The Multiple-choice Multi-dimensional Knapsack Problem (MMKP) is a problem which can be encountered in real-world applications, such as service level agreement, model of allocation resources, or as a dynamic adaptation of system of resources for multimedia multi-sessions. In this paper, we investigate the use of a new model-based Lagrangian relaxation for optimally solving the MMKP. In order to...

Multi-dimensional multi-container packing problems appear within many settings of theoretical and practical interest, including Knapsack, Strip Packing, Container Loading, and Scheduling problems. These various problem settings display different objective functions and constraints, which may explain the lack of efficient heuristics able to jointly address them. In this paper we introduce GASP G...

In this thesis, we investigate the capabilities of Ant Colony Optimization (ACO) metaheuristic tosolve combinatorial and multi-objective optimization problems. First, we propose a taxonomy ofACO algorithms proposed in the literature to solve multi-objective problems. Then, we studydifferent pheromonal strategies for the case of mono-objective multidimensional knapsackproblem. We...

Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multi-agent systems and distributed systems, and can also be found as subproblems of scheduling problems. We propose bin completion, a branch-and-bound stra...

A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient a...

Multi Expression Programming (MEP) is a Genetic Programming variant that uses linear chromosomes for solution encoding. A unique feature of MEP is its ability of encoding multiple solutions of a problem in a single chromosome. In this paper we use Multi Expression Programming for evolving digital circuits for a well-known NP-Complete problem: the knapsack (subset sum) problem. Numerical experim...

Order promising in make-to-order manufacturing often has a strong focus on resource oriented factors. Economic aspects are, if at all, only implicitly taken into account. In this paper we develop a revenue management approach to improve order promising for short-term sales in the iron and steel industry as an example of make-to-order manufacturing. We formulate a multi-dimensional knapsack prob...

In this paper, an optimisation technique based on the Particle Swarm Optimization (PSO) algorithm will be experimented upon the Multi-dimensional Knapsack Problem. Through the merging of fundamental concepts of the existing PSO algorithm and selected features of evolutionary algorithms, a novel hybrid algorithm is created. When testing the algorithm against a test suite publicly available on OR...

This paper describes and evaluates alternative branch-and-price decompositions (B&P-Ds) of the multi-dimensional knapsack problem with generalized upper bound constraints both analytically and computationally. As part of our theoretical analysis we compare the bounds available from B&P-Ds with three alternative relaxations (Lagrangean relaxation, Lagrangean decomposition, and Surrogate relaxati...