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Track to track fusion systems require a capability to perform track matching across the reporting sensors. In conditions where significant ambiguity exists, for example due to closely spaced objects, a simple single frame assignment algorithm can produce poor results. For measurement-to-track fusion this has long been recognized and sophisticated multiple hypothesis, multiple frame, data association methods considerably improve tracking performance in these challenging scenarios. The most successful of the multiple frame methods are multiple hypothesis tracking (MHT) and multiple frame assignments (MFA), which is formulated as a multidimensional assignment problem. The performance advantage of the multiple frame methods over the single frame methods follows from the ability to hold difficult decisions in abeyance until more information is available and the opportunity to change past decisions to improve current decisions. In this chapter, the multiple source track correlation and fusion problem is formulated as a multidimensional assignment problem. The computation of cost coefficients for the multiple frame correlation assignments is based on a novel batch MAP estimation approach. Based on the multidimensional assignments we introduce a novel multiple hypothesis track correlation approach that allows one to make robust track management decisions over multiple frames of data. The use of the proposed multiple hypothesis, multiple frame correlation system, is expected to improve the fusion system performance in scenarios where significant track assignment ambiguity exists. In the same way that multiple frame processing has shown improvements in the tracking performance in measurement-to-track fusion applications, we expect to achieve improvements in the track-to-track fusion problem. [ABSTRACT FROM AUTHOR]

Radiation therapy is extensively used to treat a wide range of cancers. Due to the increasing complexities of delivery mechanisms, and the improved imaging devices that allow more accurate determination of cancer location, determination of high quality treatment plans via trial-and-error methods is impractical and computer optimization approaches to planning are becoming more critical and more difficult. We outline three examples of the types of treatment planning problem that can arise in practice and strive to understand the commonalities and differences in these problems. We highlight optimization approaches to the problems, and particularly consider approaches based on mixed integer programming. Details of the mathematical formulations and algorithmic approaches are developed and pointers are given to supporting literature that shows the efficacy of the approaches in practical situations. [ABSTRACT FROM AUTHOR]

A multiperiod Mixed Integer Nonlinear Programming (MINLP) model for offshore oilfield infrastructure planning is presented where nonlinear reservoir behavior is incorporated directly into the formulation. Discrete decisions include the selection of production platforms, well platforms and wells to be installed/drilled, as well as the drilling schedule for the wells over the planning horizon. Continuous decisions include the capacities of the platforms, as well as the production profile for each well in each time period. For the solution of this model, an iterative aggregation/disaggregation algorithm is proposed in which logic-based methods, a bilevel decomposition technique, the use of convex envelopes and aggregation of time periods are integrated. Furthermore, a novel dynamic programming sub-problem is proposed to improve the aggregation scheme at each iteration in order to obtain an aggregate problem that resembles the disaggregate problem more closely. A number of examples are presented to illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In highly regulated industries, such as agrochemical and pharmaceutical, new products have to pass a number of regulatory tests related to safety, efficacy and environmental impact, to gain FDA approval. If a product fails one of these tests it cannot enter the market place and the investment in previous tests is wasted. Depending on the nature of the products, testing may last up to 10 years, and the scheduling of the tests should be made with the goal of minimizing the time to market and the cost of testing. Maravelias and Grossmann (2001) proposed a mixed-integer linear program (MILP) that considers a set of candidate products for which the cost, duration and probability of success of their tests is given, as well as the potential income if the products are successfully launched. Furthermore, there are limited resources in terms of laboratories and number of technicians. If needed, a test may be outsourced at a higher cost. The major decisions in the model are: (i) the decision to perform in-house or outsource a testing task, (ii) the assignment of resources to testing tasks, and (iii) the sequencing and timing of tests. The objective is to maximize the net present value of multiple projects. The mixed-integer linear program can become very expensive for solving real world problems (2–10 products and 50–200 tests). In order to improve the linear programming relaxation, we propose the use of logic cuts that are derived from implied precedences that arise in the graphs of the corresponding schedules. The solution of a single large-scale problem is avoided with a heuristic decomposition algorithm that relies on solving a reduced MILP model that embeds the optimal schedules obtained for the individual products. It is shown that a tight upper bound can be easily determined for this decomposition algorithm. On a set of test problems the proposed algorithm is shown to be one to two orders of magnitude faster than the full space method, yielding solutions that are optimal or near optimal. [ABSTRACT FROM AUTHOR]

Stochastic mixed integer programming (SMIP) models arise in a variety of applications. In particular they are being increasingly applied in the modelling and analysis of financial planning and supply chain management problems. SMIP models explicitly consider discrete decisions and model uncertainty and thus provide hedged decisions that perform well under several scenarios. Such SMIP models are relevant for industrial practitioners and academic researchers alike. From an industrial perspective, the need for well-hedged solutions cannot be overemphasized. On the other hand the NP-Hard nature of the underlying model (due to the discrete variables) together with the curse of dimensionality (due to the underlying random variables) make these models important research topics for academics. In this chapter we discus the contemporary developments of SMIP models and algorithms. We introduce a generic classification scheme that can be used to classify such models. Next we discuss the use of such models in supply chain planning and management. We present a case study of a strategic supply chain model modelled as a two-stage SMIP model. We propose a heuristic based on Lagrangean relaxation for processing the underlying model. Our heuristic can be generalized to an optimum-seeking branch-and-price algorithm, but we confine ourselves to a simpler approach of ranking the first-stage decisions which use the columns generated by the Lagrangean relaxation. In addition to providing integer feasible solutions, this approach has the advantage of mimicking the use of scenario analysis, while seeking good “here-and-now” solutions. The approach thus provides industrial practitioners an approach that they are able to incorporate within their decision-making methodology. Our computational investigations with this model are presented. [ABSTRACT FROM AUTHOR]

