Anytime Pareto local search

Abstract

Pareto Local Search (PLS) is a simple and effective local search method for tackling multi-objective combinatorial optimization problems. It is also a crucial component of many state-of-the-art algorithms for such problems. However, PLS may be not very effective when terminated before completion. In other words, PLS has poor anytime behavior. In this paper, we study the effect that various PLS algorithmic components have on its anytime behavior. We show that the anytime behavior of PLS can be greatly improved by using alternative algorithmic components. We also propose Dynagrid, a dynamic discretization of the objective space that helps PLS to converge faster to a good approximation of the Pareto front and continue to improve it if more time is available. We perform a detailed empirical evaluation of the new proposals on the bi-objective traveling salesman problem and the bi-objective quadratic assignment problem. Our results demonstrate that the new PLS variants not only have significantly better anytime behavior than the original PLS, but also may obtain better results for longer computation time or upon completion.

Using Parallel Strategies to Speed up Pareto Local Search

“…A similar methodology can be found in the work of Dubois-Lacoste et al [4], which intends to improve the anytime performance of PLS. Our proposal differs from those works in the sense that we aim to speed up PLS in a parallel multi-search framework.…”

“…In [4,8], the design of these components was shown to be crucially important for the anytime performance of sequential PLS. In this paper, we similarly discuss possible alternatives for these components, however our proposed alternatives are designed specifically with respect to the target parallel multi-search framework.…”

“…In practice, the basic PLS procedure shown in Algorithm 1 requires a long time to converge to a good approximation of the PS. Several speed-up strategies have been proposed in recent years [3,4,6,8], but they are in the scope of sequential algorithms. In this paper, we discuss the possible speed-up strategies of PLS in a parallel algorithm framework.…”

“…However, it is well known that the convergence speed of the basic PLS is low. Several strategies have been proposed [3,4,6,8] in order to overcome this issue. However, those strategies are inherently sequential, i.e.…”

Automatically Configuring Multi-objective Local Search Using Multi-objective Optimisation

“…include Pareto local search (PLS, 2004) [18] and its numerous variants, such as the iterated PLS (2010) [5], stochastic PLS (2012) [6], anytime PLS (2015) [7], and dominance-based multi-objective local search (DMLS, 2012) [13]. In the following, we use a parametrised general local search framework that incorporates most of the strategies used by these algorithms.…”