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Benchmark Instances (benchmark + instance)

Distribution by Scientific Domains

Mathematics and Statistics	50%

Selected Abstracts

Self evolution algorithm to minimize earliness and tardiness penalties with a common due date on a single machine

IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, Issue 6 2008
Wei Weng Non-member
Abstract Earliness and tardiness penalties are designed for such scheduling problems where the popular Just-In-Time (JIT) concept is considered to be of significant importance. In this paper, a self evolution (SE) algorithm is proposed to solve the problem of single-machine total earliness and tardiness penalties with a common due date. Up to now, no specific attention has been paid to straddling V-shaped schedules of such problems, which may be better than pure V-shaped schedules for the early due date cases; and no specific discussions have been made on the start time setting of the first job in a schedule. Therefore, in this research, efforts have been made on digging out the straddling V-shaped schedules, improving the efficiency of setting the start time of a schedule, and reducing the execution time. In addition, a new RHRM approach is proposed to create the initial solution for evolution, which helps in achieving the fast contingency of the algorithm. The performance of the proposed algorithm has been tested on 280 benchmark instances ranging from 10 to 1000 jobs from the OR Library, and the results show that the proposed SE algorithm delivers much higher efficiency in finding optimal or near-optimal solutions with both better results in total penalties and significant execution time reduction. Copyright © 2008 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source]

Adaptive beam search lookahead algorithms for the circular packing problem

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 5 2010
Hakim Akeb
Abstract This paper addresses the circular packing problem (CPP), which consists in packing n circles Ci, each of known radius ri, i,N={1, ,, n}, into the smallest containing circle C. The objective is to determine the radius r of C as well as the coordinates (xi, yi) of the center of Ci, i,N. CPP is solved using two adaptive algorithms that adopt a binary search to determine r, and a beam search to check the feasibility of packing n circles into C when the radius is fixed at r. A node of level ,, ,=1, ,, n, of the beam search tree corresponds to a partial packing of , circles of N into C. The potential of each node of the tree is assessed using a lookahead strategy that, starting with the partial packing of the current node, assigns each unpacked circle to its maximum hole degree position. The beam search stops either when the lookahead strategy identifies a feasible packing or when it has fathomed all nodes. The computational tests on a set of benchmark instances show the effectiveness of the proposed adaptive algorithms. [source]

Solving the irregular strip packing problem via guided local search for overlap minimization

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 6 2009
Shunji Umetani
Abstract The irregular strip-packing problem (ISP) requires a given set of non-convex polygons to be placed without overlap within a rectangular container having a fixed width and a variable length, which is to be minimized. As a core sub-problem to solve ISP, we consider an overlap minimization problem (OMP) whose objective is to place all polygons into a container with given width and length so that the total amount of overlap between polygons is made as small as possible. We propose to use directional penetration depths to measure the amount of overlap between a pair of polygons, and present an efficient algorithm to find a position with the minimum overlap for each polygon when it is translated in a specified direction. Based on this, we develop a local search algorithm for OMP that translates a polygon in horizontal and vertical directions alternately. Then we incorporate it in our algorithm for OMP, which is a variant of the guided local search algorithm. Computational results show that our algorithm improves the best-known values of some well-known benchmark instances. [source]

New heuristic methods for the capacitated multi-facility Weber problem

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 1 2007
Necati Aras
Abstract In this paper we consider the capacitated multi-facility Weber problem with the Euclidean, squared Euclidean, and ,p -distances. This problem is concerned with locating m capacitated facilities in the Euclidean plane to satisfy the demand of n customers with the minimum total transportation cost. The demand and location of each customer are known a priori and the transportation cost between customers and facilities is proportional to the distance between them. We first present a mixed integer linear programming approximation of the problem. We then propose new heuristic solution methods based on this approximation. Computational results on benchmark instances indicate that the new methods are both accurate and efficient. © 2006 Wiley Periodicals, Inc. Naval Research Logistics 2006 [source]

A branch-and-price-based large neighborhood search algorithm for the vehicle routing problem with time windows

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 4 2009
Eric Prescott-Gagnon
Abstract Given a fleet of vehicles assigned to a single depot, the vehicle routing problem with time windows (VRPTW) consists of determining a set of feasible vehicle routes to deliver goods to a set of customers while minimizing, first, the number of vehicles used and, second, total distance traveled. A large number of heuristic approaches for the VRPTW have been proposed in the literature. In this article, we present a large neighborhood search algorithm that takes advantage of the power of branch-and-price which is the leading methodology for the exact solution of the VRPTW. To ensure diversification during the search, this approach uses different procedures for defining the neighborhood explored at each iteration. Computational results on the Solomo's and the Gehring and Homberge's benchmark instances are reported. Compared to the best known methods, the proposed algorithm produces better solutions, especially on the largest instances where the number of vehicles used is significantly reduced. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009 [source]

Solving the minimum-weighted coloring problem

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2001
Massimiliano Caramia
Abstract Weighted coloring is a generalization of the well-known vertex (unweighted) coloring for which a number of exact algorithms have been presented in the literature. We are not aware of any optimal method specifically designed for the minimum-weighted coloring problem on arbitrary graphs. Only a few heuristics have been developed with the goal of finding tighter upper bounds for the maximum-weighted clique problem. Moreover, as shown in the paper, a straightforward reduction of a weighted instance into an unweighted one permits us to solve only very small instances. In this paper, we present a branch-and-bound algorithm for the weighted case capable of solving random graphs of up to 90 vertices for any edge density with integer weights uniformly drawn from the range [1, ,,10]. Likewise, we have used properly modified benchmark instances borrowed from vertex coloring as a further test bed for our algorithm. © 2001 John Wiley & Sons, Inc. [source]