Uma análise experimental de algoritmos exatos aplicados ao problema da árvore geradora multiobjetivo

The Multiobjective Spanning Tree Problem is NP-hard and models applications in several areas. This research presents an experimental analysis of different strategies used in the literature to develop exact algorithms to solve the problem. Initially, the algorithms are classified according to the approaches used to solve the problem. Features of two or more approaches can be found in some of those algorithms. The approaches investigated here are: the two-stage method, branch-and-bound, k-best and the preference-based approach. The main contribution of this research lies in the fact that no research was presented to date reporting a systematic experimental analysis of exact algorithms for the Multiobjective Spanning Tree Problem. Therefore, this work can be a basis for other research that deal with the same problem. The computational experiments compare the performance of algorithms regarding processing time, efficiency based on the number of objectives and number of solutions found in a controlled time interval. The analysis of the algorithms was performed for known instances of the problem, as well as instances obtained from a generator commonly used in the literature

Uma colônia de formigas para o caminho mais curto multiobjetivo

Multi-objective combinatorial optimization problems have peculiar characteristics that require optimization methods to adapt for this context. Since many of these problems are NP-Hard, the use of metaheuristics has grown over the last years. Particularly, many different approaches using Ant Colony Optimization (ACO) have been proposed. In this work, an ACO is proposed for the Multi-objective Shortest Path Problem, and is compared to two other optimizers found in the literature. A set of 18 instances from two distinct types of graphs are used, as well as a specific multiobjective performance assessment methodology. Initial experiments showed that the proposed algorithm is able to generate better approximation sets than the other optimizers for all instances. In the second part of this work, an experimental analysis is conducted, using several different multiobjective ACO proposals recently published and the same instances used in the first part. Results show each type of instance benefits a particular type of instance benefits a particular algorithmic approach. A new metaphor for the development of multiobjective ACOs is, then, proposed. Usually, ants share the same characteristics and only few works address multi-species approaches. This works proposes an approach where multi-species ants compete for food resources. Each specie has its own search strategy and different species do not access pheromone information of each other. As in nature, the successful ant populations are allowed to grow, whereas unsuccessful ones shrink. The approach introduced here shows to be able to inherit the behavior of strategies that are successful for different types of problems. Results of computational experiments are reported and show that the proposed approach is able to produce significantly better approximation sets than other methods

O problema de corte de placas defeituosas

O problema tratado neste trabalho consiste em cortar uma placa retangular em peças menores retangulares, de modo que a perda seja minimizada. A placa, entretanto, contém defeitos bem localizados. Propomos uma abordagem em grafo E/OU para representação das soluções possíveis e um método de enumeração implícita para determinar a solução ótima. Resultados computacionais demonstram a efetividade da abordagem.

Abordagens complementares para problemas de p-medianas

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

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.

A metaheuristic to solve the transmission expansion planning

In this letter, a genetic algorithm (GA) is applied to solve - the static and multistage transmission expansion planning (TEP) problem. The characteristics of the proposed GA to solve the TEP problem are presented. Results using some known systems show that the proposed GA solves a smaller number of linear programming problems in order to find the optimal solutions and obtains a better solution for the multistage TEP problem.

Tabu search algorithm for network synthesis

Large scale combinatorial problems such as the network expansion problem present an amazingly high number of alternative configurations with practically the same investment, but with substantially different structures (configurations obtained with different sets of circuit/transformer additions). The proposed parallel tabu search algorithm has shown to be effective in exploring this type of optimization landscape. The algorithm is a third generation tabu search procedure with several advanced features. This is the most comprehensive combinatorial optimization technique available for treating difficult problems such as the transmission expansion planning. The method includes features of a variety of other approaches such as heuristic search, simulated annealing and genetic algorithms. In all test cases studied there are new generation, load sites which can be connected to an existing main network: such connections may require more than one line, transformer addition, which makes the problem harder in the sense that more combinations have to be considered.

