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MULTIOBJECTIVE OPTIMUM DESIGN IN MIXED INTEGER AND DISCRETE DESIGN VARIABLE PROBLEMS

AIAA JOURNAL 1990年第4期28卷 670-675页

作者： HAJELA, P SHIH, CJ University of Florida Gainesville Florida

A min-max variant of the global criterion approach is proposed to obtain solutions to multiobjective optimum design problems involving a mix of continuous, discrete, and integer design variables. This modified global criterion approach is used in conjunction with a branch-and-bound algorithm, where the latter was configured especially to accommodate a mix of integer and discrete design variables. The use of a weighting strategy with the proposed method allows the generation of a set of Pareto optimal (noninferior) solutions for both convex and nonconvex problems. The solution strategy is applied to structural design problems involving vector design functions. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Structural Design branch and bound algorithm Nonlinear Programming Fiber Volume Fraction Simply Supported Beams Composite Structures Material Properties Structural Weight Tensile Strength Aeroplane

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STACKING-SEQUENCE OPTIMIZATION OF SIMPLY SUPPORTED LAMINATES WITH STABILITY AND STRAIN CONSTRAINTS

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AIAA JOURNAL 1992年第8期30卷 2132-2137页

作者： NAGENDRA, S HAFTKA, RT GURDAL, Z VIRGINIA POLYTECH INST & STATE UNIV AEROSP & OCEAN ENGNBLACKSBURGVA 24061

An integer programming formulation for the design of symmetric and balanced rectangular composite laminates with simply supported boundary conditions subject to buckling and strain constraints is presented. The design variables that define the stacking sequence of the laminate are ply-identity zero-one integers. The buckling constraint is linear in terms of the ply-identity design variables, but strains are nonlinear functions of these variables. A linear approximation is developed for the strain constraints so that the problem can be solved by sequential linearization using the branch and bound algorithm. Examples of graphite-epoxy plates under biaxial compression are presented. Optimum stacking sequences obtained using the linear approximation are compared with global optimum designs obtained using a genetic search procedure.

关键词： Laminated Composites branch and bound algorithm Genetic algorithm Taylor Series Aspect Ratio

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A symmetrical linear maxmin approach to disjoint bilinear programming

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MATHEMATICAL PROGRAMMING 1999年第3期85卷 573-592页

作者： Audet, C Hansen, P Jaumard, B Savard, G Rice Univ Houston TX 77005 USA Ecole Hautes Etud Commerciales GERAD Montreal PQ H3T 2A7 Canada Ecole Polytech Montreal PQ H3C 3A7 Canada GERAD Dept Math & Genie Ind Montreal PQ H3C 3A7 Canada

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.

关键词： disjoint bilinear problem linear maxmin problem branch and bound algorithm global optimization

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Trains scheduling problem with multiple lines

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SCIENTIFIC REPORTS 2024年第1期14卷 1-20页

作者： Danavulapadu, Venkata Prathap Singamsetty, Purusotham Vellore Inst Technol Sch Adv Sci Dept Math Vellore 632014 Tamil Nadu India

This study explores the problem of train scheduling (or) train timetabling and its impact on the administration of railway management. This is a highly dependable and effective public transportation system. The problem considers both single and multiple tracks along with multiple platforms with varying train capacities (like speed, passengers, and so on). Let the tracks link two major stations source and destination with intermediate stations. A subset of intermediate stations will function as junctions. A finite number of trains be available at the source for the passengers/cargo transit movements. The profit which is generated from the shipment of passengers between a pair of stations is known in advance. The train's travel time between the stations and halting time at the stations are predefined. The arrival and departure times at the stations are calculated through the travel time and halting time. All the trains should starts from the source station and continue the journey through the intermediate stations to reach the destination station. Overtaking of the trains is permitted only at the intermediate stations. The trains must make a halt at one or more intermediate stations before reaching the destination. Now the objective is to find the best train operating schedule that maximizes the profit within the admissible travel time threshold. A zero-one integer linear programming is used to model this problem mathematically. For a better understanding of this problem, a case study is considered from the Indian railway network with two major stations Chennai and Hyderabad. A branch and bound \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(B\&B)$$\end{document} algorithm is proposed to determine an optimal operating schedule. In addition, the experiments are carried out on a wide range

