General variable neighborhood search for the uncapacitated single allocation <Emphasis Type="Italic">p</Emphasis>-hub center problem

In this paper we propose a general variable neighborhood search heuristic for solving the uncapacitated single allocation p-hub center problem (USApHCP). For the local search step we develop a nested variable neighborhood descent strategy. The proposed approach is tested on benchmark instances from the literature and found to outperform the state-of-the-art heuristic based on ant colony optimization. We also test our heuristic on large scale instances that were not previously considered as test instances for the USApHCP. Moreover, exact solutions were reached by our GVNS for all instances where optimal solutions are known.     

Multi-exchange neighborhood structures for the capacitated minimum spanning tree problem

The capacitated minimum spanning tree (CMST) problem is to find a minimum cost spanning tree with an additional cardinality constraint on the sizes of the subtrees incident to a given root node. The CMST problem is an NP-complete problem, and existing exact algorithms can solve only small size problems. Currently, the best available heuristic procedures for the CMST problem are tabu search algorithms due to Amberg et al. and Sharaiha et al. These algorithms use two-exchange neighborhood structures that are based on exchanging a single node or a set of nodes between two subtrees. In this paper, we generalize their neighborhood structures to allow exchanges of nodes among multiple subtrees simultaneously; we refer to such neighborhood structures as multi-exchange neighborhood structures. Our first multi-exchange neighborhood structure allows exchanges of single nodes among several subtrees. Our second multi-exchange neighborhood structure allows exchanges that involve multiple subtrees. The size of each of these neighborhood structures grows exponentially with the problem size without any substantial increase in the computational times needed to find improved neighbors. Our approach, which is based on the cyclic transfer neighborhood structure due to Thompson and Psaraftis and Thompson and Orlin transforms a profitable exchange into a negative cost subset-disjoint cycle in a graph, called an improvement graph, and identifies these cycles using variants of shortest path label-correcting algorithms. Our computational results with GRASP and tabu search algorithms based on these neighborhood structures reveal that (i) for the unit demand case our algorithms obtained the best available solutions for all benchmark instances and improved some; and (ii) for the heterogeneous demand case our algorithms improved the best available solutions for most of the benchmark instances with improvements by as much as 18%. The running times our multi-exchange neighborhood search algorithms are comparable to those taken by two-exchange neighborhood search algorithms. Received: September 1998 / Accepted: March 2001?Published online May 18, 2001     

An Application of Tabu Search Heuristic for the Maximum Edge-Weighted Subgraph Problem

The purpose of this article is to describe an efficient search heuristic for the Maximum Edge-weighted Subgraph (MEwS) problem. This problem requires to find a subgraph such that the sum of the weights associated with the edges of the subgraph is maximized subject to a cardinality constraint. In this study a tabu search heuristic for the MEwS problem is proposed. Different algorithms to obtain an initial solution are presented. One neighborhood search strategy is also proposed. Preliminary computational results are reported for randomly generated test problems of MEwS problem with different densities and sizes. For most of test problems, the tabu search heuristic found good solutions. In addition, for large size test problems, the tabu search outperformed the local search heuristic appearing in the literature.     

A facility neighborhood search heuristic for capacitated facility location with single-source constraints and flexible demand

We consider a generalization of the well-known capacitated facility location problem with single source constraints in which customer demand contains a flexible dimension. This work focuses on providing fast and practically implementable optimization-based heuristic solution methods for very large scale problem instances. We offer a unique approach that utilizes a high-quality efficient heuristic within a neighborhood search to address the combined assignment and fixed-charge structure of the underlying optimization problem. We also study the potential benefits of combining our approach with a so-called very large-scale neighborhood search (VLSN) method. As our computational test results indicate, our work offers an attractive solution approach that can be tailored to successfully solve a broad class of problem instances for facility location and similar fixed-charge problems.     

Variable and large neighborhood search to solve the multiobjective set covering problem

In this paper, we study the multiobjective version of the set covering problem. To our knowledge, this problem has only been addressed in two papers before, and with two objectives and heuristic methods. We propose a new heuristic, based on the two-phase Pareto local search, with the aim of generating a good approximation of the Pareto efficient solutions. In the first phase of this method, the supported efficient solutions or a good approximation of these solutions is generated. Then, a neighborhood embedded in the Pareto local search is applied to generate non-supported efficient solutions. In order to get high quality results, two elaborate local search techniques are considered: a large neighborhood search and a variable neighborhood search. We intensively study the parameters of these two techniques. We compare our results with state-of-the-art results and we show that with our method, better results are obtained for different indicators.     

