Search results for "Mathematical optimization"
showing 10 items of 1300 documents
An efficient variable neighborhood search heuristic for very large scale vehicle routing problems
2007
In this paper, we present an efficient variable neighborhood search heuristic for the capacitated vehicle routing problem. The objective is to design least cost routes for a fleet of identically capacitated vehicles to service geographically scattered customers with known demands. The variable neighborhood search procedure is used to guide a set of standard improvement heuristics. In addition, a strategy reminiscent of the guided local search metaheuristic is used to help escape local minima. The developed solution method is specifically aimed at solving very large scale real-life vehicle routing problems. To speed up the method and cut down memory usage, new implementation concepts are use…
GRASP for the uncapacitated r-allocation p-hub median problem
2014
In this paper we propose a heuristic for the Uncapacitated r-Allocation p-Hub Median Problem. In the classical p-hub location problem, given a set of nodes with pairwise traffic demands, we must select p of them as hub locations and route all traffics through them at a minimum cost. We target here an extension, called the r-allocation p-hub median problem, recently proposed by Yaman [19], in which every node is assigned to r of the p selected hubs (r@?p) and we are restricted to route the traffic of the nodes through their associated r hubs. As it is usual in this type of problems, our method has three phases: location, assignment and routing. Specifically, we propose a heuristic based on t…
Best compromise solution for a new multiobjective scheduling problem
2006
In future wireless networks, a mobile terminal will be able to communicate with a service provider using several network connections. These connections to networks will have different properties and they will be priced separately. In order to minimize the total communication time and the total transmission costs, an automatic method for selecting the network connections is needed. Here, we describe the network connection selection problem and formulate it mathematically. We discuss solving the problem and analyse different multiobjective optimization approaches for it.
A branch-and-cut algorithm for the pallet loading problem
2005
We propose a branch-and-cut algorithm for the pallet loading problem. The 0-1 formulation proposed by Beasley for cutting problems is adapted to the problem, adding new constraints and new procedures for variable reduction. We then take advantage of the relationship between this problem and the maximum independent set problem to use the partial linear description of its associated polyhedron. Finally, we exploit the specific structure of our problem to define the solution graph and to develop efficient separation procedures. We present computational results for the complete sets Cover I (up to 50 boxes) and Cover II (up to 100 boxes).
A double genetic algorithm for the MRCPSP/max
2011
This paper presents a heuristic solution procedure for a very general resource-constrained project scheduling problem. Here, multiple execution modes are available for the individual activities of the project. In addition, minimum as well as maximum time lags between different activities may be given. The objective is to determine a mode and a start time for each activity such that the temporal and resource constraints are met and the project duration is minimised. Project scheduling problems of this type occur e.g. in process industries. The heuristic is a two-phased genetic algorithm with different representation, fitness, crossover operator, etc., in each of them. One of the contribution…
Active-guided evolution strategies for large-scale capacitated vehicle routing problems
2007
We present an adaptation of the active-guided evolution strategies metaheuristic for the capacitated vehicle routing problem. The capacitated vehicle routing problem is a classical problem in operations research in which a set of minimum total cost routes must be determined for a fleet of identical capacitated vehicles in order to service a number of demand or supply points. The applied metaheuristic combines the strengths of the well-known guided local search and evolution strategies metaheuristics into an iterative two-stage procedure. The computational experiments were carried out on a set of 76 benchmark problems. The results demonstrate that the suggested method is highly competitive, …
On the approximability of the range assignment problem on radio networks in presence of selfish agents
2005
AbstractWe consider the range assignment problem in ad-hoc wireless networks in the context of selfish agents: A network manager aims to assigning transmission ranges to the stations in order to achieve strong connectivity of the network within a minimal overall power consumption. Station is not directly controlled by the manager and may refuse to transmit with a certain transmission range because it might be costly in terms of power consumption.We investigate the existence of payment schemes which induce the stations to follow the decisions of a network manager in computing a range assignment, that is, truthful mechanisms for the range assignment problem. We provide both positive and negat…
Scheduling in a continuous galvanizing line
2009
In this paper we address a sequencing problem in a Continuous Galvanizing Line of a Spanish Steel Company. Production scheduling in this context is an extremely complex task which needs to take into account many constraints. We present a conceptually simple model and a Tabu Search (TS) algorithm that efficiently solves it. The TS moves are defined in order to repair non-satisfied constraints, leading to smaller and more efficient neighbourhoods. The TS co-ordinates several intensification and diversification procedures guided by an evaluation function based on a shifting penalty strategy. This function reinforces the anticycling mechanism and makes the algorithm avoid already visited soluti…
GRASP and path relinking for the equitable dispersion problem
2013
The equitable dispersion problem consists in selecting a subset of elements from a given set in such a way that a measure of dispersion is maximized. In particular, we target the Max-Mean dispersion model in which the average distance between the selected elements is maximized. We first review previous methods and mathematical formulations for this and related dispersion problems and then propose a GRASP with a Path Relinking in which the local search is based on the Variable Neighborhood methodology. Our method is specially suited for instances in which the distances represent affinity and are not restricted to take non-negative values. The computational experience with 120 instances shows…
Variable neighborhood search for the linear ordering problem
2006
Given a matrix of weights, the linear ordering problem (LOP) consists of finding a permutation of the columns and rows in order to maximize the sum of the weights in the upper triangle. This NP-complete problem can also be formulated in terms of graphs, as finding an acyclic tournament with a maximal sum of arc weights in a complete weighted graph. In this paper, we first review the previous methods for the LOP and then propose a heuristic algorithm based on the variable neighborhood search (VNS) methodology. The method combines different neighborhoods for an efficient exploration of the search space. We explore different search strategies and propose a hybrid method in which the VNS is cou…