GPU-accelerated Parallel Solutions to the Quadratic Assignment Problem

The Quadratic Assignment Problem (QAP) is an important combinatorial optimization problem with applications in many areas including logistics and manufacturing. QAP is known to be NP-hard, a computationally challenging problem, which requires the use of sophisticated heuristics in finding acceptable solutions for most real-world data sets. In this paper, we present GPU-accelerated implementations of a 2opt and a tabu search algorithm for solving the QAP. For both algorithms, we extract parallelism at multiple levels and implement novel code optimization techniques that fully utilize the GPU hardware. On a series of experiments on the well-known QAPLIB data sets, our solutions, on average run an order-of-magnitude faster than previous implementations and deliver up to a factor of 63 speedup on specific instances. The quality of the solutions produced by our implementations of 2opt and tabu is within 1.03% and 0.15% of the best known values. The experimental results also provide key insight into the performance characteristics of accelerated QAP solvers. In particular, the results reveal that both algorithmic choice and the shape of the input data sets are key factors in finding efficient implementations.Comment: 25 pages, 9 figures; parts of this work appeared as short papers in XSEDE14 and XSEDE15 conferences. This version of the paper is a substantial extension of previous work with optimizations for newer GPU platforms and extended experimental result

A GPU-based Iterated Tabu Search for Solving the Quadratic 3-dimensional Assignment Problem

International audienceThe quadratic 3-dimensional assignment problem (Q3AP) is an extension of the well-known NP-hard quadratic assignment problem. It has been proved to be one of the most difficult combinatorial optimization problems. Local search (LS) algorithms are a class of heuristics which have been successfully applied to solve such hard optimization problem. These methods handle with a single solution iteratively improved by exploring its neighborhood in the solution space. In this paper, we propose an iterated tabu search for solving the Q3AP. The design of this algorithm is essentially based on a new large neighborhood structure. Indeed, in LS heuristics, designing operators to explore large promising regions of the search space may improve the quality of the obtained solutions. However, designing such neighborhood is at the expense of a highly computationally process. Therefore, the use of graphics processing units (GPUs) provides an efficient complementary way to speed up the search. The proposed GPU-based iterated tabu search has been experimented on 5 different Q3AP instances. The obtained results are convincing both in terms of efficiency, quality and robustness of the provided solutions at run time

Parallel Hybrid Evolutionary Algorithms on GPU

International audienceOver the last years, interest in hybrid metaheuristics has risen considerably in the field of optimization. Combinations of methods such as evolutionary algorithms and local searches have provided very powerful search algorithms. However, due to their complexity, the computational time of the solution search exploration remains exorbitant when large problem instances are to be solved. Therefore, the use of GPU-based parallel computing is required as a complementary way to speed up the search. This paper presents a new methodology to design and implement efficiently and effectively hybrid evolutionary algorithms on GPU accelerators. The methodology enables efficient mappings of the explored search space onto the GPU memory hierarchy. The experimental results show that the approach is very efficient especially for large problem instances

GPU-based Approaches for Multiobjective Local Search Algorithms. A Case Study: the Flowshop Scheduling Problem

International audienceMultiobjective local search algorithms are efficient methods to solve complex problems in science and industry. Even if these heuristics allow to significantly reduce the computational time of the solution search space exploration, this latter cost remains exorbitant when very large problem instances are to be solved. As a result, the use of GPU computing has been recently revealed as an efficient way to accelerate the search process. This paper presents a new methodology to design and implement efficiently GPU-based multiobjective local search algorithms. The experimental results show that the approach is promising especially for large problem instances

GPU Computing for Parallel Local Search Metaheuristics

International audienceLocal search metaheuristics (LSMs) are efficient methods for solving complex problems in science and industry. They allow significantly to reduce the size of the search space to be explored and the search time. Nevertheless, the resolution time remains prohibitive when dealing with large problem instances. Therefore, the use of GPU-based massively parallel computing is a major complementary way to speed up the search. However, GPU computing for LSMs is rarely investigated in the literature. In this paper, we introduce a new guideline for the design and implementation of effective LSMs on GPU. Very efficient approaches are proposed for CPU-GPU data transfer optimization, thread control, mapping of neighboring solutions to GPU threads and memory management. These approaches have been experimented using four well-known combinatorial and continuous optimization problems and four GPU configurations. Compared to a CPU-based execution, accelerations up to x80 are reported for the large combinatorial problems and up to x240 for a continuous problem. Finally, extensive experiments demonstrate the strong potential of GPU-based LSMs compared to cluster or grid-based parallel architectures