关键词： Train scheduling Routing branch and bound algorithm Zero-one integer programming

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Concavity cuts for disjoint bilinear programming

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MATHEMATICAL PROGRAMMING 2001年第2期90卷 373-398页

作者： Alarie, S Audet, C Jaurnard, B Savard, G Ecole Polytech GRPR Montreal PQ H3C 3A7 Canada Ecole Polytech GERAD Montreal PQ H3C 3A7 Canada Ecole Polytech Dept Genie Elect & Genie Informat Montreal PQ H3C 3A7 Canada Ecole Polytech Dept Math & Genie Ind Montreal PQ H3C 3A7 Canada

We pursue the study of concavity cuts for the disjoint bilinear programming problem. This optimization problem has two equivalent symmetric linens maxmin reformulations, leading to two sets of concavity cuts. We first examine the depth of these cuts by considering the assumptions on the boundedness of the feasible regions of both maxmin and bilinear formulations. We next propose a branch and bound algorithm which make use of concavity cuts. We also present a procedure that eliminates degenerate solutions. Extensive computational experiences are reported. Sparse problems with up to 500 variables in each disjoint sets and 100 constraints, and dense problems with up to 60 variables again in each sets and 60 constraints are solved in reasonable computing times.

关键词： concavity cuts disjoint bilinear programming linear maxmin programming branch and bound algorithm global optimization

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Global optimization algorithm for a generalized linear multiplicative programming

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2012年第1-2期40卷 551-568页

作者： Jiao, Hongwei Liu, Sanyang Chen, Yongqiang Xidian Univ Dept Math Sci Xian 710071 Peoples R China Henan Inst Sci & Technol Dept Math Xinxiang 453003 Peoples R China Henan Normal Univ Coll Math & Informat Xinxiang 453007 Peoples R China

This article present a branch and bound algorithm for globally solving generalized linear multiplicative programming problems with coefficients. The main computation involve solving a sequence of linear relaxation programming problems, and the algorithm economizes the required computations by conducting the branch and bound search in R-p, rather than in R-n, where p is the number of rank and n is the dimension of decision variables. The proposed algorithm will be convergent to the global optimal solution by means of the subsequent solutions of the series of linear relaxation programming problems. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm.

关键词： Multiplicative programming Global optimization branch and bound algorithm Deterministic algorithm

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Formulating and solving a multi-mode resource-collaboration and constrained scheduling problem (MRCCSP)

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ANNALS OF OPERATIONS RESEARCH 2013年第1期206卷 311-339页

作者： Pinto, Gaby Ben-Dov, Yariv T. Rabinowitz, Gad Jerusalem Coll Engn JCE Dept Ind Engn & Management IL-91035 Jerusalem Israel Ben Gurion Univ BGU Negev Dept Ind Engn & Management IL-84105 Beer Sheva Israel

The main motivation of this study is to provide, for the first time, a formulation and solution for a class of production scheduling problems (as in cluster tools) characterized mainly by resource collaboration to perform an operation and while allowing batches and considering alternative production methods. We develop a formulation for the new problem and term it a multiple mode per operation, resource collaboration, and constrained scheduling problem (MRCCSP). Some of the important new characteristics we consider are: multiple products (families);multiple orders (jobs) per family;precedence restrictions among the operations that constitute a job;alternative modes for the performance of an operation (each of which needs a set of collaborating resources) may be defined;complementary and exclusive restrictions between operation-modes;batch production is allowed;and setup times may depend on sequence and batch-size. The objective of the MRCCSP is to minimize makespan. We formulate the MRCCSP as a mixed integer linear programming model, and acknowledging the considerable size of the monolithic formulation required, we prescribe a specific method to achieve size reduction. Finally, a customized branch and bound algorithm for optimally solving this problem is proposed and examined experimentally.

