The simple plant location problem (SPLP) is considered and a genetic algorithm is proposed to solve this problem. By using the developed algorithm it is possible to solve SPLP with more than 1000 facility sites and customers. Computational results are presented and compared to dual based algorithms.

The design of the distribution system is a strategic issue for almost every company. The problem of locating facilities and allocating customers covers the core topics of distribution system design. Model formulations and solution algorithms which address the issue vary widely in terms of fundamental assumptions, mathematical complexity and computational performance. This paper reviews some of the contributions to the current state-of-the-art. In particular, continuous location models, network location models, mixed-integer programming models, and applications are summarized.

We introduce a generalization of the well-known Uncapacitated Facility Location Problem, in which clients can be served not only by single facilities but also by sets of facilities. The problem, called Generalized Uncapacitated Facility Location Problem (GUFLP), was inspired by the Index Selection Problem in physical database design. We formulate GUFLP as a Set Packing Problem, showing that our model contains all the clique inequalities (in polynomial number). Moreover, we describe an exact separation procedure for odd-hole inequalities, based on the particular structure of the problem. These results are used within a branch-and-cut algorithm for the exact solution of GUFLP. Computational results on two different classes of test problems are given.

This paper considers the problem of minimizing the response time for a given database workload by a proper choice of indexes. This problem is NP-hard and known in the literature as the Index Selection Problem (ISP).

In combinatorial optimization, a popular approach to NP-hard problems is the design of approximation algorithms. These algorithms typically run in polynomial time and are guaranteed to produce a solution which is within a known multiplicative factor of optimal. Unfortunately, the known factor is often known to be large in pathological instances. Conventional wisdom holds that, in practice, approximation algorithms will produce solutions closer to optimal than their proven guarantees. In this paper, we use the rigorous-analysis-of-heuristics framework to investigate this conventional wisdom. We analyze the performance of 3 related approximation algorithms for the uncapacitated facility location problem (from [Jain, Mahdian, Markakis, Saberi, Vazirani, 2003] and [Mahdian, Ye, Zhang, 2002]) when each is applied to an instances created by placing n points uniformly at random in the unit square. We find that, with high probability, these 3 algorithms do not find asymptotically optimal solutions, and, also with high probability, a simple plane partitioning heuristic does find an asymptotically optimal solution.

We review the models for telecommunication network design where there is a location problem involved. We classify the models into three classes as uncapacitated, capacitated and dynamic models. For each class, we discuss the core problem, its generalizations and the solution methods in the literature.

The Index Selection Problem (ISP) is a phase of fundamental importance in the physical design of databases, calling for a set of indexes to be built in a database so as to minimize the overall execution time for a given database workload. The problem is a generalization of the well-known Uncapacitated Facility Location Problem (UFLP). In [6], we formulate ISP as a set packing problem, showing that our mathematical model contains all the clique inequalities, and describe a branch-and-cut algorithm based on the separation of odd-hole inequalities. In this paper, we describe an effective exact separation procedure for a suitably-defined family of lifted odd-hole inequalities, obtained by applying a Chvátal-Gomory derivation to the clique inequalities. Our analysis goes in the direction of determining a new class of inequalities over which ecient separation is possible, rather than introducing new classes of (facet-de ning) inequalities that later turn out to be difficult to separate. Our separation procedure is embedded within our branch-and-cut algorithm for the exact solution of ISP. Computational results on two different classes of instances are given, showing the e ectiveness of the new approach. We also test our algorithm on UFLP instances both taken from the literature and randomly generated.

Abstract The uncapacitated warehouse location problem is considered. Since it belongs to the class of NP complete problems, we use the genetic algorithms in the solving of this problem. Genetic algorithms are rooted in the mechanisms of the evolution and natural selection. They are relatively general and practicale way for the finding a suboptimal solution (heuristic) in the problems of optimization. According to the uncapacitated warehouse location problem, we should find provision plan with minimal total cost. The storage cost for every warehouse and the cost of shipment from every warehouse to an arbitrary customer are known. We use simple genetic algorithm for the solving of uncapacitated warehouse location problem.. The item-code is represented by the binary array of indicators denoting the inclusion of warehouse into provision plan. This approach seems to be a good compromise between the quality of solution and execution time. The improvements are possible by introducing of o...

Bichromatic reverse nearest neighbor (BRNN) has been extensively studied in spatial database literature. In this paper, we study a related problem called MaxBRNN: find an optimal region that maximizes the size of BRNNs. Such a problem has many real life applications, including the problem of finding a new server point that attracts as many customers as possible by proximity. A straightforward approach is to determine the BRNNs for all possible points that are not feasible since there are a large (or infinite) number of possible points. To the best of our knowledge, the fastest known method has exponential time complexity on the data size. Based on some interesting properties of the problem, we come up with an efficient algorithm called MaxOverlap. Extensive experiments are conducted to show that our algorithm is many times faster than the best-known technique. 1.

The ultimate goal of data mining is to extract knowledge from massive data. Knowledge is ideally represented as human-comprehensible patterns from which end-users can gain intuitions and insights. Axis-parallel hyper-rectangles provide interpretable generalizations for multi-dimensional data points with numerical attributes. In this dissertation, we study the fundamental problem of rectangle-based discriminative data generalization in the context of several useful data mining applications: cluster description, rule learning, and Nearest Rectangle classification. Clustering is one of the most important data mining tasks. However, most clustering methods output sets of points as clusters and do not generalize them into interpretable patterns. We perform a systematic study of cluster description, where we propose novel description formats leading to enhanced expressive power and introduce novel description problems specifying different trade-offs between interpretability and accuracy. We also present efficient heuristic algorithms for the introduced problems in the proposed formats. If-then rules are