In the present work we study the problems of integer linear optimi- zation, at first from the theoretical point of view (Part I) and subsequently on the basis of empirical data (Part II). First section explains with w...
详细信息
In the present work we study the problems of integer linear optimi- zation, at first from the theoretical point of view (Part I) and subsequently on the basis of empirical data (Part II). First section explains with what this field deals with and where is applied. Other sections contain annotated mathematical formulation of problems, definitions and theorems needed to understand the general methods for solving integer linear programs. In the last section of Part I, we introduce the two best known groups of algorithms that are used by commercial software. The second part provides more details on an Internet library that contains some practical problems, that has been needed to be solved in the past. Furthermore, there are sections dealing with solvers and the advanced options of GAMS. The last section presents data obtained in the course of solving problems using several codes (solvers) of software. 1
The optimization of scheduling problems is based on different criteria to optimize. One of the most important criteria is the minimization of completion time of the last task on the last machine called makespan. In th...
详细信息
The optimization of scheduling problems is based on different criteria to optimize. One of the most important criteria is the minimization of completion time of the last task on the last machine called makespan. In this paper, we present a parallel algorithm for solving the permutation flow shop problem. Our algorithm is a basic parallel distributed algorithm deployed in a grid of computer (Grid' 5000). The objective of this work is minimizing the total makespan of the tasks. Our algorithm uses the exact branch and bound method to find optimal solutions of the problem through the distribution of the tasks among the available processors. Computational results of our parallel algorithm using well known Taillard's benchmarks, showed encouraging results. In particular, we succeeded to solve two new instances to optimality which had never been resolved before neither in sequential nor in parallel [29].
In order to realize scientific planning the layout of strategic loading station,the strategic-loading-station location problem was proposed,which is related to determine the location of each stay with station and the ...
详细信息
In order to realize scientific planning the layout of strategic loading station,the strategic-loading-station location problem was proposed,which is related to determine the location of each stay with station and the transportation plan on the precise of satisfying the general location constraints and problem related special constraintsBased on theory of capacitated facility location with multiple souring in two stage supply chain,one mixed integer linear programming model was established which took whole logistic cost embedding transportation and location costs as objectiveWhen confronted with small and medium size problem,this model could be exactly solved by optimization software using branch and bound algorithm,and when the problem size was big,this model could be heuristically solved by genetic algorithm which used 0-1 and priority-based combined encoding method to represent solution,cost-based and random-generated combined method to generate initial solution,solution repaired strategy and penalty method and special fitness function to deal illegal individual,and greedy based method to heuristically solve transshipment problemAt last,according to computational tests on randomly generated data demonstrated the practical feasibility of this method
Network-on-Chip (NoC) architecture is drawing intensive attention since it promises to maintain high performance in handling complex communication issues as the number of on-chip components increases. An effective...
详细信息
Network-on-Chip (NoC) architecture is drawing intensive attention since it promises to maintain high performance in handling complex communication issues as the number of on-chip components increases. An effective method of mapping multitask applications on multicores is necessary to effectively use the NoC potential. In this paper, we propose an approach of quadratic programming (QP) formulation at the first time for the mapping problem, and it can overcome the unacceptable complexity of Integer Linear Programming (ILP) in dealing with problems with large size due to the decrease in the number of variables. Experimental results show that, QP method is at least 10 times faster than ILP method for 20 given benchmarks.
In the scheduling literature, it is often assumed that jobs arrive either simultaneously or individually. However, this assumption is invalid in most practical situations because jobs usually arrive in batches, e.g., ...
详细信息
In the scheduling literature, it is often assumed that jobs arrive either simultaneously or individually. However, this assumption is invalid in most practical situations because jobs usually arrive in batches, e.g., the final testing house in the manufacturing of semiconductor. The concept of batch arrivals has been mentioned in some studies, but it has not been explored from an operational viewpoint. This paper first addresses an identical parallel machine problem with batch arrivals to minimize the total completion time. Since the problem is NP-hard, a heuristic based on binary integer program is proposed. Computational results show that the proposed heuristic can efficiently obtain good solutions for medium and large size problems with an average percentage error of 2.12 from the lower bound. (C) 2009 Elsevier B.V. All rights reserved.
Most transit agencies require government support for the replacement of their aging fleet A procedure for equitable resource allocation among competing transit agencies for the purpose of transit fleet management is p...
