An Exponential Neighborhood Local Search Algorithm for the Single Row Facility Location Problem

In this work we present a local search algorithm for the single row facility location problem. In contrast to other local search algorithms for the problem, our algorithm uses an exponential neighborhood structure. Our computations indicate that our local search algorithm generates solutions to benchmark instances of the problem whose costs are on average within 2% of costs of optimal solutions within reasonable execution time.

A Diversification Operator for Genetic Algorithms

Conventional genetic algorithms suffer from a dependence on the initial generation used by the algorithm. In case the generation cosnsists of solutions which are not close enough to a global optimum but some of which are close to a relatively good local optimum, the algorithm is often guided a converge to the local optimum. In this paper, we provide a method which allows a genetic algorithm to search the solution space more effectively, and increases its chance to attain a global optimum. We provide computational experience with real-valued genetic algorithms on functions of two variables.

On the Blowout Preventer Testing Problem: An Approach to Checking for Leakage in BOP Networks

Blowout Preventers (BOPs) and choke manifolds are key pieces of drilling rig equipment to prevent the uncontrolled release of potentially hazardous formation fluids to surface. The blowout prevention testing problem is that of testing BOP valves to check if they are functional or not. Several type of testing is done on these valves. This paper deals with the check if the valves are capable of holding pressure. We present a decision model that allows a structured and time saving approach to minimize the number of test sets in order to identify leakage. Recently the BOP terminology has gained prominence and public attention as a result of the Macondo blow-out and resulting oil-spill in the Gulf of Mexico off the coast of the USA.

Solving Medium to Large Sized Euclidean Generalized Minimum Spanning Tree Problems

The generalized minimum spanning tree problem is a generalization of the minimum spanning tree problem. This network design problems finds several practical applications, especially when one considers the design of a large-capacity backbone network connecting several individual networks. In this paper we study the performance of six neighborhood search heuristics based on tabu search and variable neighborhood search on this problem domain. Our principal finding is that a tabu search heuristic almost always provides the best quality solution for small to medium sized instances within short execution times while variable neighborhood decomposition search provides the best quality solutions for most large instances.

A Probabilistic Tabu Search Algorithm for the Generalized Minimum Spanning Tree Problem

In this paper we present a probabilistic tabu search algorithm for the generalized minimum spanning tree problem. The basic idea behind the algorithm is to use preprocessing operations to arrive at a probability value for each vertex which roughly corresponds to its probability of being included in an optimal solution, and to use such probability values to shrink the size of the neighborhood of solutions to manageable proportions. We report results from computational experiments that demonstrate the superiority of this method over the generic tabu search method.

A Multilevel Search Algorithm for the Maximization of Submodular Functions

We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a complete description of the class of probability density functions such that the objective function is convex. This result is also stated in terms of random variables. Next, we present a class of convex approximations of the objective function, which are obtained by perturbing the distributions of the right-hand side parameters. We derive a uniform bound on the absolute error of the approximation. Finally, we give a representation of convex simple integer recourse problems as continuous simple recourse problems, so that they can be solved by existing special purpose algorithms

Evaluating Downside Risks in Reliable Networks

Reliable networks are those in which network elements have a positive probability of failing. Conventional performance measures for such networks concern themselves either with expected network performance or with the performance of the network when it is performing well. In reliable networks modeling critical functions, decision makers are often more concerned with network performance when the network is not performing well. In this paper, we study the single-source single-destination maximum flow problem through reliable networks and propose two risk measures to evaluate such downside performance. We propose an algorithm called COMPUTE-RISK to compute downside risk measures, and report our computational experience with the proposed algorithm.

Spotting Difficult Weakly Correlated Binary Knapsack Problems

In this paper, we examine the possibility of quickly deciding whether or not an instance of a binary knapsack problem is difficult for branch and bound algorithms. We first observe that the distribution of the objective function values is smooth and unimodal. We define a measure of difficulty of solving knapsack problems through branch and bound algorithms, and examine the relationship between the degree of correlation between profit and cost values, the skewness of the distribution of objective function values and the difficulty in solving weakly correlated binary knapsack problems. We see that the even though it is unlikely that an exact relationship exists for individual problem instances, some aggregate relationships may be observed. Key words: Binary Knapsack Problems; Skewness; Computational Experiments.

A review of the Tabu Search Literature on Traveling Salesman Problems

The Traveling Salesman Problem (TSP) is one of the most widely studied problems inrncombinatorial optimization. It has long been known to be NP-hard and hence research onrndeveloping algorithms for the TSP has focused on approximate methods in addition to exactrnmethods. Tabu search is one of the most widely applied metaheuristic for solving the TSP. Inrnthis paper, we review the tabu search literature on the TSP, point out trends in it, and bringrnout some interesting research gaps in this literature.

A Lin-Kernighan Heuristic for Single Row Facility Layout

The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, while minimizing the weighted sum of the distances between all pairs of facilities. The problem is known to be NP-hard. In this paper, we present a neighborhood search heuristic called LK-INSERT which uses a Lin-Kernighan neighborhood structure built on insertion neighborhoods. To the best of our knowledge this is the first such heuristic for the SRFLP. Our computational experiments show that LK-INSERT is competitive and improves the best known solutions for several large sized benchmark SRFLP instances.