Parallel simulated annealing applied to long term transmission network expansion planning

The simulated annealing optimization technique has been successfully applied to a number of electrical engineering problems, including transmission system expansion planning. The method is general in the sense that it does not assume any particular property of the problem being solved, such as linearity or convexity. Moreover, it has the ability to provide solutions arbitrarily close to an optimum (i.e. it is asymptotically convergent) as the cooling process slows down. The drawback of the approach is the computational burden: finding optimal solutions may be extremely expensive in some cases. This paper presents a Parallel Simulated Annealing, PSA, algorithm for solving the long term transmission network expansion planning problem. A strategy that does not affect the basic convergence properties of the Sequential Simulated Annealing algorithm have been implementeded and tested. The paper investigates the conditions under which the parallel algorithm is most efficient. The parallel implementations have been tested on three example networks: a small 6-bus network, and two complex real-life networks. Excellent results are reported in the test section of the paper: in addition to reductions in computing times, the Parallel Simulated Annealing algorithm proposed in the paper has shown significant improvements in solution quality for the largest of the test networks.

Stochastic scheduling - A flow shop no wait application and solutions

Minimizing the makespan of a flow-shop no-wait (FSNW) schedule where the processing times are randomly distributed is an important NP-Complete Combinatorial Optimization Problem. In spite of this, it can be found only in very few papers in the literature. By considering the Start Interval Concept, this problem can be formulated, in a practical way, in function of the probability of the success in preserve FSNW constraints for all tasks execution. With this formulation, for the particular case with 3 machines, this paper presents different heuristics solutions: by integrating local optimization steps with insertion procedures and by using genetic algorithms for search the solution space. Computational results and performance evaluations are commented. Copyright (C) 1998 IFAC.

A Lagrangian bound for many-to-many assignment problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Genetic algorithm of chu and beasley for static and multistage transmission expansion planning

In this paper the genetic algorithm of Chu and Beasley (GACB) is applied to solve the static and multistage transmission expansion planning problem. The characteristics of the GACB, and some modifications that were done, to efficiently solve the problem described above are also presented. Results using some known systems show that the GACB is very efficient. To validate the GACB, we compare the results achieved using it with the results using other meta-heuristics like tabu-search, simulated annealing, extended genetic algorithm and hibrid algorithms. © 2006 IEEE.

Interactive system for placement and coordination of overcurrent protective devices

In this paper, an expert and interactive system for developing protection system for overhead and radial distribution feeders is proposed. In this system the protective devices can be allocated through heuristic and an optimized way. In the latter one, the placement problem is modeled as a mixed integer non-linear programming, which is solved by genetic algorithm (GA). Using information stored in a database as well as a knowledge base, the computational system is able to obtain excellent conditions of selectivity and coordination for improving the feeder reliability indices. Tests for assessment of the algorithm efficiency were carried out using a real-life 660-nodes feeder. © 2006 IEEE.

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.

GRASP with evolutionary path-relinking for the capacitated arc routing problem

The Capacitated Arc Routing Problem (CARP) is a well-known NP-hard combinatorial optimization problem where, given an undirected graph, the objective is to find a minimum cost set of tours servicing a subset of required edges under vehicle capacity constraints. There are numerous applications for the CARP, such as street sweeping, garbage collection, mail delivery, school bus routing, and meter reading. A Greedy Randomized Adaptive Search Procedure (GRASP) with Path-Relinking (PR) is proposed and compared with other successful CARP metaheuristics. Some features of this GRASP with PR are (i) reactive parameter tuning, where the parameter value is stochastically selected biased in favor of those values which historically produced the best solutions in average; (ii) a statistical filter, which discard initial solutions if they are unlikely to improve the incumbent best solution; (iii) infeasible local search, where high-quality solutions, though infeasible, are used to explore the feasible/infeasible boundaries of the solution space; (iv) evolutionary PR, a recent trend where the pool of elite solutions is progressively improved by successive relinking of pairs of elite solutions. Computational tests were conducted using a set of 81 instances, and results reveal that the GRASP is very competitive, achieving the best overall deviation from lower bounds and the highest number of best solutions found. © 2011 Elsevier Ltd. All rights reserved.

Domain reduction using GRASP construction phase for transmission expansion planning problem

This paper proposes a new strategy to reduce the combinatorial search space of a mixed integer linear programming (MILP) problem. The construction phase of greedy randomized adaptive search procedure (GRASP-CP) is employed to reduce the domain of the integer variables of the transportation model of the transmission expansion planning (TM-TEP) problem. This problem is a MILP and very difficult to solve specially for large scale systems. The branch and bound (BB) algorithm is used to solve the problem in both full and the reduced search space. The proposed method might be useful to reduce the search space of those kinds of MILP problems that a fast heuristic algorithm is available for finding local optimal solutions. The obtained results using some real test systems show the efficiency of the proposed method. © 2012 Springer-Verlag.