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A branch and bound algorithm for Transmission Network Expansion Planning Using Nonconvex Mixed-Integer Nonlinear Programming Models

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IEEE ACCESS 2022年 10卷 39875-39888页

作者： Zoppei, Reinaldo T. Delgado, Marcos A. J. Macedo, Leonardo H. Rider, Marcos J. Romero, Ruben Fed Univ Rondonopolis Inst Exact & Nat Sci BR-78736900 Rondonopolis Mato Grosso Brazil Sao Paulo State Univ Dept Elect Engn BR-15385000 Ilha Solteira SP Brazil Univ Estadual Campinas Dept Syst & Energy BR-13083852 Campinas SP Brazil

The branch and bound (BB) algorithm is widely used to obtain the global solution of mixed-integer linear programming (MILP) problems. On the other hand, when the traditional BB structure is directly used to solve nonconvex mixed-integer nonlinear programming (MINLP) problems, it becomes ineffective, mainly due to the nonlinearity and nonconvexity of the feasible region of the problem. This article presents the difficulties and ineffectiveness of the direct use of the traditional BB algorithm for solving nonconvex MINLP problems and proposes the formulation of an efficient BB algorithm for solving this category of problems. The algorithm is formulated taking into account particular aspects of nonconvex MINLP problems, including (i) how to deal with the nonlinear programming (NLP) subproblems, (ii) how to detect the infeasibility of an NLP subproblem, (iii) how to treat the nonconvexity of the problem, and (iv) how to define the fathoming rules. The proposed BB algorithm is used to solve the transmission network expansion planning (TNEP) problem, a classical problem in power systems optimization, and its performance is compared with the performances of off-the-shelf optimization solvers for MINLP problems. The results obtained for four test systems, with different degrees of complexity, indicate that the proposed BB algorithm is effective for solving the TNEP problem with and without considering losses, showing equal or better performance than off-the-shelf optimization solvers.

关键词： Search problems Propagation losses Planning Metaheuristics Linear programming Biological system modeling Programming profession branch and bound algorithm mixed-integer nonlinear programming optimization transmission network expansion planning

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A branch and bound algorithm for optimal cyclic scheduling in a robotic cell with processing time windows

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2010年第21期48卷 6461-6480页

作者： Yan, Pengyu Chu, Chengbin Yang, Naiding Che, Ada NW Polytech Univ Sch Management Xian 710072 Peoples R China Univ Technol Troyes F-10010 Troyes France Ecole Cent Paris Lab Genie Ind F-92295 Chatenay Malabry France

A branch and bound algorithm is described for optimal cyclic scheduling in a robotic cell with processing time windows. The objective is to minimise the cycle time by determining the exact processing time on each machine which is limited within a time window. The problem is formulated as a set of prohibited intervals of the cycle time, which is usually applied in the robotic cyclic scheduling problem with fixed processing times. Since both bounds of these prohibited intervals are linear expressions of the processing times, we divide these prohibited intervals into a series of the subsets and transform the problem into enumerating the non-prohibited intervals of cycle time in each subset. This enumeration procedure is completed by an efficient branch and bound algorithm, which could find an optimal solution by enumerating partial non-prohibited intervals. Computational results on the benchmark instances and randomly generated test instances indicate that the algorithm is effective.

关键词： robotic cell cyclic scheduling processing time windows method of prohibited intervals branch and bound algorithm

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A branch and bound algorithm for minimizing total completion time on a single batch machine with incompatible job families and dynamic arrivals

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COMPUTERS & OPERATIONS RESEARCH 2012年第5期39卷 939-951页

作者： Yao, Shiqing Jiang, Zhibin Li, Na Shanghai Jiao Tong Univ Dept Ind Engn & Logist Management Shanghai 200030 Peoples R China

In this paper, we consider a single batch machine scheduling problem with incompatible job families and dynamic job arrivals. The objective is to minimize the total completion time. This problem is known to be strongly NP-hard. We present several dominance properties and two types of lower bounds, which are incorporated to construct a basic branch and bound algorithm. Furthermore, according to the characteristics of dynamic job arrivals, a decomposed branch and bound algorithm is proposed to improve the efficiency. The proposed algorithms are tested on a large set of randomly generated problem instances. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： branch and bound algorithm Dynamic arrivals Batch scheduling Incompatible job families