A 3-flip neighborhood local search for the set covering problem

The set covering problem (SCP) calls for a minimum cost family of subsets from n given subsets, which together covers the entire ground set. In this paper, we propose a local search algorithm for SCP, which has the following three characteristics. (1) The use of 3-flip neighborhood, which is the set of solutions obtainable from the current solution by exchanging at most three subsets. As the size of 3-flip neighborhood is O(n³), the neighborhood search becomes expensive if implemented naively. To overcome this, we propose an efficient implementation that reduces the number of candidates in the neighborhood without sacrificing the solution quality. (2) We allow the search to visit the infeasible region, and incorporate the strategic oscillation technique realized by adaptive control of penalty weights. (3) The size reduction of the problem by using the information from the Lagrangian relaxation is incorporated, which is indispensable for solving very large instances. According to computational comparisons on benchmark instances with other existing heuristic algorithms for SCP, our algorithm performs quite effectively for various types of problems, especially for very large-scale instances.     

Variable neighborhood search: Principles and applications

Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using any local search algorithm as a subroutine. Its effectiveness is illustrated by solving several classical combinatorial or global optimization problems. Moreover, several extensions are proposed for solving large problem instances: using VNS within the successive approximation method yields a two-level VNS, called variable neighborhood decomposition search (VNDS); modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed VNS (SVNS) heuristic. Finally, we show how to stabilize column generation algorithms with help of VNS and discuss various ways to use VNS in graph theory, i.e., to suggest, disprove or give hints on how to prove conjectures, an area where metaheuristics do not appear to have been applied before.     

Complete Local Search with Memory

Neighborhood search heuristics like local search and its variants are some of the most popular approaches to solve discrete optimization problems of moderate to large size. Apart from tabu search, most of these heuristics are memoryless. In this paper we introduce a new neighborhood search heuristic that makes effective use of memory structures in a way that is different from that in common implementations of tabu search. We report computational experiments with this heuristic on the traveling salesperson problem and the subset sum problem.     

A hybrid iterated local search heuristic for the maximum weight independent set problem

This paper presents a hybrid iterated local search (ILS) algorithm for the maximum weight independent set (MWIS) problem, a generalization of the classical maximum independent set problem. Two efficient neighborhood structures are proposed and they are explored using the variable neighborhood descent procedure. Moreover, we devise a perturbation mechanism that dynamically adjusts the balance between intensification and diversification during the search. The proposed algorithm was tested on two well-known benchmarks (DIMACS-W and BHOSLIB-W) and the results obtained were compared with those found by state-of-the-art heuristics and exact methods. Our heuristic outperforms the best-known heuristic for the MWIS as well as the best heuristics for the maximum weight clique problem. The results also show that the hybrid ILS was capable of finding all known optimal solutions in milliseconds.     

A unified heuristic for a large class of Vehicle Routing Problems with Backhauls

The Vehicle Routing Problem with Backhauls is a generalization of the ordinary capacitated vehicle routing problem where goods are delivered from the depot to the linehaul customers, and additional goods are brought back to the depot from the backhaul customers. Numerous ways of modeling the backhaul constraints have been proposed in the literature, each imposing different restrictions on the handling of backhaul customers. A survey of these models is presented, and a unified model is developed that is capable of handling most variants of the problem from the literature. The unified model can be seen as a Rich Pickup and Delivery Problem with Time Windows, which can be solved through an improved version of the large neighborhood search heuristic proposed by Ropke and Pisinger [An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows, Technical Report, DIKU, University of Copenhagen, 2004]. The results obtained in this way are comparable to or improve on similar results found by state of the art heuristics for the various variants of the problem. The heuristic has been tested on 338 problems from the literature and it has improved the best known solution for 227 of these. An additional benefit of the unified modeling and solution method is that it allows the dispatcher to mix various variants of the Vehicle Routing Problem with Backhauls for the individual customers or vehicles.