Daniel Tuyttens

MOSA method: a tool for solving multiobjective combinatorial optimization problems

The success of modern heuristics (Simulated Annealing (S.A.), Tabu Search, Genetic Algorithms, …) in solving classical combinatorial optimization problems has drawn the attention of the research community in multicriteria methods. In fact, for large-scale problems, the simultaneous difficulties of -hard complexity and of multiobjective framework make most Multiobjective Combinatorial Optimization (MOCO) problems intractable for exact methods. This paper develops the so-called MOSA (Multiobjective Simulated Annealing) method to approximate the set of efficient solutions of a MOCO problem. Different options for the implementation are illustrated and extensive experiments prove the efficiency of the approach. Its results are compared to exact methods on bi-objective knapsack problems. Copyright

A parallel bi-objective hybrid metaheuristic for energy-aware scheduling for cloud computing systems

In this paper, we investigate the problem of scheduling precedence-constrained parallel applications on heterogeneous computing systems (HCSs) like cloud computing infrastructures. This kind of application was studied and used in many research works. Most of these works propose algorithms to minimize the completion time (makespan) without paying much attention to energy consumption. We propose a new parallel bi-objective hybrid genetic algorithm that takes into account, not only makespan, but also energy consumption. We particularly focus on the island parallel model and the multi-start parallel model. Our new method is based on dynamic voltage scaling (DVS) to minimize energy consumption. In terms of energy consumption, the obtained results show that our approach outperforms previous scheduling methods by a significant margin. In terms of completion time, the obtained schedules are also shorter than those of other algorithms. Furthermore, our study demonstrates the potential of DVS.

Solving multi-objective production scheduling problems using metaheuristics

Abstract Most of research in production scheduling is concerned with the optimization of a single criterion. However the analysis of the performance of a schedule often involves more than one aspect and therefore requires a multi-objective treatment. In this paper we first present ( Section 1 ) the general context of multi-objective production scheduling, analyze briefly the different possible approaches and define the aim of this study i.e. to design a general method able to approximate the set of all the efficient schedules for a large set of scheduling models. Then we introduce ( Section 2 ) the models we want to treat––one machine, parallel machines and permutation flow shops––and the corresponding notations. The method used––called multi-objective simulated annealing––is described in Section 3 . Section 4 is devoted to extensive numerical experiments and their analysis. Conclusions and further directions of research are discussed in the last section.

Performance of the MOSA Method for the Bicriteria Assignment Problem

The classical linear Assignment problem is considered with two objectives. The aim is to generate the set of efficient solutions. An exact method is first developed based on the two-phase approach. In the second phase a new upper bound is proposed so that larger instances can be solved exactly. The so-called MOSA (Multi-Objective Simulated Annealing) is then recalled; its efficiency is improved by initialization with a greedy approach. Its results are compared to those obtained with the exact method. Extensive numerical experiments have been realized to measure the performance of the MOSA method.

On large scale nonlinear network optimization

Partial separability and partitioned quasi-Newton updating have been recently introduced and experimented with success in large scale nonlinear optimization, large nonlinear least squares calculations and in large systems of nonlinear equations. It is the purpose of this paper to apply this idea to large dimensional nonlinear network optimization problems. The method proposed thus uses these techniques for handling the cost function, while more classical tools as variable partitioning and specialized data structures are used in handling the network constraints. The performance of a code implementing this method, as well as more classical techniques, is analyzed on several numerical examples.

On iterative algorithms for linear least squares problems with bound constraints

Three new iterative methods for the solution of the linear least squares problem with bound constraints are presented and their performance analyzed. The first is a modification of a method proposed by Lotstedt, while the two others are characterized by a technique allowing for fast active set changes, resulting in noticeable improvements in the speed with which constraints active at the solution are identified. The numerical efficiency of those algorithms is experimentally studied, with particular emphasis on the dependence on the starting point and the use of preconditioning for ill-conditioned problems.

An interactive heuristic method for multi-objective combinatorial optimization

Abstract We have previously developed an adaptation of the simulated annealing for multi-objective combinatorial optimization (MOCO) problems to construct an approximation of the efficient set of such problem. In order to deal with large-scale problems, we transform this approach to propose an interactive procedure. The method is tested on the multi-objective knapsack problem and the multi-objective assignment problem. Scope and purpose Meta-heuristics methods are intensively used with success to solve optimization problems and especially combinatorial problems (Pirlot. EJOR 1996;92:493–511). In the case of a single objective problem, such methods compute an approximation to the unique optimal solution. Recently, some meta-heuristics have been adapted to treat multi-objective problems. These methods construct an approximation of the set of all efficient solutions. For large-scale multi-objective combinatorial problems, the number of efficient solutions may become very large. In order to help a decision maker to make a choice between these solutions, an interactive procedure is developed in this paper.

Using metaheuristics for solving a production scheduling problem in a chemical firm. A case study

Abstract The problem is raised by a workshop management team in a chemical industry producing materials of different types. The workshop contains several equipments in parallel and in series which can be used for the production of each job. The equipments in series are connected by a piping system forming a network by which the material runs out. Some connections are shared by several pairs of equipments so that the use of such a connection for one pair of equipments makes this connection unavailable at the same time for other pairs. Several particular constraints must be satisfied and deadlines exist for some jobs. The objectives are to minimize the makespan and the tardiness. A method is proposed to heuristically obtain a satisfying production schedule. The procedure involves two stages. In a first step, given a fixed order of the jobs, a conventional heuristic is proposed to successively assign the jobs to the available equipments. In a second step, the simulated annealing or tabu metaheuristics are applied to optimize the order of the jobs. The method was implemented on a PC and applied to an instance of the problem. Some comparisons are made to analyse and compare the efficiency of the heuristics.

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.

Combining multi-core and GPU computing for solving combinatorial optimization problems

In this paper, we revisit the design and implementation of Branch-and-Bound (B&B) algorithms for solving large combinatorial optimization problems on GPU-enhanced multi-core machines. B&B is a tree-based optimization method that uses four operators (selection, branching, bounding and pruning) to build and explore a highly irregular tree representing the solution space. In our previous works, we have proposed a GPU-accelerated approach in which only a single CPU core is used and only the bounding operator is performed on the GPU device. Here, we extend the approach (LL-GB&B) in order to minimize the CPU-GPU communication latency and thread divergence. Such an objective is achieved through a GPU-based fine-grained parallelization of the branching and pruning operators in addition to the bounding one. The second contribution consists in investigating the combination of a GPU with multi-core processing. Two scenarios have been explored leading to two approaches: a concurrent (RLL-GB&B) and a cooperative one (PLL-GB&B). In the first one, the exploration process is performed concurrently by the GPU and the CPU cores. In the cooperative approach, the CPU cores prepare and off-load to GPU pools of tree nodes using data streaming while the GPU performs the exploration. The different approaches have been extensively experimented on the Flowshop scheduling problem. Compared to a single CPU-based execution, LL-GB&B allows accelerations up to (x160) for large problem instances. Moreover, when combining multi-core and GPU, we figure out that using RLL-GB&B is not beneficial while PLL-GB&B enables an improvement up to 36% compared to LL-GB&B.