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

Parallel Grasp With Path-Relinking For Job Shop Scheduling

In the job shop scheduling problem (JSP), a finite set of jobs is processed on a finite set of machines. Each job is required to complete a set of operations in a fixed order. Each operation is processed on a specific machine for a fixed duration. A machine can process no more than one job at a time and once a job initiates processing on a given machine it must complete processing without interruption. A schedule is an assignment of operations to time slots on the machines. The objective of the JSP is to find a schedule that minimizes the maximum completion time, or makespan, of the jobs. In this paper, we describe a parallel greedy randomized adaptive search procedure (GRASP) with path-relinking for the JSP. A GRASP is a metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and of a local search. Path-relinking is an intensification strategy that explores trajectories that connect high quality solutions. Independent and cooperative parallelization strategies are described and implemented. Computational experience on a large set of standard test problems indicates that the parallel GRASP with path-relinking finds goodquality approximate solutions of the job shop scheduling problem

GRASP with path relinking for the three-index assignement problem

This paper proposes and tests variants of GRASP (greedy randomized adaptive search procedure) with path relinking for the three-index assignment problem (AP3). GRASP is a multistart metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and of a local search. Path relinking is an intensification strategy that explores trajectories that connect high-quality solutions. Several variants of the heuristic are proposed and tested. Computational results show clearly that this GRASP for AP3 benefits from path relinking and that the variants considered in this paper compare well with previously proposed heuristics for this problem. GRASP with path relinking was able to improve the solution quality of heuristics proposed by Balas and Saltzman (1991), Burkard et al. (1996), and Crama and Spieksma (1992) on all instances proposed in those papers. We show that the random variable “time to target solution,� for all proposed GRASP with path-relinking variants, fits a two-parameter exponential distribution. To illustrate the consequence of this, one of the variants of GRASP with path relinking is shown to benefit from parallelization

Cooperative Multi-Thread Parallel Tabu Search with an Application to Circuit Partitioning

. In this work, we propose a cooperative multi-thread parallel tabu search heuristic for the circuit partitioning problem. This procedure is based on the cooperation of multiple search threads. Each thread implements a different variant of a sequential tabu search algorithm, using a different combination of initial solution algorithm and move attribute definition. These threads communicate by exchanging elite solutions. PVM and Linda are used in the implementation of the parallel tabu search procedure. Numerical results reported for a set of ISCAS benchmark circuits illustrate the effectiveness of the parallel tabu search procedure. Comparative results illustrating the efficiency of the implementations in PVM and Linda are also assessed. 1 Introduction The logical test of integrated VLSI circuits is one of the main phases of their design and fabrication. Testing a circuit amounts to submitting it to different input patterns and checking whether the observed outputs are exactly those e..

OSCILLATOR: A system for analysis of diurnal leaf growth using infrared photography combined with wavelet transformation

<p>Abstract</p> <p>Background</p> <p>Quantification of leaf movement is an important tool for characterising the effects of environmental signals and the circadian clock on plant development. Analysis of leaf movement is currently restricted by the attachment of sensors to the plant or dependent upon visible light for time-lapse photography. The study of leaf growth movement rhythms in mature plants under biological relevant conditions, <it>e.g.</it> diurnal light and dark conditions, is therefore problematic.</p> <p>Results</p> <p>Here we present OSCILLATOR, an affordable system for the analysis of rhythmic leaf growth movement in mature plants. The system contains three modules: (1) Infrared time-lapse imaging of growing mature plants (2) measurement of projected distances between leaf tip and plant apex (leaf tip tracking growth-curves) and (3) extraction of phase, period and amplitude of leaf growth oscillations using wavelet analysis. A proof-of-principle is provided by characterising parameters of rhythmic leaf growth movement of different <it>Arabidopsis thaliana</it> accessions as well as of <it>Petunia hybrida</it> and <it>Solanum lycopersicum</it> plants under diurnal conditions. The amplitude of leaf oscillations correlated to published data on leaf angles, while amplitude and leaf length did not correlate, suggesting a distinct leaf growth profile for each accession. Arabidopsis mutant accession Landsberg <it>erecta</it> displayed a late phase (timing of peak oscillation) compared to other accessions and this trait appears unrelated to the <it>ERECTA</it> locus.</p> <p>Conclusions</p> <p>OSCILLATOR is a low cost and easy to implement system that can accurately and reproducibly quantify rhythmic growth of mature plants for different species under diurnal light/dark cycling.</p

Constraint-Based Local Search for the Costas Array Problem

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