Data-Collection for the Sloan Digital Sky Survey: a Network-Flow Heuristic

The goal of the Sloan Digital Sky Survey is ``to map in detail one-quarter of the entire sky, determining the positions and absolute brightnesses of more than 100 million celestial objects''. The survey will be performed by taking ``snapshots'' through a large telescope. Each snapshot can capture up to 600 objects from a small circle of the sky. This paper describes the design and implementation of the algorithm that is being used to determine the snapshots so as to minimize their number. The problem is NP-hard in general; the algorithm described is a heuristic, based on Lagriangian-relaxation and min-cost network flow. It gets within 5-15% of a naive lower bound, whereas using a ``uniform'' cover only gets within 25-35%.Comment: proceedings version appeared in ACM-SIAM Symposium on Discrete Algorithms (1998

A computational analysis of lower bounds for big bucket production planning problems

In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide crucial insights on why these problems are hard to solve, and this is addressed by a thorough analysis in the paper. We conclude with computational results on a variety of widely used test sets, and a discussion of future research

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Exploring multiple viewshed analysis using terrain features and optimisation techniques

The calculation of viewsheds is a routine operation in geographic information systems and is used in a wide range of applications. Many of these involve the siting of features, such as radio masts, which are part of a network and yet the selection of sites is normally done separately for each feature. The selection of a series of locations which collectively maximise the visual coverage of an area is a combinatorial problem and as such cannot be directly solved except for trivial cases. In this paper, two strategies for tackling this problem are explored. The first is to restrict the search to key topographic points in the landscape such as peaks, pits and passes. The second is to use heuristics which have been applied to other maximal coverage spatial problems such as location-allocation. The results show that the use of these two strategies results in a reduction of the computing time necessary by two orders of magnitude, but at the cost of a loss of 10% in the area viewed. Three different heuristics were used, of which Simulated Annealing produced the best results. However the improvement over a much simpler fast-descent swap heuristic was very slight, but at the cost of greatly increased running times. © 2004 Elsevier Ltd. All rights reserved

A taxonomy for emergency service station location problem

The emergency service station (ESS) location problem has been widely studied in the literature since 1970s. There has been a growing interest in the subject especially after 1990s. Various models with different objective functions and constraints have been proposed in the academic literature and efficient solution techniques have been developed to provide good solutions in reasonable times. However, there is not any study that systematically classifies different problem types and methodologies to address them. This paper presents a taxonomic framework for the ESS location problem using an operations research perspective. In this framework, we basically consider the type of the emergency, the objective function, constraints, model assumptions, modeling, and solution techniques. We also analyze a variety of papers related to the literature in order to demonstrate the effectiveness of the taxonomy and to get insights for possible research directions

A heuristic approach for big bucket multi-level production planning problems

Multi-level production planning problems in which multiple items compete for the same resources frequently occur in practice, yet remain daunting in their difficulty to solve. In this paper, we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot-sizing problems. In addition, unlike many other heuristics, it generates high quality lower bounds using strong formulations, and its simple scheme allows it to be easily implemented in the Xpress-Mosel modeling language. Extensive computational results from widely used test sets that include a variety of problems demonstrate the efficiency of the heuristic, particularly for challenging problems

The continuous p-centre problem: An investigation into variable neighbourhood search with memory

A VNS-based heuristic using both a facility as well as a customer type neighbourhood structure is proposed to solve the p-centre problem in the continuous space. Simple but effective enhancements to the original Elzinga-Hearn algorithm as well as a powerful ‘locate-allocate’ local search used within VNS are proposed. In addition, efficient implementations in both neighbourhood structures are presented. A learning scheme is also embedded into the search to produce a new variant of VNS that uses memory. The effect of incorporating strong intensification within the local search via a VND type structure is also explored with interesting results. Empirical results, based on several existing data set (TSP-Lib) with various values of p, show that the proposed VNS implementations outperform both a multi-start heuristic and the discrete-based optimal approach that use the same local search

Facility layout problem: Bibliometric and benchmarking analysis

Facility layout problem is related to the location of departments in a facility area, with the aim of determining the most effective configuration. Researches based on different approaches have been published in the last six decades and, to prove the effectiveness of the results obtained, several instances have been developed. This paper presents a general overview on the extant literature on facility layout problems in order to identify the main research trends and propose future research questions. Firstly, in order to give the reader an overview of the literature, a bibliometric analysis is presented. Then, a clusterization of the papers referred to the main instances reported in literature was carried out in order to create a database that can be a useful tool in the benchmarking procedure for researchers that would approach this kind of problems