详细信息
Most transit agencies require government support for the replacement of their aging fleet A procedure for equitable resource allocation among competing transit agencies for the purpose of transit fleet management is presented in this study The proposed procedure is a 3-dimensional model that includes the choice of a fleet improvement program, agencies that may receive them, and the timing of investments Earlier efforts to solve this problem involved the application of 1- or 2-dimensional models for each year of the planning period These may have resulted in suboptimal solution as the models are blind to the impact of the fleet management program of the subsequent years Therefore, a new model to address a long-term planning horizon is proposed. The model is formulated as a non-linear optimization problem of maximizing the total weighted average remaining life of the fleet subjected to improvement program and budgetary constraints Two variants of the problem, one with an annual budget constraint and the other with a single budget constraint for the entire planning period, are formulated. Two independent approaches, namely, branch and bound algorithm and genetic algorithm are used to obtain the solution An example problem is solved and results are discussed in details. Finally, the model is applied to a large scale real-world problem and a detailed analysis of the results is presented. (C) 2010 Elsevier Ltd All rights reserved.
This paper considers the problem of finding a nonpreemptive schedule for a single machine to minimize the maximum lateness with release dates and precedence constraints. A branch and bound algorithm is developed. The ...
详细信息
This paper considers the problem of finding a nonpreemptive schedule for a single machine to minimize the maximum lateness with release dates and precedence constraints. A branch and bound algorithm is developed. The algorithm uses four different heuristics to find upper bounds at the initial branch node: early release date heuristic, modified Schrage's heuristic, heuristic BLOCK, and a variable neighborhood descent procedure. At each branch node, two branches evolve from a schedule found by heuristic BLOCK using a binary branching rule based on bottleneck and critical jobs, and a lower bound is obtained by optimally solving the relaxed problem with preemption. The algorithm solves 14,984 out of the 15,000 systematically generated instances with up to 1,000 jobs within I minute of CPU time. (C) 2009 Elsevier Ltd. All rights reserved.
For linear bilevel programming, the branch and bound algorithm is the most successful algorithm to deal with the complementary constraints arising from Kuhn Tucker conditions. However, one principle challenge is that ...
详细信息
For linear bilevel programming, the branch and bound algorithm is the most successful algorithm to deal with the complementary constraints arising from Kuhn Tucker conditions. However, one principle challenge is that it could not well handle a linear bilevel programming problem when the constraint functions at the upper-level are of arbitrary linear form. This paper proposes an extended branch and bound algorithm to solve this problem. The results have demonstrated that the extended branch and bound algorithm can solve a wider class of linear bilevel problems can than current capabilities permit. (c) 2006 Elsevier Inc. All rights reserved.
Wind turbine blades are usually made in batches and then matched in pairs or triples to form the rotor. This paper considers matching with the aim of avoiding or reducing the need for further adjustment of, say, the b...
详细信息
Wind turbine blades are usually made in batches and then matched in pairs or triples to form the rotor. This paper considers matching with the aim of avoiding or reducing the need for further adjustment of, say, the blade mass. Matching is considered optimal when it minimises the sum of the squared differences in the chosen matching parameter for all blade pairs or triples in a batch. It is proved that use of a simple parameter such as blade mass, or centre of mass, leads to optimal matching by ordering in terms of that parameter. More complex matching based on, say, minimising the eccentricity of the centre of mass, causes the parameter for one blade to depend on at least one other blade. Then ordering does not necessarily produce the optimal matching but, in all cases considered, it comes very close. A branch and bound algorithm is developed for complex matching and is shown to provide the optimal matching in a realistic time for batches of at least 20 blades.
This paper proposes an exact algorithm to solve a cyclic hoist scheduling problem in a printed circuit board (PCB) electroplating facility, where multi-type parts with fixed processing times are processed in the same ...
详细信息
This paper proposes an exact algorithm to solve a cyclic hoist scheduling problem in a printed circuit board (PCB) electroplating facility, where multi-type parts with fixed processing times are processed in the same time and the parts are not allowed to wait in the tanks or on the hoist. Finding an optimal schedule in such a production line is equivalent to finding two types of related sequences: part input sequence and hoist move sequence. We show that the entering times of the parts are the decision variables of the problem. We formulate our problem using the notion of prohibited intervals and solve it by enumerating the non-prohibited intervals of the decision variables. This enumeration is accomplished more efficiently with a dynamic branch and bound procedure, which utilises relaxed solutions to eliminate redundant non-prohibited intervals in the search process. The proposed algorithm is polynomial in the number of tanks if the number of part types is fixed, but exponential if it is arbitrary. Computational results on randomly generated test instances indicate that the algorithm is effective.
暂无评论