A hybrid Lagrangian genetic algorithm for the prize collecting Steiner tree problem

Haouari, Mohamed; Siala, Jouhaina Chaouachi

doi:10.1016/j.cor.2004.09.017

Cited by 34 publications

(22 citation statements)

References 14 publications

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“…Ways of integrating information gained in LR into a tabu search algorithm is given in [56] and computational results are presented for an example application to the capacitated warehouse location problem. Other, recent examples of using LR to direct SLS algorithms include a genetic algorithm for the prize collecting Steiner tree problem [59], exploiting Lagrangean decomposition for an evolutionary algorithm for the knapsack constrained maximum spanning tree problem [91], or hybrid approaches to the design of the last mile in fiber optic networks [69].…”

Section: Discussionmentioning

confidence: 99%

Usage of Exact Algorithms to Enhance Stochastic Local Search Algorithms

Dumitrescu

Stützle

2009

Matheuristics

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Exact mathematical programming techniques such as branch-andbound or dynamic programming and stochastic local search techniques have traditionally been seen as being two general but distinct approaches for the effective solution of combinatorial optimization problems, each having particular advantages and disadvantages. In several research efforts true hybrid algorithms, which exploit ideas from both fields, have been proposed. In this chapter we review some of the main ideas of several such combinations and illustrate them with examples from the literature. Our focus here is on algorithms that have the main framework given by the local search and use exact algorithms to solve subproblems.

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Section: Discussionmentioning

confidence: 99%

Usage of Exact Algorithms to Enhance Stochastic Local Search Algorithms

Dumitrescu

Stützle

2009

Matheuristics

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“…As this maximization problem is convex and piecewise linear, subgradient algorithms are well suited for this purpose [13]. While different variants of such methods exist, the Volume Algorithm [1] has proven to be more effective than several alternatives on various occasions [14,15], and we therefore apply it here. Also, our preliminary comparisons indicate the superiority of this algorithm over the standard subgradient strategy as described in [13].…”

Section: Lagrangian Decompositionmentioning

confidence: 99%

“…Referring to the description of the Volume algorithm in [15], we further configured it as follows: The target value T is set to T = 1.1z UB with z UB being the actual upper bound unless the actual lower bound z LB > 0.9 T in which case T is multiplied by 1.1. We initially set f = 0.1 and α = 0.01.…”

Section: Combining Lagrangian Decomposition and Variable Neighborhoodmentioning

confidence: 99%

Lagrangian Decomposition, Metaheuristics, and Hybrid Approaches for the Design of the Last Mile in Fiber Optic Networks

Leitner

Raidl

2008

Hybrid Metaheuristics

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Abstract. We consider a generalization of the (Price Collecting) Steiner Tree Problem on a graph with special redundancy requirements for customer nodes. The problem occurs in the design of the last mile of real-world communication networks. We formulate it as an abstract integer linear program and apply Lagrangian Decomposition to obtain relatively tight lower bounds as well as feasible solutions. Furthermore, a Variable Neighborhood Search and a GRASP approach are described, utilizing a new construction heuristic and special neighborhoods. In particular, hybrids of these methods are also studied and turn out to often perform superior. By comparison to previously published exact methods we show that our approaches are applicable to larger problem instances, while providing high quality solutions together with good lower bounds.

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“…In the second phase, tabu search is enforced to search to around the best possible solution to these relaxed problems [81]. Another work reported by Haouari and Siala (2006) presents the hybrid Lagrangian genetic algorithm for prize collecting steiner tree problem. Hereby genetic algorithm makes use of a Lagrangian relaxation.…”

Section: Hybridizing Metaheuristics With Problem Relaxationmentioning

confidence: 99%

“…Hereby genetic algorithm makes use of a Lagrangian relaxation. Meaningful initial solutions are generated by reducing the graph by cutting edge and the objective function is modified by cost reduction [75]. For the knapsack constrained maximum spanning tree problem, [104] a hybridization of Lagrangian decomposition and a genetic algorithm is proposed by Pirkwieser et al (2007).…”

Section: Hybridizing Metaheuristics With Problem Relaxationmentioning

confidence: 99%

Survey of Metaheuristic Algorithms for Combinatorial Optimization

Baghel¹,

Agrawal²,

Silakari³

2012

IJCA

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This paper is intended to give a review of metaheuristic and their application to combinatorial optimization problems. This paper comprises a snapshot of the rapid evolution of metaheuristic concepts, their convergence towards a unified framework and the richness of potential application in combinatorial optimization problems. Over the years, combinatorial optimization problems are gaining awareness of the researchers both in scientific as well as industrial world. This paper aims to present a brief survey of different metaheuristic algorithms for solving the combinatorial optimization problems. Basically we have divided the metaheuristic into three broad categories namely trajectory methods, population based methods and hybrid methods. Trajectory methods are those that deal with a single solution. These include simulated annealing, tabu search, variable neighborhood search and greedy randomized adaptive search procedure. Population based methods deal with a set of solutions. These include genetic algorithm, ant colony optimization and particle swarm optimization. Hybrid methods deal with the hybridization of single point search methods and population based methods. These are further categorized into five different types. Finally we conclude the paper by giving some issues which are needed to develop a well performed metaheuristic algorithm.

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A hybrid Lagrangian genetic algorithm for the prize collecting Steiner tree problem

Cited by 34 publications

References 14 publications

Usage of Exact Algorithms to Enhance Stochastic Local Search Algorithms

Usage of Exact Algorithms to Enhance Stochastic Local Search Algorithms

Lagrangian Decomposition, Metaheuristics, and Hybrid Approaches for the Design of the Last Mile in Fiber Optic Networks

Survey of Metaheuristic Algorithms for Combinatorial Optimization

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