It decomposes a combinatorial multiobjective problem into a number of single objective optimization problems using an aggregation method. MOMAD evolves three populations: 1) population PLfor recording the current solution to each subproblem; 2) population PPfor storing starting solutions for Pareto local search; and 3) an external population PEfor maintaining all the nondominated solutions found so far during the search. A problem-specific single objective heuristic can be applied to these subproblems to initialize the three populations. At each generation, a Pareto local search method is first applied to search a neighborhood of each solution in PPto update PLand PE. Then a single objective local search is applied to each perturbed solution in PLfor improving PLand PE, and reinitializing PP. The procedure is repeated until a stopping condition is met. MOMAD provides a generic hybrid multiobjective algorithmic framework in which problem specific knowledge, well developed single objective local search and heuristics and Pareto local search methods can be hybridized. It is a population based iterative method and thus an anytime algorithm. Extensive experiments have been conducted in this paper to study MOMAD and compare it with some other state-of-the-art algorithms on the multiobjective traveling salesman problem and the multiobjective knapsack problem. The experimental results show that our proposed algorithm outperforms or performs similarly to the best so far heuristics on these two problems

Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives

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 nondominated Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper investigates 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.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

Local Optimal Sets and Bounded Archiving on Multi-objective NK-Landscapes with Correlated Objectives

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 nondominated Pareto local optimal (PLO) solutions, that is, a PLO-set. This paper investigates 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.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

Generation of the exact Pareto set in multi-objective traveling salesman and set covering problems

The calculation of the exact set in Multi-Objective Combinatorial Optimization (MOCO) problems is one of the most computationally demanding tasks as most of the problems are NP-hard. In the present work we use AUGMECON2 a Multi-Objective Mathematical Programming (MOMP) method which is capable of generating the exact Pareto set in Multi-Objective Integer Programming (MOIP) problems for producing all the Pareto optimal solutions in two popular MOCO problems: The Multi-Objective Traveling Salesman Problem (MOTSP) and the Multi-Objective Set Covering problem (MOSCP). The computational experiment is confined to two-objective problems that are found in the literature. The performance of the algorithm is slightly better to what is already found from previous works and it goes one step further generating the exact Pareto set to till now unsolved problems. The results are provided in a dedicated site and can be useful for benchmarking with other MOMP methods or even Multi-Objective Meta-Heuristics (MOMH) that can check the performance of their approximate solution against the exact solution in MOTSP and MOSCP problems