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

B&B@Grid : une approche efficace pour la gridification d'un algorithme Branch and Bound

La résolution exacte de problèmes d'optimisation combinatoire de grande taille, tels que les problèmes d'ordonnancement, constitue un vrai défi pour les grilles informatiques. En effet, il est nécessaire de repenser les algorithmes de résolution pour prendre en compte les caractéristiques de tels environnements, notamment leur grande échelle, l'hétérogénéité et la disponibilité dynamique de leurs ressources, et leur nature multi-domaine d'administration. Dans cet article, nous proposons une nouvelle approche de passage sur grilles de calcul des méthodes exactes de type Branch-and-Bound appelée B&B@Grid. Cette approche est basée sur un codage des unités de travail (sous problèmes) sous forme d'intervalles permettant de minimiser le coût des communications induites par les opérations de régulation de charge, de tolérance aux pannes et de détection de la terminaison. Cette approche, beaucoup plus performante en terme de coût de communication et de sauvegarde que les meilleures approches connues dans la littérature, a permis la résolution optimale sur la grille nationale Grid'5000 d'une instance standard du problème du Flow-Shop restée non résolue depuis une quinzaine d'années. Le Flow-Shop est l'un des problèmes d'ordonnancement les plus étudiés

Reducing thread divergence in a GPU-accelerated branch-and-bound algorithm

International audienceIn this paper, we address the design and implementation of GPU-accelerated Branch-and-Bound algorithms (B&B) for solving Flow-shop scheduling optimization problems (FSP). Such applications are CPU-time consuming and highly irregular. On the other hand, GPUs are massively multi-threaded accelerators using the SIMD model at execution. A major issue which arises when executing on GPU a B&B applied to FSP is thread or branch divergence. Such divergence is caused by the lower bound function of FSP which contains many irregular loops and conditional instructions. Our challenge is therefore to revisit the design and implementation of B&B applied to FSP dealing with thread divergence. Extensive experiments of the proposed approach have been carried out on well-known FSP benchmarks using an Nvidia Tesla C2050 GPU card. Compared to a CPU-based execution, accelerations up to ×77.46 are achieved for large problem instances

A Grid-enabled Branch and Bound Algorithm for Solving Challenging Combinatorial Optimization Problems

Solving exactly large scale instances of combinatorial optimization problems requires a huge amount of computational resources. In this paper, we propose an adaptation of the parallel Branch and Bound algorithm for computational grids. We consequently propose new ways to efficiently deal with some crucial issues, mainly dynamic adaptive load balancing, fault tolerance, global information sharing and termination detection of the algorithm. A special coding of the work units distributed and folded/unfolded during the exploration of the search tree allows to optimize the involved communications. The algorithm has been implemented following a large scale idle time stealing paradigm. It has been experimented on a Flow-Shop problem instance (Ta056) that has never been solved exactly. The optimal solution has been found with proof of optimality within 25 days using about 1900 processors belonging to 9 Nation-wide distinct clusters (administration domains). During the resolution, the worker processors were exploited with an average to 97% while the farmer processor was exploited only 1.7% of the time. These two rates are good indicators on the parallel efficiency of the proposed approach and its scalability

Simulation-Based Genetic Algorithm towards an Energy-Efficient Railway Traffic Control

The real-time traffic control has an important impact on the efficiency of the energy utilization in the modern railway network. This study is aimed to develop an energy-efficient railway traffic control solution for any specified railway. In other words, it is expected to define suitable driving profiles for all the trains running within a specified period through the targeted network with an objective to minimize their total energy consumption. How to optimize the train synchronization so as to benefit from the energy regenerated by electronic braking is also considered in this study. A method based on genetic algorithm and empirical single train driving strategies is developed for this objective. Six monomode strategies and one multimode strategy are tested and compared with the four scenarios extracted from the Belgian railway system. The results obtained by simulation show that the multi-mode control strategy overcomes the mono-mode control strategies with regard to global energy consumption, while there is no firm relation between the utilization rate of energy regenerated by dynamic braking operations and the reduction of total energy consumption