PGAGrid: A Parallel Genetic Algorithm of Fine-Grained implemented on GPU to find solutions near the optimum to the Quadratic Assignment Problem (QAP)

This work consists in implementing a fine-grained parallel genetic algorithm improved with a greedy 2-opt heuristic to find near-optimal solutions to the Quadratic Assignment Problem (QAP). The proposed algorithm was fully implemented on Graphics Processing Units (GPUs). A two-dimensional GPU grid of size 8x8 defines the population of the genetic algorithm (set of permutations of the QAP), and each GPU block consists of n GPU threads, where n is the size of the QAP. Each GPU block was used to represent the chromosome of a single individual, and each GPU thread represents a gene of such chromosome. The proposed algorithm was tested on a subset of the standard QAPLIB data set. Results show that this implementation is able to find good solutions for large QAP instances in few parallel iterations of the evolutionary process.Resumen: Este trabajo consiste en implementar un algoritmo genético paralelo de grano fino mejorado con una heurística 2-opt voraz para encontrar soluciones cercanas al óptimo al problema de Asignación Cuadrática (QAP). El algoritmo propuesto fue completamente implementado sobre Unidades de Procesamiento Gráfico (GPUs). Una retícula GPU bidimensional de tamaño 8×8 define la población del algoritmo genético (conjunto de permutaciones del QAP) y cada bloque GPU consiste de n hilos GPU donde n es el tamaño del QAP. Cada bloque GPU fue utilizado para representar el cromosoma de un solo individuo y cada hilo GPU representa un gen de tal cromosoma. El algoritmo propuesto fue comprobado sobre un subconjunto de problemas de la librería estándar QAPLIB. Los resultados muestran que esta implementación es capaz de encontrar buenas soluciones para grandes instancias del QAP en pocas iteraciones del proceso evolutivo.Doctorad

GPU parallelization strategies for metaheuristics: a survey

Metaheuristics have been showing interesting results in solving hard optimization problems. However, they become limited in terms of effectiveness and runtime for high dimensional problems. Thanks to the independency of metaheuristics components, parallel computing appears as an attractive choice to reduce the execution time and to improve solution quality. By exploiting the increasing performance and programability of graphics processing units (GPUs) to this aim, GPU-based parallel metaheuristics have been implemented using different designs. RecentresultsinthisareashowthatGPUstendtobeeffectiveco-processors forleveraging complex optimization problems.In thissurvey, mechanisms involvedinGPUprogrammingforimplementingparallelmetaheuristicsare presentedanddiscussedthroughastudyofrelevantresearchpapers. Metaheuristics can obtain satisfying results when solving optimization problems in a reasonable time. However, they suffer from the lack of scalability. Metaheuristics become limited ahead complex highdimensional optimization problems. To overcome this limitation, GPU based parallel computing appears as a strong alternative. Thanks to GPUs, parallelmetaheuristicsachievedbetterresultsintermsofcomputation,and evensolutionquality

Parallelised and vectorised ant colony optimization

Ant Colony Optimisation (ACO) is a versatile population-based optimisation metaheuristic based on the foraging behaviour of certain species of ant, and is part of the Evolutionary Computation family of algorithms. While ACO generally provides good quality solutions to the problems it is applied to, two key limitations prevent it from being truly viable on large-scale problems: A high memory requirement that grows quadratically with instance size, and high execution time. This thesis presents a parallelised and vectorised implementation of ACO using OpenMP and AVX SIMD instructions; while this alone is enough to improve upon the execution time of the algorithm, this implementation also features an alternative memory structure and a novel candidate set approach, the use of which significantly reduces the memory requirement of ACO. This parallelism is enabled through the use of Max-Min Ant System, an ACO variant that only utilises local memory during the solution process and therefore risks no synchronisation issues, and an adaptation of vRoulette, a vector-compatible variant of the common roulette wheel selection method. Through the use of these techniques ACO is also able to find good quality solutions for the very large Art TSPs, a problem set that has traditionally been unfeasible to solve with ACO due to high memory requirements and execution time. These techniques can also benefit ACO when it comes to solving other problems. In this case the Virtual Machine Placement problem, in which Virtual Machines have to be efficiently allocated to Physical Machines in a cloud environment, is used as a benchmark, with significant improvements to execution time

Optimization of storage and picking systems in warehouses

La croissance du commerce électronique exige une hausse des performances des systèmes d'entreposage, qui sont maintenant repensés pour faire face à un volume massif de demandes à être satisfait le plus rapidement possible. Le système manuel et le système à robots mobile (SRM) sont parmi les plus utilisés pour ces activités. Le premier est un système centré sur l'humain pour réaliser des opérations complexes que les robots actuels ne peuvent pas effectuer. Cependant, les nouvelles générations de robots autonomes mènent à un remplacement progressif par le dernier pour augmenter la productivité. Quel que soit le système utilisé, plusieurs problèmes interdépendants doivent être résolus pour avoir des processus de stockage et de prélèvement efficaces. Les problèmes de stockage concernent les décisions d'où stocker les produits dans l'entrepôt. Les problèmes de prélèvement incluent le regroupement des commandes à exécuter ensemble et les itinéraires que les cueilleurs et les robots doivent suivre pour récupérer les produits demandés. Dans le système manuel, ces problèmes sont traditionnellement résolus à l'aide de politiques simples que les préparateurs peuvent facilement suivre. Malgré l'utilisation de robots, la même stratégie de solution est répliquée aux problèmes équivalents trouvés dans le SRM. Dans cette recherche, nous étudions les problèmes de stockage et de prélèvement rencontrés lors de la conception du système manuel et du SRM. Nous développons des outils d'optimisation pour aider à la prise de décision pour mettre en place leurs processus, en améliorant les mesures de performance typiques de ces systèmes. Certains problèmes traditionnels sont résolus avec des techniques améliorées, tandis que d'autres sont intégrés pour être résolus ensemble au lieu d'optimiser chaque sous-système de manière indépendante. Nous considérons d'abord un système manuel avec un ensemble connu de commandes et intégrons les décisions de stockage et de routage. Le problème intégré et certaines variantes tenant compte des politiques de routage communes sont modélisés mathématiquement. Une métaheuristique générale de recherche de voisinage variable est présentée pour traiter des instances de taille réelle. Des expériences attestent de l'efficience de la métaheuristique proposée par rapport aux modèles exacts et aux politiques de stockage communes. Lorsque les demandes futures sont incertaines, il est courant d'utiliser une stratégie de zonage qui divise la zone de stockage en zones et attribue les produits les plus demandés aux meilleures zones. Les tailles des zones sont à déterminer. Généralement, des dimensions arbitraires sont choisies, mais elles ignorent les caractéristiques de l'entrepôt et des demandes. Nous abordons le problème de dimensionnement des zones pour déterminer quels facteurs sont pertinents pour choisir de meilleures tailles de zone. Les données générées à partir de simulations exhaustives sont utilisées pour trainer quatre modèles de régression d'apprentissage automatique - moindres carrés ordinaire, arbre de régression, forêt aléatoire et perceptron multicouche - afin de prédire les dimensions optimales des zones en fonction de l'ensemble de facteurs pertinents identifiés. Nous montrons que tous les modèles entraînés suggèrent des dimensions sur mesure des zones qui performent meilleur que les dimensions arbitraires couramment utilisées. Une autre approche pour résoudre les problèmes de stockage pour le système manuel et pour le SRM considère les corrélations entre les produits. L'idée est que les produits régulièrement demandés ensemble doivent être stockés près pour réduire les coûts de routage. Cette politique de stockage peut être modélisée comme une variante du problème d'affectation quadratique (PAQ). Le PAQ est un problème combinatoire traditionnel et l'un des plus difficiles à résoudre. Nous examinons les variantes les plus connues du PAQ et développons une puissante métaheuristique itérative de recherche tabou mémétique en parallèle capable de les résoudre. La métaheuristique proposée s'avère être parmi les plus performantes pour le PAQ et surpasse considérablement l'état de l'art pour ses variantes. Les SRM permettent de repositionner facilement les pods d'inventaire pendant les opérations, ce qui peut conduire à un processus de prélèvement plus économe en énergie. Nous intégrons les décisions de repositionnement des pods à l'attribution des commandes et à la sélection des pods à l'aide d'une stratégie de prélèvement par vague. Les pods sont réorganisés en tenant compte du moment et de l'endroit où ils devraient être demandés au futur. Nous résolvons ce problème en utilisant la programmation stochastique en tenant compte de l'incertitude sur les demandes futures et suggérons une matheuristique de recherche locale pour résoudre des instances de taille réelle. Nous montrons que notre schéma d'approximation moyenne de l'échantillon est efficace pour simuler les demandes futures puisque nos méthodes améliorent les solutions trouvées lorsque les vagues sont planifiées sans tenir compte de l'avenir. Cette thèse est structurée comme suit. Après un chapitre d'introduction, nous présentons une revue de la littérature sur le système manuel et le SRM, et les décisions communes prises pour mettre en place leurs processus de stockage et de prélèvement. Les quatre chapitres suivants détaillent les études pour le problème de stockage et de routage intégré, le problème de dimensionnement des zones, le PAQ et le problème de repositionnement de pod. Nos conclusions sont résumées dans le dernier chapitre.The rising of e-commerce is demanding an increase in the performance of warehousing systems, which are being redesigned to deal with a mass volume of demands to be fulfilled as fast as possible. The manual system and the robotic mobile fulfillment system (RMFS) are among the most commonly used for these activities. The former is a human-centered system that handles complex operations that current robots cannot perform. However, newer generations of autonomous robots are leading to a gradual replacement by the latter to increase productivity. Regardless of the system used, several interdependent problems have to be solved to have efficient storage and picking processes. Storage problems concern decisions on where to store products within the warehouse. Picking problems include the batching of orders to be fulfilled together and the routes the pickers and robots should follow to retrieve the products demanded. In the manual system, these problems are traditionally solved using simple policies that pickers can easily follow. Despite using robots, the same solution strategy is being replicated to the equivalent problems found in the RMFS. In this research, we investigate storage and picking problems faced when designing manual and RMFS warehouses. We develop optimization tools to help in the decision-making process to set up their processes and improve typical performance measures considered in these systems. Some classic problems are solved with improved techniques, while others are integrated to be solved together instead of optimizing each subsystem sequentially. We first consider a manual system with a known set of orders and integrate storage and routing decisions. The integrated problem and some variants considering common routing policies are modeled mathematically. A general variable neighborhood search metaheuristic is presented to deal with real-size instances. Computational experiments attest to the effectiveness of the metaheuristic proposed compared to the exact models and common storage policies. When future demands are uncertain, it is common to use a zoning strategy to divide the storage area into zones and assign the most-demanded products to the best zones. Zone sizes are to be determined. Commonly, arbitrary sizes are chosen, which ignore the characteristics of the warehouse and the demands. We approach the zone sizing problem to determine which factors are relevant to choosing better zone sizes. Data generated from exhaustive simulations are used to train four machine learning regression models - ordinary least squares, regression tree, random forest, and multilayer perceptron - to predict the optimal zone sizes given the set of relevant factors identified. We show that all trained models suggest tailor-made zone sizes with better picking performance than the arbitrary ones commonly used. Another approach to solving storage problems, both in the manual and RMFS, considers the correlations between products. The idea is that products constantly demanded together should be stored closer to reduce routing costs. This storage policy can be modeled as a quadratic assignment problem (QAP) variant. The QAP is a traditional combinatorial problem and one of the hardest to solve. We survey the most traditional QAP variants and develop a powerful parallel memetic iterated tabu search metaheuristic capable of solving them. The proposed metaheuristic is shown to be among the best performing ones for the QAP and significantly outperforms the state-of-the-art for its variants. The RMFS allows easy repositioning of inventory pods during operations that can lead to a more energy-efficient picking process. We integrate pod repositioning decisions with order assignment and pod selection using a wave picking strategy such that pods are parked after being requested considering when and where they are expected to be requested next. We solve this integrated problem using stochastic programming considering the uncertainty about future demands and suggest a local search matheuristic to solve real-size instances. We show that our sample average approximation scheme is effective to simulate future demands since our methods improve solutions found when waves are planned without considering the future demands. This thesis is structured as follows. After an introductory chapter, we present a literature review on the manual and RMFS, and common decisions made to set up their storage and picking processes. The next four chapters detail the studies for the integrated storage and routing problem, the zone sizing problem, the QAP, and the pod repositioning problem. Our findings are summarized in the last chapter