We consider the problem of assigning a set of jobs to a system of m identical processors in order to maximize the earliest processor completion time. It was known that the LPT-heuristic gives an approximation of worst...
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We consider the problem of assigning a set of jobs to a system of m identical processors in order to maximize the earliest processor completion time. It was known that the LPT-heuristic gives an approximation of worst case ratio at most 3/4. In this note we show that the exact worst case ratio of LPT is (3m - 1)/(4m - 2).
In this paper we discuss lower bounds for the asymptotic worst case ratio of on-line algorithms for different kind of bin packing problems. Recently, Galambos and Frenk gave a simple proof of the 1.536... lower bound ...
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In this paper we discuss lower bounds for the asymptotic worst case ratio of on-line algorithms for different kind of bin packing problems. Recently, Galambos and Frenk gave a simple proof of the 1.536... lower bound for the 1-dimensional bin packing problem. Following their ideas, we present a general technique that can be used to derive lower bounds for other bin packing problems as well. We apply this technique to prove new lower bounds for the 2-dimensional (1.802...) and 3-dimensional (1.974...) bin packing problem.
We describe an approximation algorithm for the problem of finding the minimum makespan in a job shop. The algorithm is based on simulated annealing, a generalization of the well known iterative improvement approach to...
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We describe an approximation algorithm for the problem of finding the minimum makespan in a job shop. The algorithm is based on simulated annealing, a generalization of the well known iterative improvement approach to combinatorial optimization problems. The generalization involves the acceptance of cost-increasing transitions with a nonzero probability to avoid getting stuck in local minima. We prove that our algorithm asymptotically converges in probability to a globally minimal solution, despite the fact that the Markov chains generated by the algorithm are generally not irreducible. Computational experiments show that our algorithm can find shorter makespans than two recent approximation approaches that are more tailored to the job shop scheduling problem. This is, however, at the cost of large running times.
The three-dimensional bin-packing problem is the problem of orthogonally packing a set of boxes into a minimum number of three-dimensional bins. In this paper we present a heuristic algorithm based on guided local sea...
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The three-dimensional bin-packing problem is the problem of orthogonally packing a set of boxes into a minimum number of three-dimensional bins. In this paper we present a heuristic algorithm based on guided local search. Starting with an upper bound on the number of bins obtained by a greedy heuristic, the presented algorithm iteratively decreases the number of bins, each time searching for a feasible packing of the boxes. The process terminates when a given time limit has been reached or the upper bound matches a pre-computed lower bound. The algorithm can also be applied to two-dimensional bin-packing problems by having a constant depth for all boxes and bins. Computational experiments are reported for two- and three-dimensional instances with up to 200 boxes, showing that the algorithm on average finds-better solutions than do heuristics from the literature.
The problem of estimating the global optimal values of intractable combinatorial optimization problems is of interest to researchers developing and evaluating heuristics for these problems. In this paper we present a ...
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The problem of estimating the global optimal values of intractable combinatorial optimization problems is of interest to researchers developing and evaluating heuristics for these problems. In this paper we present a method for combining statistical optimum prediction techniques with local search methods such as simulated annealing and tabu search and illustrate the approach on a single machine scheduling problem. Computational experiments show that the approach yields useful estimates of optimal values with very reasonable computational effort.
We consider a version of the on-line bounded-space bin-packing problem where repacking the items within the active bins is allowed. For this problem, the 1.69103 lower bound of Lee and Lee [7] for the worst case ratio...
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We consider a version of the on-line bounded-space bin-packing problem where repacking the items within the active bins is allowed. For this problem, the 1.69103 lower bound of Lee and Lee [7] for the worst case ratios of bounded-space approximation algorithms still applies. We present a polynomial time approximation algorithm that reaches the best possible worst case ratio matching the Lee and Lee lower bound while using only three active bins.
For a given list of 3m items with positive lengths we look for a partition into m subsets containing 3 elements each, such that the ratio of the largest sum of lengths to the smallest sum of lengths is as small as pos...