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A branch and bound algorithm for optimal television commercial scheduling

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MATHEMATICAL BIOSCIENCES AND ENGINEERING 2022年第5期19卷 4933-4945页

作者： Lu-Wen Liao Natl Taichung Univ Sci & Technol Dept Intelligent Prod Engn Taichung 40401 Taiwan

In the current era of multimedia, television (TV) plays an important role in transmitting advertising messages. In addition, advertising is the primary source of revenue for the TV industry. Thus, a critical issue for TV stations is the scheduling of commercials in suitable advertising breaks on different TV channels to maximize revenue and minimize penalties. This type of TV commercial scheduling problem is similar to the machine scheduling problem, and both have availability constraints. However, the literature on TV commercial scheduling has not considered this perspective. Motivated by this, we consider the problem of scheduling commercials with specific service-level requirements on TV channels while minimizing the maximum lateness. The lateness of a commercial is defined to be its completion time minus its due date, and the maximum lateness is the maximum value of lateness among all commercials. We propose an exact branch and bound algorithm based on the LFJ (least flexible job first)/EDD (earliest due date first) rules and network flow methods, which were developed to solve the machine scheduling problem with availability constraints. Computational analysis shows that the bounding scheme proposed is highly effective, and a very low percentage of nodes is generated by the branch and bound algorithm. The algorithm can obtain an optimal solution for the problem.

关键词： TV commercials service level requirement scheduling LFJ EDD rule branch and bound algorithm

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A branch and bound algorithm for computing optimal replacement policies in consecutive k-out-of-n-systems

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NAVAL RESEARCH LOGISTICS 2002年第3期49卷 288-302页

作者： Flynn, J Chung, CS Cleveland State Univ Dept Operat Management & Business Stat Cleveland OH 44115 USA

This paper presents a branch and bound algorithm for computing opt inial replacement policies in a discrete-time, infinite-horizon, dynamic programming model of a binary coherent system with n statistically independent components, and then specializes the algorithm to consecutive k-out-of-n systems. The objective is to minimize the long-run expected average undiscounted cost per period. (Costs arise when the system fails and when failed components are replaced.) An earlier paper established the optimality of following a critical component policy (CCP), i.e., a policy specified by a critical component set and the rule: Replace a component if and only if it is failed and in the critical component set. Computing an optimal CCP is a optimization problem with it binary variables and a nonlinear objective function. Our branch and bound algorithm for solving this problem has memory storage requirement O(n) for consecutive k-out-of-n systems. Extensive computational experiments on such systems involving over 350,000 test problems with n ranging from 10 to 150 find this algorithm to be effective when n less than or equal to 40 or k is near n.

关键词： optimal replacement policies branch and bound algorithm

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A branch and bound algorithm for scheduling trains in a railway network

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第2期183卷 643-657页

作者： D'Ariano, Andrea Pacciarelli, Dario Pranzo, Marco Univ Studi Roma Tre Dipartimento Automat & Informat I-00146 Rome Italy Delft Univ Technol Dept Transport & Planning NL-2600 GA Delft Netherlands Univ Siena Dipartimento Ingn Informaz I-53100 Siena Italy

The paper studies a train scheduling problem faced by railway infrastructure managers during real-time traffic control. When train operations are perturbed, a new conflict-free timetable of feasible arrival and departure times needs to be recomputed, such that the deviation from the original one is minimized. The problem can be viewed as a huge job shop scheduling problem with no-store constraints. We make use of a careful estimation of time separation among trains, and model the scheduling problem with an alternative graph formulation. We develop a branch and bound algorithm which includes implication rules enabling to speed up the computation. An experimental study, based on a bottleneck area of the Dutch rail network, shows that a truncated version of the algorithm provides proven optimal or near optimal solutions within short time limits. (c) 2006 Elsevier B.V. All rights reserved.

