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1

The art and science of modeling decision-making under severe uncertainty

Sniedovich M.

Decision Making in Manufacturing and Services

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2007

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Vol. 1, no. 1-2

111-136

EN

For obvious reasons, models for decision-making under severe uncertainty are austere. Simply put, there is precious little to work with under these conditions. This fact highlights the great importance of utilizing in such cases the ingredients of the mathematical model to the fullest extent, which in turn brings under the spotlight the art of mathematical modeling. In this discussion we examine some of the subtle considerations that are called for in the mathematical modeling of decision-making under severe uncertainty in general, and worst-case analysis in particular. As a case study we discuss the lessons learnt on this front from the Info-Gap experience.

2

The corridor method: a dynamic programming inspired metaheuristic

Sniedovich M., Viß S.

Control and Cybernetics

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2006

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Vol. 35, no 3

551-578

EN

This paper presents a dynamic programming inspired metaheuristic called Corridor Method. It can be classified as a method-based iterated local search in that it deploys method-based neighborhoods. By this we mean that the search for a new candidate solution is carried out by a fully-fledged optimization method and generates a global optimal solution over the neighborhood. The neighborhoods are thus constructed to be suitable domains for the fully-fledged optimization method used. Typically, these neighborhoods are obtained by the imposition of exogenous constraints on the decision space of the target problem and therefore must be compatible with the optimization method used to search these neighborhoods. This is in sharp contrast to traditional metaheuristics where neighborhoods are move-based, that is, they are generated by subjecting the candidate solution to small changes called moves. While conceptually this method-based paradigm applies to any optimization method, in practice it is best suited to support optimization methods such as dynamic programming, where it is easy to control the size of a problem, hence the complexity of algorithms, by means of exogenous constraints. The essential features of the Corridor Method are illustrated by a number of examples, including the traveling salesman problem, where exponentially large neighborhoods are searched by a linear time/space dynamic programming algorithm.

3

Dynamic Programming: an overview

Sniedovich M.

Control and Cybernetics

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2006

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Vol. 35, no 3

513-533

EN

Dynamic programing is one of the major problem-solving methodologies in a number of disciplines such as operations research and computer science. It is also a very important and powerful tool of thought. But not all is well on the dynamic programming front. There is definitely lack of commercial software support and the situation in the classroom is not as good as it should be. In this paper we take a bird's view of dynamic programming so as to identify ways to make it more accessible to students, academics and practitioners alike.

4

Dijkstra's algorithm revisited: the dynamic programming connexion

Sniedovich M.

Control and Cybernetics

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2006

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Vol. 35, no 3

599-620

EN

Dijkstra's Algorithm is one of the most popular algorithms in computer science. It is also popular in operations research. It is generally viewed and presented as a greedy algorithm. In this paper we attempt to change this perception by providing a dynamic programming perspective on the algorithm. In particular, we are reminded that this famous algorithm is strongly inspired by Bellman's Principle of Optimality and that both conceptually and technically it constitutes a dynamic programming successive approximation procedure par excellence. One of the immediate implications of this perspective is that this popular algorithm can be incorporated in the dynamic programming syllabus and in turn dynamic programming should be (at least) alluded to in a proper exposition/teaching of the algorithm.