A statistical model for global optimization is constructed generalizing some properties of the Wiener process to the multidimensional case. A new approach, which is similar to the branch and bound approach, is propose...
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We consider the problem of minimizing the mean flow time on a single-batch processing machine. The machine can process at most B jobs simultaneously as a batch, and the processing time of a batch is equal to the proce...
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We consider the problem of minimizing the mean flow time on a single-batch processing machine. The machine can process at most B jobs simultaneously as a batch, and the processing time of a batch is equal to the processing time of the longest job in the batch. We present a new dominance property and develop a branch and bound method. Finally, the computational results of the method are discussed.
The disjoint bilinear programming problem can be reformulated using two distinct linear maxmin programming problems. There is a simple bijection between the optimal solutions of the reformulations and the bilinear pro...
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The disjoint bilinear programming problem can be reformulated using two distinct linear maxmin programming problems. There is a simple bijection between the optimal solutions of the reformulations and the bilinear problem. Moreover, the number of local optima of the reformulations is less or equal to that of the bilinear problem. In that sense, the reformulations do not introduce additional complexity. Necessary optimality conditions (complementarity and monotonicity) of both reformulations are used to obtain a finitely convergent and exact branch and bound algorithm for the bilinear problem. Determining if the optimal value of a bilinear programming problem is bounded is shown to be strongly NP-complete. The proposed algorithm may be used to answer this question.
The article studies the scheduling problem of a material handling hoist in a circuit board production line. The existing models for the problem assume that the times required to perform inter-tank moves are given cons...
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The article studies the scheduling problem of a material handling hoist in a circuit board production line. The existing models for the problem assume that the times required to perform inter-tank moves are given constants. However, as shown in a simple example, the optimal solutions obtained under this assumption may not be the actual optimal solutions. In this article the times for inter-tank moves are decision variables of a mixed integer program proposed for the problem. An efficient branch and bound algorithm is developed for solving the problem optimally. A numerical example is used to illustrate the algorithm. Computational experience with benchmark problems and randomly generated test problems is discussed.
A method is proposed to combine the branch-and-bound (BAB) algorithm with the Bayes classifier. Given the input feature vector from an unknown class, the BAB algorithm is efficient for searching for the nearest neighb...
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A method is proposed to combine the branch-and-bound (BAB) algorithm with the Bayes classifier. Given the input feature vector from an unknown class, the BAB algorithm is efficient for searching for the nearest neighbor (NN) from among the set of reference vectors. Hence BAB is often used to implement the k-NN classifier. However, it is known that the k-NN classifier is not as accurate as the Bayes classifier, which has the highest recognition rate provided the class statistics are known. Hence it is attractive to combine the BAB algorithm with the Bayes classifier so that the resulting system will inherit improved speed and accuracy. In this article, an extension of the BAB algorithm is proposed so that it can be used to implement the Bayes classifier. Gaussian statistics are assumed in modeling the class conditional densities. A system for recognizing printed Chinese characters is implemented, and satisfactory results are obtained. (C) 1998 Elsevier Science Ltd. All rights reserved.
In this study we consider the problem of sequencing n jobs on one machine under the dual objective of minimizing the maximum earliness (E-max) with minimum number of tardy jobs (n(T)). A procedure is first proposed to...
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In this study we consider the problem of sequencing n jobs on one machine under the dual objective of minimizing the maximum earliness (E-max) with minimum number of tardy jobs (n(T)). A procedure is first proposed to schedule for minimizing the maximum earliness when the set of non-tardy jobs is specified. A branch and bound algorithm is presented to obtain the optimal schedule that minimizes the maximum earliness with minimum number of tardy jobs by connecting Moore's algorithm. (C) 1998 Elsevier Science B.V. All rights reserved.
We consider a single-machine problem of scheduling n independent jobs to minimize makespan, in which the processing time of job J(j) grows by w(j) with each time unit its start is delayed beyond a given common critica...
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We consider a single-machine problem of scheduling n independent jobs to minimize makespan, in which the processing time of job J(j) grows by w(j) with each time unit its start is delayed beyond a given common critical date d. This processing time is p(j) if J(j) starts by d. We show that this problem is NP-hard, give a pseudopolynomial algorithm that runs in O(nd Sigma(j=1)(n) P-j) time and O(nd) space, and develop a branch-and-boundalgorithm that solves instances with up to 100 jobs in a reasonable amount of time. We also introduce the case of bounded deterioration, where the processing time of a job grows no further if the job starts after a common maximum deterioration date D > d. For this case, we give two pseudopolynomial time algorithms: one runs in O(n(2)d(D - d) Sigma(j=1)(n) p(j)) time and O(nd(D - d)) space, the other runs in O(nd Sigma(j=1)(n) w(j)(Sigma(j=1)(n) p(j))(2)) time and O(nd Sigma(j=1)(n) w(j) Sigma(j=1)(n) p(j)) space. (C) 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 511-523, 1998.
Formulating the minimum concave cost capacitated network flow problem as an integer concave minimization problem, we establish finite branch and bound algorithms, in which the branching operation is the so-called inte...
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Formulating the minimum concave cost capacitated network flow problem as an integer concave minimization problem, we establish finite branch and bound algorithms, in which the branching operation is the so-called integral rectangular partition and the bounding procedure is performed by the classical minimum linear cost flow problem on subnetworks. For the special case that the flow cost function is concave on a fixed number of arcs and linear on the others, an upper bound of the running time is given.
We consider a single‐machine problem of scheduling n independent jobs to minimize makespan, in which the processing time of job J j grows by w j with each time unit its start is delayed beyond a given common critical...
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The sequential branch and bound algorithm is the most established method for solving mixed integer and discrete programming problems. It is based on the tree search of the possible subproblems of the original problem....
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The sequential branch and bound algorithm is the most established method for solving mixed integer and discrete programming problems. It is based on the tree search of the possible subproblems of the original problem. There are two goals in carrying out a tree search, namely, (i) finding a good and ultimately the best integer solution, and (ii) to prove that the best solution has been found or no integer feasible solution exists. We call these the stage 1 and stage 2 of tree search. In general it is extremely difficult to choose the ideal search strategy in stage 1 or stage 2 for a given integer programming (IP) problem. On the other hand by investigating a number of different strategies (and hence different search trees) a good solution can be reached quickly in respect of many practical IP problems. Starting from this observation a parallel branch and bound algorithm has been designed which exploits this two stage approach. In the first stage we investigate a number of alternative search trees (forest search) in the hope of finding a good solution quickly. This we call the multiple heuristic search (MHS). In this approach the best integer solution is broadcast to other processors involved in MHS tree development. In the second stage we reorganise the search to investigate branches of a chosen tree in parallel. This two stage algorithm has been implemented on a cluster of SUN workstations using the Parallel Virtual Machine (PVM) harness [12]. The results of our investigation for a range of well known test problems taken from the MIPLIB set and others from the literature are reported here.
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