关键词： train scheduling real-time conflict resolution alternative graph branch and bound algorithm

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Enhanced branch and bound algorithm: Minimizing Subproblem Complexity in Power Dispatch

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IEEE ACCESS 2024年 12卷 93753-93760页

作者： Cesur, Elif Cesur, Muhammet Rasit Abraham, Ajith Istanbul Medeniyet Univ Ind Engn Dept TR-34700 Istanbul Turkiye Bennett Univ Sch Comp Sci Engn & Technol Greater Noida 201310 Uttar Pradesh India

The branch and bound (BB) algorithm, while ensuring optimality, often encounters performance bottlenecks, characterized by slow execution and high computational overhead, especially when dealing with intricate or extensive problem instances (NP-Hard). This study introduces an innovative approach by dividing the problem into partial (local) problems in a manner that would not compromise optimality and solving sub-problems of each local problem individually, to shrink the solution space. In the initial phase, this research establishes and validates the mathematical foundation of the proposed algorithm, which involves a pruning approach. Subsequently, enhancements are incorporated into the existing BB to partition the solution space into more manageable sub-spaces and consolidate solutions from these sub-spaces. In the final phase, the Enhanced branch and bound (EBB) algorithm is applied to a real-world power dispatching optimization case study. The outcomes of this investigation reveal the following: 1) For smaller problem instances, both the conventional BB and the proposed EBB algorithm yield identical optimal solutions. 2) In contrast, the EBB algorithm demonstrates significantly improved performance in solving NP-hard problems that pose challenges for the BB and BB with pruning. The primary contribution of this research is the introduction of EBB, an enhanced version of BB, specifically designed to effectively tackle NP-hard problems. This approach can be integrated with all pruning, branching, and bounding strategies used in BB, thereby boosting its performance and making it applicable to all problems solved by BB variations.

关键词： Optimization Search problems NP-hard problem Machine learning algorithms Dispatching Surveys Problem-solving Power distribution branch and bound algorithm pruning strategy enhanced branch and bound algorithm power dispatching optimization

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A branch and bound algorithm based process-planning system for plastic injection mould bases

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2001年第9期18卷 624-632页

作者： Gan, PY Lee, KS Zhang, YF Natl Univ Singapore Dept Mech Engn Singapore 117548 Singapore

This paper describes the use of artificial intelligence in the process planning of plastic injection mould bases. The computer-aided process-planning system, developed for IMOLD(R) will extract and identify the operations required for machining. These operations are considered together with their precedence constraints and the available machines before the process plan for the mould base plate is generated. The process plan is optimised by a branch and bound based algorithm. Overall machining time has been proposed as the objective function for optimisation. The ability of this algorithm to search intelligently for a feasible optimised solution is illustrated by an industrial case study. A brief comparison with a genetic algorithm based process planning system is also made. The result of this development will allow users to optimise process plans easily for any given mould base, with options to suit dynamic changes on the manufacturing shop floor.

关键词： branch and bound algorithm computer-aided process-planning (CAPP) optimisation plastic injection mould base

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A branch and bound algorithm to minimize the total weighted flowtime for the two-stage assembly scheduling problem

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COMPUTERS & OPERATIONS RESEARCH 2003年第2期30卷 309-320页

作者： Tozkapan, A Kirca, Ö Chung, CS Cleveland State Univ Dept Operat Management & Business Stat Cleveland OH 44114 USA Middle E Tech Univ Dept Ind Engn TR-06531 Ankara Turkey

In this paper, a two-stage assembly scheduling problem is considered with the objective of minimizing the total weighted flowtime. A lower bounding procedure and a dominance criterion are developed and incorporated into a branch and bound procedure. A heuristic procedure is also used to derive an initial upper bound. Computational results of the algorithm are presented.

关键词： scheduling two-stage assembly flowshop branch and bound algorithm total weighted flowtime

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A novel branch and bound algorithm for scheduling flowshop plants with uncertain processing times

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COMPUTERS & CHEMICAL ENGINEERING 2002年第1期26卷 41-57页

作者： Balasubramanian, J Grossmann, IE Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

We address the problem of scheduling a flowshop plant with uncertain processing times described by discrete probability distributions. The objective is to find a sequence of batches that minimizes the expected makespan. To circumvent the problem of combinatorially explosive state spaces, we propose a novel and rigorous branch and bound algorithm that provides the optimal solution and is based on the result that a lower bound to the expected makespan can be obtained by evaluating over an aggregated probability model. Numerical results for a number of example problems show that the solution times for the proposed method are several orders of magnitude smaller than those for a multiperiod model. In addition, an important extension of this method is proposed for the case of continuous probability distributions of certain forms, using discretization schemes that give excellent approximations. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： mixed integer linear program (MILP) flowshop branch and bound algorithm scheduling uncertainty

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