Over the last few years wireless communications have experienced an unprecedented growth providing ubiquitous services irrespective of users’ location and mobility patterns. This chapter reviews different resource management strategies for wireless cellular networks that employ Code Division Multiple Access (CDMA). The main aim of the formulated optimization problems is to provide efficient utilization of the scarce radio resources, namely power and transmission rate. Due to the fact that practical systems allow discrete rate transmissions, the corresponding optimization problems are discrete in their domains. Additionally, these optimizations problems are also non-linear in their nature. We focus on power minimization and throughput maximization formulations both for single time period and multiple period models. We provide a new method for solving resource management problems in CDMA networks, formulated as dynamic programming problems. A linear approximate dynamic programming algorithm is implemented that estimates the optimal resource allocation policies in real time. The algorithm is compared with baseline heuristics and it is shown that it provides a significant improvement in utilizing the radio network resources. [ABSTRACT FROM AUTHOR]

This chapter describes some of the most important models and algorithms for the classical vehicle routing problem and for several families of arc routing problems. Exact methods (mostly based on branch-and-cut) and heuristics (mostly based on tabu search) are described, and computational results are presented. [ABSTRACT FROM AUTHOR]

Networks form the backbone of many familiar, and economically critical, activities in our modern life, as exemplified by electrical grid systems, computer systems, telecommunication systems, and transportation systems. Network models, and associated optimization algorithms, are important in ensuring the smooth and efficient operation of such systems. In this chapter, we wish to introduce the reader to a variety of less apparent network models. Such models are drawn from application areas such as genomics, sports, artificial intelligence, and decision analysis as well as transportation and communication. Our objective is to illustrate how network modelling can be useful in formulating problems occurring in these diverse areas — problems that at first blush seem quite remote from the standard applications of networks. [ABSTRACT FROM AUTHOR]

In this chapter we present various equivalent formulations or models for the Mutually Orthogonal Latin Squares (MOLS) problem and its generalization. The most interesting feature of the problem is that for some parameters the problem may be infeasible. Our evaluation of different formulations is geared to tackling this feasibility problem. Starting from a Constraint Programming (CP) formulation which emanates naturally from the problem definition, we develop several Integer Programming (IP) formulations. We also discuss a hybrid CP-IP approach in both modelling and algorithmic terms. A non-linear programming formulation and an interesting modelling approach based on the intersection of matroids are also considered. [ABSTRACT FROM AUTHOR]

Logic-based modeling can result in decision models that are more natural and easier to debug. The addition of logical constraints to mixed integer programming need not sacrifice computational speed and can even enhance it if the constraints are processed correctly. They should be written or automatically reformulated so as to be as nearly consistent or hyperarc consistent as possible. They should also be provided with a tight continuous relaxation. This chapter shows how to accomplish these goals for a number of logic-based constraints: formulas of propositional logic, cardinality formulas, 0–1 linear inequalities (viewed as logical formulas), cardinality rules, and mixed logical/linear constraints. It does the same for three global constraints that are popular in constraint programming systems: the all-different, element and cumulative constraints. [ABSTRACT FROM AUTHOR]

This chapter contains short expository notes on applying continuous approaches for solving discrete optimization problems. We discuss some general aspects of the connection between integer programming and continuous optimization problems, along with several specific examples. The considered problems include maximum clique, satisfiability, the Steiner tree problem, minimax and semidefinite programming. [ABSTRACT FROM AUTHOR]

This introductory chapter first discusses the applicability of Discrete Optimisation and how Integer Programming is the most satisfactory method of solving such problems. It then describes a number of modelling techniques, such as linearisng products of variables, special ordered sets of variables, logical conditions, disaggregating constraints and variables, column generation etc. The main solution methods are described, i.e. Branch-and-Bound and Cutting Planes. Finally alternative methods such as Lagrangian Relaxation and non-optimising methods such as Heuristics and Constraint Satisfaction are outlined. [ABSTRACT FROM AUTHOR]

Let G(V,E) denote an undirected graph, V and E being the sets of its nodes and edges, respectively. A matching in G(V,E) is a subset of edges with no common endpoints. Finding a matching of maximum cardinality constitutes the maximum cardinality matching (MCM) problem. For a thorough theoretical discussion we refer to [6]. The MCM problem is of specific interest from a Constraint Programming (CP) point of view because it can model several logical constraints (predicates) like the all_different and the symmetric all_different predicates [7]. Thus, the definition of a maximum cardinality matching constraint provides a framework encompassing other predicates. Along this line of research, we define a global constraint with respect to the MCM and address the issue of consistency. Establishing hyper-arc consistency implies the identification of edges that cannot participate in any maximum cardinality matching. Evidently, this issue (also called filtering) is related to the methods developed for solving the problem. Solving this problem for bipartite graphs was common knowledge long before Edmonds proposed an algorithm for the non-bipartite case [3]. Regarding hyper-arc consistency, the problem has been resolved only for the bipartite case [1]. [ABSTRACT FROM AUTHOR]

A GRASP with path-relinking for finding good-quality solutions of the weighted maximum satisfiability problem (MAX-SAT) is described in this paper. GRASP, or Greedy Randomized Adaptive Search Procedure, is a randomized multi-start metaheuristic, where at each iteration locally optimal solutions are constructed, each independent of the others. Previous experimental results indicate its effectiveness for solving weighted MAX-SAT instances. Path-relinking is a procedure used to intensify the search around good-quality isolated solutions that have been produced by the GRASP heuristic. Experimental comparison of the pure GRASP (without path-relinking) and the GRASP with path-relinking illustrates the effectiveness of path-relinking in decreasing the average time needed to find a good-quality solution for the weighted maximum satisfiability problem. [ABSTRACT FROM AUTHOR]