A GPU-accelerated Branch-and-Bound Algorithm for the Flow-Shop Scheduling Problem

Branch-and-Bound (B&B) algorithms are time intensive tree-based exploration methods for solving to optimality combinatorial optimization problems. In this paper, we investigate the use of GPU computing as a major complementary way to speed up those methods. The focus is put on the bounding mechanism of B&B algorithms, which is the most time consuming part of their exploration process. We propose a parallel B&B algorithm based on a GPU-accelerated bounding model. The proposed approach concentrate on optimizing data access management to further improve the performance of the bounding mechanism which uses large and intermediate data sets that do not completely fit in GPU memory. Extensive experiments of the contribution have been carried out on well known FSP benchmarks using an Nvidia Tesla C2050 GPU card. We compared the obtained performances to a single and a multithreaded CPU-based execution. Accelerations up to x100 are achieved for large problem instances

On the Neutrality of Flowshop Scheduling Fitness Landscapes

Solving efficiently complex problems using metaheuristics, and in particular local searches, requires incorporating knowledge about the problem to solve. In this paper, the permutation flowshop problem is studied. It is well known that in such problems, several solutions may have the same fitness value. As this neutrality property is an important one, it should be taken into account during the design of optimization methods. Then in the context of the permutation flowshop, a deep landscape analysis focused on the neutrality property is driven and propositions on the way to use this neutrality to guide efficiently the search are given.Comment: Learning and Intelligent OptimizatioN Conference (LION 5), Rome : Italy (2011

Some recent results in the analysis of greedy algorithms for assignment problems

We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems

An O(nlogn) algorithm for the two-machine flow shop problem with controllable machine speeds

Production Planning;Scheduling;produktieleer/ produktieplanning

Combinatorial Ant Optimization and the Flowshop Problem

Researchers have developed efficient techniques, meta-heuristics to solve many Combinatorial Optimization (CO) problems, e.g., Flow shop Scheduling Problem, Travelling Salesman Problem (TSP) since the early 60s of the last century. Ant Colony Optimization (ACO) and its variants were introduced by Dorigo et al. [DBS06] in the early 1990s which is a technique to solve CO problems. In this thesis, we used the ACO technique to find solutions to the classic Flow shop Scheduling Problem and proposed a novel method for solution improvement. Our solution is composed of two phases; in the first phase, we solved TSP using ACO technique which gave us an initial permutation or tour. We used the same trip as an initial solution for our problem and then improved it by using 2-opt exchanges which yielded in a promising result. Furthermore, we introduced another improvement technique which gave us a more promising result. We have compared our results with the best (optimal) and worst solution known till date. A comprehensive experimental study using existing dataset proves that our approach remarkably gives good results

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex con guration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases