A Weight-coded Evolutionary Algorithm for the Multidimensional Knapsack Problem

A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computational results show that the RWCEA performs better than a weight-coded evolutionary algorithm proposed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.Comment: Submitted to Applied Mathematics and Computation on April 8, 201

Resource and Bandwidth Allocation in Hybrid Wireless Mobile Networks

In the lead up to the implementation of 802.16 and 4G wireless networks, there have been many proposals for addition of multi-hop MANET zones or relay stations in order to cut the cost of building a new backbone infrastructure from the ground up. These types of Hybrid Wireless Networks will certainly be a part of wireless network architecture in the future, and as such, simple problems such as resource allocation must be explored to maximize their potential. This study explores the resource allocation problem in three distinct ways. First, this study highlights two existing backbone architectures: max-coverage and max-resource, and how hybridization will affect bandwidth allocation, with special emphasis on OFDM-TMA wireless networks. Secondly, because of the different goals of these types of networks, the addition of relay stations or MANET zones will affect resource availability differently, and I will show how the addition of relay stations impacts the backbone network. Finally, I will discuss specific allocation algorithms and policies such as top-down, bottom-up, and auction-based allocation, and how each kind of allocation will maximize the revenue of both the backbone network as well as the mobile subscribers while maintaining a minimum Quality of Service (or fairness). Each of these approaches has merit in different hybrid wireless systems, and I will summarize the benefits of each in a study of a network system with a combination of the elements discussed in the previous chapters

Moldable Items Packing Optimization

This research has led to the development of two mathematical models to optimize the problem of packing a hybrid mix of rigid and moldable items within a three-dimensional volume. These two developed packing models characterize moldable items from two perspectives: (1) when limited discrete configurations represent the moldable items and (2) when all continuous configurations are available to the model. This optimization scheme is a component of a lean effort that attempts to reduce the lead-time associated with the implementation of dynamic product modifications that imply packing changes. To test the developed models, they are applied to the dynamic packing changes of Meals, Ready-to-Eat (MREs) at two different levels: packing MRE food items in the menu bags and packing menu bags in the boxes. These models optimize the packing volume utilization and provide information for MRE assemblers, enabling them to preplan for packing changes in a short lead-time. The optimization results are validated by running the solutions multiple times to access the consistency of solutions. Autodesk Inventor helps visualize the solutions to communicate the optimized packing solutions with the MRE assemblers for training purposes

Contribution à la résolution de problèmes d'optimisation combinatoire : méthodes séquentielles et parallèles

Les problèmes d'optimisation combinatoire sont souvent des problèmes très difficiles dont la résolution par des méthodes exactes peut s'avérer très longue ou peu réaliste. L'utilisation de méthodes heuristiques permet d'obtenir des solutions de bonne qualité en un temps de résolution raisonnable. Les heuristiques sont aussi très utiles pour le développement de méthodes exactes fondées sur des techniques d'évaluation et de séparation. Nous nous sommes intéressés dans un premier temps à proposer une méthode heuristique pour le problème du sac à dos multiple MKP. L'approche proposée est comparée à l'heuristique MTHM et au solveur CPLEX. Dans un deuxième temps nous présentons la mise en oeuvre parallèle d'une méthode exacte de résolution de problèmes d'optimisation combinatoire de type sac à dos sur architecture GPU. La mise en oeuvre CPU-GPU de la méthode de Branch and Bound pour la résolution de problèmes de sac à dos a montré une accélération de 51 sur une carte graphique Nvidia Tesla C2050. Nous présentons aussi une mise en oeuvre CPU-GPU de la méthode du Simplexe pour la résolution de problèmes de programmation linéaire. Cette dernière offre une accélération de 12.7 sur une carte graphique Nvidia Tesla C2050. Enfin, nous proposons une mise en oeuvre multi-GPU de l'algorithme du Simplexe, mettant à contribution plusieurs cartes graphiques présentes dans une même machine (2 cartes Nvidia Tesla C2050 dans notre cas). Outre l'accélération obtenue par rapport à la mise en oeuvre séquentielle de la méthode du Simplexe, une efficacité de 96.5 % est obtenue, en passant d'une carte à deux cartes graphiques.Combinatorial optimization problems are difficult problems whose solution by exact methods can be time consuming or not realistic. The use of heuristics permits one to obtain good quality solutions in a reasonable time. Heuristics are also very useful for the development of exact methods based on branch and bound techniques. The first part of this thesis concerns the Multiple Knapsack Problem (MKP). We propose here a heuristic called RCH which yields a good solution for the MKP problem. This approach is compared to the MTHM heuristic and CPLEX solver. The second part of this thesis concerns parallel implementation of an exact method for solving combinatorial optimization problems like knapsack problems on GPU architecture. The parallel implementation of the Branch and Bound method via CUDA for knapsack problems is proposed. Experimental results show a speedup of 51 for difficult problems using a Nvidia Tesla C2050 (448 cores). A CPU-GPU implementation of the simplex method for solving linear programming problems is also proposed. This implementation offers a speedup around 12.7 on a Tesla C2050 board. Finally, we propose a multi-GPU implementation of the simplex algorithm via CUDA. An efficiency of 96.5% is obtained when passing from one GPU to two GPUs

An exact algorithm for the knapsack sharing problem

International audienceIn this paper, we develop an exact algorithm for solving the knapsack sharing problem. The algorithm is a new version of the method proposed in Hifi and Sadfi (J. Combin. Optim. 6 (2002) 35). It seems quite efficient in the sense that it solves quickly some large problem instances. Its main principle consists of (i) finding a good set of capacities, representing a set of critical elements, using a heuristic approach, and (ii) varying the values of the obtained set in order to stabilize the optimal solution of the problem. Then, by exploiting dynamic programming properties, we obtain good equilibrium which lead to significant improvements. The performance of the proposed algorithm, based on a set of medium and large problem instances, is compared to the standard version of Hifi and Sadfi (2002). Encouraging results have been obtained