A Beam Search Method to Solve the Problem of Assignment Cells to Switches in a Cellular Mobile Network

Assigning cells to switches in a cellular mobile network is known as an NP-hard optimization problem. This means that the alternative for the solution of this type of problem is the use of heuristic methods, because they allow the discovery of a good solution in a very satisfactory computational time. This paper proposes a Beam Search method to solve the problem of assignment cell in cellular mobile networks. Some modifications in this algorithm are also presented, which allows its parallel application. Computational results obtained from several tests confirm the effectiveness of this approach and provide good solutions for large scale problems.

Problem of assignment cells to switches in a cellular mobile network via beam search method

The problem of assigning cells to switches in a cellular mobile network is an NP-hard optimization problem. So, real size mobile networks could not be solved by using exact methods. The alternative is the use of the heuristic methods, because they allow us to find a good quality solution in a quite satisfactory computational time. This paper proposes a Beam Search method to solve the problem of assignment cell in cellular mobile networks. Some modifications in this algorithm are also presented, which allows its parallel application. Computational results obtained from several tests confirm the effectiveness of this approach to provide good solutions for medium- and large-sized cellular mobile network.

A Lagrangian bound for many-to-many assignment problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Lagrangian heuristic for a class of the generalized assignment problems

A Lagrangian based heuristic is proposed for many-to-many assignment problems taking into account capacity limits for task and agents. A modified Lagrangian bound studied earlier by the authors is presented and a greedy heuristic is then applied to get a feasible Lagrangian-based solution. The latter is also used to speed up the subgradient scheme to solve the modified Lagrangian dual problem. A numerical study is presented to demonstrate the efficiency of the proposed approach. (C) 2010 Elsevier Ltd. All rights reserved.

Comparison of Lagrangian Bounds for One Class of Generalized Assignment Problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A heuristic algorithm based on multi-assignment procedures for nurse scheduling

This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses' preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust. © 2013 Springer Science+Business Media New York.

Métodos de geração de colunas para problemas de atribuição

Este trabalho apresenta métodos de geração de colunas para dois importantes problemas de atribuição: o Problema Generalizado de Atribuição (PGA) e o Problema de Atribuição de Antenas a Comutadores (PAAC). O PGA é um dos mais representativos problemas de Otimização Combinatória e consiste em otimizar a atribuição de n tarefas a m agentes, de forma que cada tarefa seja atribuída a exatamente um agente e a capacidade de cada agente seja respeitada. O PAAC consiste em atribuir n antenas a m comutadores em uma rede de telefonia celular, de forma a minimizar os custos de cabeamento entre antenas e comutadores e os custos de transferência de chamadas entre comutadores. A abordagem tradicional de geração de colunas é comparada com as propostas neste trabalho, que utilizam a relaxação lagrangeana/surrogate. São apresentados testes computacionais que demonstram a efetividade dos algoritmos propostos.

Relax and cut: limitantes duais para o problema do caixeiro viajante

Pós-graduação em Matemática - IBILCE

Simple heuristics for the assembly line worker assignment and balancing problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimization Strategies Based on Sequential Quadratic Programming Applied for a Fermentation Process for Butanol Production

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Optimal pest control problem in population dynamics

One of the main goals of the pest control is to maintain the density of the pest population in the equilibrium level below economic damages. For reaching this goal, the optimal pest control problem was divided in two parts. In the first part, the two optimal control functions were considered. These functions move the ecosystem pest-natural enemy at an equilibrium state below the economic injury level. In the second part, the one optimal control function stabilizes the ecosystem in this level, minimizing the functional that characterizes quadratic deviations of this level. The first problem was resolved through the application of the Maximum Principle of Pontryagin. The Dynamic Programming was used for the resolution of the second optimal pest control problem.

On an approximate analytical solution to a nonlinear vibrating problem, excited by a nonideal motor

This paper analyzes through Multiple Scales Method a response of a simplified nonideal and nonlinear vibrating system. Here, one verifies the interactions between the dynamics of the DC motor (excitation) and the dynamics of the foundation (spring, damper, and mass). We remarked that we consider cubic nonlinearity (spring) and quadratic nonlinearity (DC motor) of the same order of magnitude according to experimental results. Both analytical and numerical results that we have obtained had good agreement.

Designing a modified Hopfield network to solve an Economic Dispatch problem with nonlinear cost function

Economic Dispatch (ED) problems have recently been solved by artificial neural networks approaches. In most of these dispatch models, the cost function must be linear or quadratic. Therefore, functions that have several minimum points represent a problem to the simulation since these approaches have not accepted nonlinear cost function. Another drawback pointed out in the literature is that some of these neural approaches fail to converge efficiently towards feasible equilibrium points. This paper discusses the application of a modified Hopfield architecture for solving ED problems defined by nonlinear cost function. The internal parameters of the neural network adopted here are computed using the valid-subspace technique, which guarantees convergence to equilibrium points that represent a solution for the ED problem. Simulation results and a comparative analysis involving a 3-bus test system are presented to illustrate efficiency of the proposed approach.

Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrodinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case. (C) 2004 Elsevier B.V. All rights reserved.

Studying properties of Lagrangian bounds for many-to-many assignment problems

Classical and modified Lagrangian bounds for the optimal value of optimization problems with a double decomposable structure are studied. For the class of many-to-many assignment problems, this property of constraints is used to design a subgradient algorithm for solving the modified dual problem. Numerical results are presented to compare the quality of classical and modified bounds, as well as the properties of the corresponding Lagrangian solutions.