762 research outputs found
Local search heuristics for multi-index assignment problems with decomposable costs.
The multi-index assignment problem (MIAP) with decomposable costs is a natural generalization of the well-known assignment problem. Applications of the MIAP arise for instance in the field of multi-target multi-sensor tracking. We describe an (exponentially sized) neighborhood for a solution of the MIAP with decomposable costs, and show that one can find a best solution in this neighborhood in polynomial time. Based on this neighborhood, we propose a local search algorithm. We empirically test the performance of published constructive heuristics and the local search algorithm on random instances; a straightforward tabu search is also tested. Finally, we compute lower bounds to our problem, which enable us to assess the quality of the solutions found.Assignment; Costs; Heuristics; Problems; Applications; Performance;
The structure of problem-solving knowledge and the structure of organisations
This work presents a model of organisational problem solving able to account for the relationships between problem complexity, tasks decentralilzation and problem solving efficiency. Whenever problem solving requires the coordination of a multiplicity of interdependent elements, the varying degrees of decentralization of cognitive and operational tasks shape the solution which can be generated, tested and selected. Suboptimality and path-dependence are shown to be ubiquitous features of organisational problem solving. At the same time, the model allows a precise exploration of the possible trade-offs between decompostion patterns and search efficiency involved in different organisational architectures.-
Local Search Heuristics For The Multidimensional Assignment Problem
The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case
of s dimensions) is an extension of the well-known assignment problem. The most
studied case of MAP is 3-AP, though the problems with larger values of s also
have a large number of applications. We consider several known neighborhoods,
generalize them and propose some new ones. The heuristics are evaluated both
theoretically and experimentally and dominating algorithms are selected. We
also demonstrate a combination of two neighborhoods may yield a heuristics
which is superior to both of its components.Comment: 30 pages. A preliminary version is published in volume 5420 of
Lecture Notes Comp. Sci., pages 100-115, 200
A New Approach to Population Sizing for Memetic Algorithms: A Case Study for the Multidimensional Assignment Problem
Memetic algorithms are known to be a powerful technique in solving hard optimization problems. To design a memetic algorithm, one needs to make a host of decisions. Selecting the population size is one of the most important among them. Most of the algorithms in the literature fix the population size to a certain constant value. This reduces the algorithm's quality since the optimal population size varies for different instances, local search procedures, and runtimes. In this paper we propose an adjustable population size. It is calculated as a function of the runtime of the whole algorithm and the average runtime of the local search for the given instance. Note that in many applications the runtime of a heuristic should be limited and, therefore, we use this bound as a parameter of the algorithm. The average runtime of the local search procedure is measured during the algorithm's run. Some coefficients which are independent of the instance and the local search are to be tuned at the design time;we provide a procedure to find these coefficients. The proposed approach was used to develop a memetic algorithm for the multidimensional assignment problem (MAP). We show that our adjustable population size makes the algorithm flexible to perform efficiently for a wide range of running times and local searches and this does not require any additional tuning of the algorithm
Routing in multi-class queueing networks
PhD ThesisWe consider the problem of routing (incorporating local scheduling) in a distributed
network. Dedicated jobs arrive directly at their specified station for processing. The
choice of station for generic jobs is open. Each job class has an associated holding cost
rate. We aim to develop routing policies to minimise the long-run average holding cost
rate.
We first consider the class of static policies. Dacre, Glazebrook and Nifio-Mora (1999)
developed an approach to the formulation of static routing policies, in which the work at
each station is scheduled optimally, using the achievable region approach. The achievable
region approach attempts to solve stochastic optimisation problems by characterising
the space of all possible performances and optimising the performance objective over
this space. Optimal local scheduling takes the form of a priority policy. Such static
routing policies distribute the generic traffic to the stations via a simple Bernoulli routing
mechanism. We provide an overview of the achievements made in following this approach
to static routing. In the course of this discussion we expand upon the study of Becker et al.
(2000) in which they considered routing to a collection of stations specialised in processing
certain job classes and we consider how the composition of the available stations affects
the system performance for this particular problem. We conclude our examination of
static routing policies with an investigation into a network design problem in which the
number of stations available for processing remains to be determined.
The second class of policies of interest is the class of dynamic policies. General DP
theory asserts the existence of a deterministic, stationary and Markov optimal dynamic
policy. However, a full DP solution may be unobtainable and theoretical difficulties posed
by simple routing problems suggest that a closed form optimal policy may not be available.
This motivates a requirement for good heuristic policies. We consider two approaches to
the development of dynamic routing heuristics. We develop an idea proposed, in the
context of simple single class systems, by Krishnan (1987) by applying a single policy
improvement step to some given static policy. The resulting dynamic policy is shown
to be of simple structure and easily computable. We include an investigation into the
comparative performance of the dynamic policy with a number of competitor policies and
of the performance of the heuristic as the number of stations in the network changes. In
our second approach the generic traffic may only access processing when the station has
been cleared of all (higher priority) jobs and can be considered as background work. We
deploy a prescription of Whittle (1988) developed for RBPs to develop a suitable approach
to station indexation. Taking an approximative approach to Whittle's proposal results
in a very simple form of index policy for routing the generic traffic. We investigate the
closeness to optimality of the index policy and compare the performance of both of the
dynamic routing policies developed here
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