Parallel Evolutionary Algorithms for Energy Aware Scheduling

International audienceReducing energy consumption is an increasingly important issue in computing and embedded systems. In computing systems, minimizing energy consumption can significantly reduces the amount of energy bills. The demand for computing systems steadily increases and the cost of energy continues to rise. In embedded systems, reducing the use of energy allows to extend the autonomy of these systems. In addition, the reduction of energy decreases greenhouse gas emissions. Therefore, many researches are carried out to develop new methods in order to consume less energy. This chapter gives an overview of the main methods used to reduce the energy consumption in computing and embedded systems. As a use case and to give an example of a method, the chapter describes our new parallel bi-objective hybrid genetic algorithm that takes into account the completion time and the 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

A computationally efficient Branch-and-Bound algorithm for the permutation flow-shop scheduling problem

International audienceIn this work we propose an efficient branch-and-bound (B&B) algorithm for the permutation flow-shop problem (PFSP) with makespan objective. We present a new node decomposition scheme that combines dynamic branching and lower bound refinement strategies in a computationally efficient way. To alleviate the computational burden of the two-machine bound used in the refinement stage, we propose an online learning-inspired mechanism to predict promising couples of bottleneck machines. The algorithm offers multiple choices for branching and bounding operators and can explore the search tree either sequentially or in parallel on multi-core CPUs. In order to empirically determine the most efficient combination of these components, a series of computational experiments with 600 benchmark instances is performed. A main insight is that the problem size, aswell as interactions between branching and bounding operators substantially modify the trade-off between the computational requirements of a lower bound and the achieved tree size reduction. Moreover, we demonstrate that parallel tree search is a key ingredient for the resolution of largeproblem instances, as strong super-linear speedups can be observed. An overall evaluation using two well-known benchmarks indicates that the proposed approach is superior to previously published B&B algorithms. For the first benchmark we report the exact resolution – within less than20 minutes – of two instances defined by 500 jobs and 20 machines that remained open for more than 25 years, and for the second a total of 89 improved best-known upper bounds, including proofs of optimality for 74 of them

Hybrid Acquisition Processes in Surrogate-based Optimization. Application to Covid-19 Contact Reduction

International audienceParallel Surrogate-Assisted Evolutionary Algorithms (P-SAEAs) are based on surrogate-informed reproduction operators to propose new candidates to solve computationally expensive optimization problems. Differently, Parallel Surrogate-Driven Algorithms (P-SDAs) rely on the optimization of a surrogate-informed metric of promisingness to acquire new solutions. The former are promoted to deal with moderately computationally expensive problems while the latter are put forward on very costly problems. This paper investigates the design of hybrid strategies combining the acquisition processes of both P-SAEAs and P-SDAs to retain the best of both categories of methods. The objective is to reach robustness with respect to the computational budgets and parallel scalability

Evolution Control Ensemble Models for Surrogate-Assisted Evolutionary Algorithms

International audienceFinding the trade-off between exploitation and exploration in a Surrogate-Assisted Evolutionary Algorithm is challenging as the focus on the landscape being optimized moves during the search. The balancing is mainly guided by Evolution Controls, that decide to simulate, predict or discard newly generated candidate solutions. Combining Evolution Controls in ensembles allows to regulate the degree of exploitation and exploration during the search. In this study, we propose ensemble strategies between multiple Evolution Controls in order to adapt the trade-off for each region scrutinized during the search. Experiments led on benchmark problems and on a real-world application of SARS-CoV-2 Transmission Control reveal that favoring exploration at the beginning of the search and favoring exploitation at the end of the search is beneficial in many cases

Towards Dynamic Selection of Evolution Controls in Parallel Bayesian Neural Network-assisted Genetic Algorithm

International audienc