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For a given list of 3m items with positive lengths we look for a partition into m subsets containing 3 elements each, such that the ratio of the largest sum of lengths to the smallest sum of lengths is as small as possible. Let rho(G) be the value of this ratio using a Greedy-heuristic and rho* the optimal value of this ratio;furthermore let beta be the ratio of the largest length of an item to the smallest length. Then we will show that for 1 less-than-or-equal-to beta less-than-or-equal-to 4 the inequality rho(G)/rho* less-than-or-equal-to (4beta + 7)(2beta + 5) holds and this bound is tight.
In this note, we give a 1.47-approximation algorithm for the preemptive scheduling of jobs with release dates on a single machine so as to minimize the weighted sum of job completion times;this problem is denoted by 1...
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In this note, we give a 1.47-approximation algorithm for the preemptive scheduling of jobs with release dates on a single machine so as to minimize the weighted sum of job completion times;this problem is denoted by 1\r(j), pmtn\ Sigma(j)w(j)C(j) in the notation of Lawler et al. (Handbooks in Operations Research and Management Science, Vol. 4, Logistics of Production and Inventory, North-Holland, Amsterdam, pp. 445-522). Our result improves on a 2-approximation algorithm due to Hall et al. Math. Oper. Res. 22 (1997) 513-544, and also yields an improved bound on the quality of a well-known linear programming relaxation of the problem. (C) 2000 Elsevier Science B.V. All rights reserved.
The author presents a sequence of linear-time, bounded-space, on-line, bin-packing algorithms that are based on the ''HARMONIC'' algorithms H(k) introduced by Lee and Lee [J. Assoc. Comput. Mach., 32 (...
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The author presents a sequence of linear-time, bounded-space, on-line, bin-packing algorithms that are based on the ''HARMONIC'' algorithms H(k) introduced by Lee and Lee [J. Assoc. Comput. Mach., 32 (1985), pp. 562-572]. The algorithms in this paper guarantee the worst case performance of H(k), whereas they only use O(log log k) instead of k active bins. For k greater-than-or-equal-to 6. the algorithms in this paper outperform all known heuristics using k active bins. For example, the author gives an algorithm that has worst case ratio less than 17/10 and uses only six active bins.
A Distributed Battle Manager (DBM) system based on Concurrent MACro Partially Observable Markov Decision Processes (CMAC-POMDP) is proposed to manage multiple competing missions. Implementation details are presented f...
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ISBN:
(纸本)9781467375573
A Distributed Battle Manager (DBM) system based on Concurrent MACro Partially Observable Markov Decision Processes (CMAC-POMDP) is proposed to manage multiple competing missions. Implementation details are presented for a semi-autonomous management of multiple ad-hoc teams of UAVs operating under extreme uncertainty in a contested environment. The proposed solution is semi-autonomous since command and control teams perform target confirmation, weapon selection, weapon release, and bomb damage assessment. Our proposed approach decomposes the resource management requirements into specialized mission timelines. There would be one adaptive mission timeline for each system objective, and each timeline would be represented by a POMDP. At any time, the DBM would be controlling multiple concurrent timelines that are competing for system resources. Each timeline is solved independently to obtain the optimal MDP solution parameters. These solution parameters are then combined using linear programming with constraints to obtain a suboptimal system solution. The resulting suboptimal solutions provide satisfactory real-time system performance. Under extreme uncertainty, it is preferable to maximize robustness utilizing an adequately performing solution as opposed to finding an optimal but brittle solution. Performance results of the core CMAC-POMDP algorithm are presented for a system implemented to manage multiple heterogeneous sensors addressing multiple simultaneous threats. This simpler resource management system utilizes the same timeline for all of the threats. Simulations demonstrate better than real-time performance even for large numbers of threats. Furthermore, computational requirements are shown to grow linearly with the number of threats. Extension to multiple simultaneous timelines for the DBM system is straightforward.
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