Jérémie Dubois-Lacoste

A hybrid TP+PLS algorithm for bi-objective flow-shop scheduling problems

This paper presents a new, carefully designed algorithm for five bi-objective permutation flow shop scheduling problems that arise from the pairwise combinations of the objectives (i) makespan, (ii) the sum of the completion times of the jobs, and (iii) both, the weighted and non-weighted total tardiness of all jobs. The proposed algorithm combines two search methods, two-phase local search and Pareto local search, which are representative of two different, but complementary, paradigms for multi-objective optimization in terms of Pareto-optimality. The design of the hybrid algorithm is based on a careful experimental analysis of crucial algorithmic components of these two search methods. We compared our algorithm to the two best algorithms identified, among a set of 23 candidate algorithms, in a recent review of the bi-objective permutation flow-shop scheduling problem. We have reimplemented carefully these two algorithms in order to assess the quality of our algorithm. The experimental comparison in this paper shows that the proposed algorithm obtains results that often dominate the output of the two best algorithms from the literature. Therefore, our analysis shows without ambiguity that the proposed algorithm is a new state-of-the-art algorithm for the bi-objective permutation flow-shop problems studied in this paper.

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.

Anytime Pareto local search

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.

Automatic configuration of state-of-the-art multi-objective optimizers using the TP+PLS framework

The automatic configuration of algorithms is a dynamic field of research. Its potential for producing highly performing algorithms may change the way we design algorithms. So far, automatic algorithm configuration tools have almost exclusively been applied to configure single-objective algorithms. In this paper, we investigate the usage of automatic algorithm configuration tools to improve multi-objective algorithms. In fact, this is the first article we are aware of where state-of-the-art multi-objective optimizers are configured in an automatic way. This automatic configuration is done for five variants of multi-objective flow-shop problems. Our experimental results show that we can reach at least the same and often a better final quality than a recently proposed state-of-the-art algorithm for these problems.

Grammar-based generation of stochastic local search heuristics through automatic algorithm configuration tools

Several grammar-based genetic programming algorithms have been proposed in the literature to automatically generate heuristics for hard optimization problems. These approaches specify the algorithmic building blocks and the way in which they can be combined in a grammar; the best heuristic for the problem being tackled is found by an evolutionary algorithm that searches in the algorithm design space defined by the grammar. In this work, we propose a novel representation of the grammar by a sequence of categorical, integer, and real-valued parameters. We then use a tool for automatic algorithm configuration to search for the best algorithm for the problem at hand. Our experimental evaluation on the one-dimensional bin packing problem and the permutation flowshop problem with weighted tardiness objective shows that the proposed approach produces better algorithms than grammatical evolution, a well-established variant of grammar-based genetic programming. The reasons behind such improvement lie both in the representation proposed and in the method used to search the algorithm design space.

Combining Two Search Paradigms for Multi-objective Optimization: Two-Phase and Pareto Local Search

In this chapter, we review metaheuristics for solving multi-objective combinatorial optimization problems, when no information about the decision maker’s preferences is available, that is, when problems are tackled in the sense of Pareto optimization. Most of these metaheuristics follow one of the two main paradigms to tackle such problems in a heuristic way. The first paradigm is to rely on Pareto dominance when exploring the search space. The second paradigm is to tackle several single-objective problems to find several solutions that are non-dominated for the original problem; in this case, one may exploit existing, efficient single-objective algorithms, but the performance depends on the definition of the set of scalarized problems. There are also a number of approaches in the literature that combine both paradigms. However, this is usually done in a relatively ad-hoc way. In this chapter, we review two conceptually simple methods representative of each paradigm: Pareto local search and Two-phase local search. The hybridization of these two strategies provides a general framework for engineering stochastic local search algorithms that can be used to improve over the state-of-the-art for several, widely studied problems.

From Grammars to Parameters: Automatic Iterated Greedy Design for the Permutation Flow-Shop Problem with Weighted Tardiness

Recent advances in automatic algorithm configuration have made it possible to configure very flexible algorithmic frameworks in order to fine-tune them for particular problems. This is often done by the use of automatic methods to set the values of algorithm parameters. A rather different approach uses grammatical evolution, where the possible algorithms are implicitly defined by a context-free grammar. Possible algorithms may then be instantiated by repeated applications of the rules in the grammar. Through grammatical evolution, such an approach has shown to be able to generate heuristic algorithms. In this paper we show that the process of instantiating such a grammar can be described in terms of parameters. The number of parameters increases with the maximum number of applications of the grammar rules. Therefore, this approach is only practical if the number of rules and depth of the derivation tree are bounded and relatively small. This is often the case in the heuristic-generating grammars proposed in the literature, and, in such cases, we show that the parametric representation may lead to superior performance with respect to the representation used in grammatical evolution. In particular, we first propose a grammar that generates iterated greedy IG algorithms for the permutation flow-shop problem with weighted tardiness minimization. Next, we show how this grammar can be represented in terms of parameters. Finally, we compare the quality of the IG algorithms generated by an automatic configuration tool using the parametric representation versus using the codon-based representation of grammatical evolution. In our scenario, the parametric approach leads to significantly better IG algorithms.

Effective Hybrid Stochastic Local Search Algorithms for Biobjective Permutation Flowshop Scheduling

This paper presents the steps followed in the design of hybrid stochastic local search algorithms for biobjective permutation flow shop scheduling problems. In particular, this paper tackles the three pairwise combinations of the objectives (i) makespan, (ii) the sum of the completion times of the jobs, and (iii) the weighted total tardiness of all jobs. The proposed algorithms are combinations of two local search methods: two-phase local search and Pareto local search. The design of the algorithms is based on a careful experimental analysis of crucial algorithmic components of the two search methods. The final results show that the newly developed algorithms reach very high performance: The solutions obtained frequently improve upon the best nondominated solutions previously known, while requiring much shorter computation times.

A comparative study of three GPU-based metaheuristics

In this paper we compare GPU-based implementations of three metaheuristics: Particle Swarm Optimization, Differential Evolution, and Scatter Search. A GPU-based implementation, obviously, does not change the general properties of the algorithms. As well, we give for granted that GPU-based implementation of both algorithm and fitness function produces a significant speed-up with respect to a sequential implementation. Accordingly, the main goal of this work has been to fairly assess the efficiency of the GPU-based implementations of the three metaheuristics, based on the statistical analysis of the results they obtain in optimizing a benchmark of twenty functions within a prefixed limited time.

Adaptive Anytime two-phase local search

Two-Phase Local Search (TPLS) is a general algorithmic framework for multi-objective optimization. TPLS transforms a multiobjective problem into a sequence of single-objective ones by means of weighted sum aggregations. This paper studies different sequences of weights for defining the aggregated problems for the bi-objective case. In particular, we propose two weight setting strategies that show better anytime search characteristics than the original weight setting strategy used in the TPLS algorithm.