Experiments on local search for bi-objective unconstrained binary quadratic programming

International audienceThis article reports an experimental analysis on stochastic local search for approximating the Pareto set of bi-objective unconstrained binary quadratic programming problems. First, we investigate two scalarizing strategies that iteratively identify a high-quality solution for a sequence of sub-problems. Each sub-problem is based on a static or adaptive definition of weighted-sum aggregation coefficients, and is addressed by means of a state-of-the-art single-objective tabu search procedure. Next, we design a Pareto local search that iteratively improves a set of solutions based on a neighborhood structure and on the Pareto dominance relation. At last, we hybridize both classes of algorithms by combining a scalarizing and a Pareto local search in a sequential way. A comprehensive experimental analysis reveals the high performance of the proposed approaches, which substantially improve upon previous best-known solutions. Moreover, the obtained results show the superiority of the hybrid algorithm over non-hybrid ones in terms of solution quality, while requiring a competitive computational cost. In addition, a number of structural properties of the problem instances allow us to explain the main difficulties that the different classes of local search algorithms have to face

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

Phase transitions in a ferrofluid at magnetic field induced microphase separation

In the presence of a magnetic field applied perpendicular to a thin sample layer, a suspension of magnetic colloidal particles (ferrofluid) can form spatially modulated phases with a characteristic length determined by the competition between dipolar forces and short-range forces opposing density variations. We introduce models for thin-film ferrofluids in which magnetization and particle density are viewed as independent variables and in which the non-magnetic properties of the colloidal particles are described either by a lattice-gas entropy or by the Carnahan-Starling free energy. Our description is particularly well suited to the low-particle density regions studied in many experiments. Within mean-field theory, we find isotropic, hexagonal and stripe phases, separated in general by first-order phase boundaries.Comment: 12 pages, RevTex, to appear in PR

New Initialisation Techniques for Multi-Objective Local Search Application to the Bi-objective Permutation Flowshop

International audienc

An Analysis of Local Search for the Bi-objective Bidimensional Knapsack Problem

Local search techniques are increasingly often used in multi-objective combinatorial optimization due to their ability to improve the performance of metaheuristics. The efficiency of multi-objective local search techniques heavily depends on factors such as (i) neighborhood operators, (ii) pivoting rules and (iii) bias towards good regions of the objective space. In this work, we conduct an extensive experimental campaign to analyze such factors in a Pareto local search (PLS) algorithm for the bi-objective bidimensional knapsack problem (bBKP). In the first set of experiments, we investigate PLS as a stand-alone algorithm, starting from random and greedy solutions. In the second set, we analyze PLS as a post-optimization procedure. © 2013 Springer-Verlag.SCOPUS: cp.kinfo:eu-repo/semantics/publishe

On the Empirical Scaling of Running Time for Finding Optimal Solutions to the TSP

We study the empirical scaling of the running time required by state-of-the-art exact and inexact TSP algorithms for finding optimal solutions to Euclidean TSP instances as a function of instance size. In particular, we use a recently introduced statistical approach to obtain scaling models from observed performance data and to assess the accuracy of these models. For Concorde, the long-standing state-of-the-art exact TSP solver, we compare the scaling of the running time until an optimal solution is first encountered (the finding time) and that of the overall running time, which adds to the finding time the additional time needed to complete the proof of optimality. For two state-of-the-art inexact TSP solvers, LKH and EAX, we compare the scaling of their running time for finding an optimal solution to a given instance; we also compare the resulting models to that for the scaling of Concorde’s finding time, presenting evidence that both inexact TSP solvers show significantly better scaling behaviour than Concorde.</p

Improving the Anytime Behavior of Two-Phase Local Search

Algorithms based on the two-phase local search (TPLS) framework are a powerful method to efficiently tackle multi-objective combinatorial optimization problems. TPLS algorithms solve a sequence of scalarizations, that is, weighted sum aggregations, of the multi-objective problem. Each successive scalarization uses a different weight from a predefined sequence of weights. TPLS requires defining the stopping criterion (the number of weights) a priori, and it does not produce satisfactory results if stopped before completion. Therefore, TPLS has poor "anytime" behavior. This article examines variants of TPLS that improve its "anytime" behavior by adaptively generating the sequence of weights while solving the problem. The aim is to fill the "largest gap" in the current approximation to the Pareto front. The results presented here show that the best adaptive TPLS variants are superior to the "classical" TPLS strategies in terms of anytime behavior, matching, and often surpassing, them in terms of final quality, even if the latter run until completion. © 2011 Springer Science+Business Media B.V.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Zur Rezeption der Wiener Schule in Marburg/Maribor und Ostslowenien

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