关键词： Resource-sharing and scheduling problem Resource constrained scheduling problem Mixed integer linear programming branch and bound algorithm

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Minimizing maximum tardiness and delivery costs with batch delivery and job release times

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APPLIED MATHEMATICAL MODELLING 2015年第16期39卷 4909-4927页

作者： Rostami, Mohammad Kheirandish, Omid Ansari, Nima Iran Univ Sci & Technol Dept Ind Engn Tehran Iran Univ Tehran Dept Ind Engn Tehran 14174 Iran

Due to high delivery costs, manufacturers are usually required to dispatch their jobs as batches. However, this approach causes several crucial problems in scheduling-related objective functions such as minimizing the maximum tardiness. In this study, we address the scheduling of a set of jobs with specific release times, which need to be processed by a single machine and dispatched to a customer or another machine in a batch delivery condition. Each batch has a particular delivery cost. The aim is to minimize the costs of maximum tardiness plus delivery. First, a mixed integer programming (MIP) model is developed and solved by the CPLEX solver within the GAMS modeling environment. Next, a branch and bound algorithm is developed based on the LP relaxation of the MIP model. Using heuristics, appropriate values for the upper and lower bounds are predicted. The heuristics and pruning rules can obtain the solutions of large problems in logical run times. The problem can be deduced as being NP-hard, so the MIP model is not expected to be solved for extremely large sizes within a reasonable (i.e., polynomially-bounded) CPU time. Hence, by exploiting the features of the problem, two metaheuristic algorithms are developed, i.e., a fast discrete particle swarm optimization and a genetic algorithm. Finally, we present computational results to analyze and verify the solutions obtained. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Batch delivery branch and bound algorithm Discrete particle swarm optimization algorithm Genetic algorithm Maximum tardiness Release time

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Load Control Problems in Direct Current Distribution Networks: Optimality, Equilibrium of Games

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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 2020年第2期28卷 347-360页

作者： Zou, Suli Ma, Zhongjing Liu, Shan BIT Sch Automat Beijing 100081 Peoples R China BIT Natl Key Lab Complex Syst Intelligent Control & D Beijing 100081 Peoples R China

Due to the promising development of direct current (dc) distribution networks, we focus on the demand-side management (DSM) problems which aim at the minimization of operational costs in dc distribution networks. Based on the established voltage model of power electronic loads, we formulate a DSM optimization problem that coordinates the bus voltage by minimizing the system cost, and the underlying optimization problem is nonconvex. In order to solve this nonconvex problem, we first reformulate it as a difference of convex programming problem, and then propose a novel algorithm based on branch and bound to implement the optimal solution. It is shown that the system is guaranteed to converge to the global optimum under the proposed method. As demonstrated with numerical examples, we analyze the convergence and global optimality of the proposed method, and discuss the computational complexity and scalability with respect to the size of distribution networks. Moreover, in case each of individual loads can make its own decisions by itself, the underlying optimization problem is implemented in the context of the noncooperative game. The existence of the Nash equilibrium is verified and demonstrated through simulation results.

关键词： Optimization Games Load modeling Power electronics Resistance Programming Convergence branch and bound algorithm dc distribution networks demand-side management (DSM) global optimality Nash equilibrium (NE) nonconvex optimization power electronic loads (PELs)

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Spacecraft trajectory planning with avoidance constraints using mixed-integer linear programming

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2002年第4期25卷 755-764页

作者： Richards, A Schouwenaars, T How, JP Feron, E MIT Space Syst Lab Cambridge MA 02139 USA MIT Informat & Decis Syst Lab Cambridge MA 02139 USA

A method tar finding fuel-optimal trajectories for spacecraft subjected to avoidance requirements is introduced. These include avoidance of collisions with obstacles or other vehicles and prevention of thruster plumes from one spacecraft impinging on another spacecraft. The necessary logical constraints for avoidance are appended to a fuel-optimizing linear program by including binary variables in the optimization. The resulting problem is a mixed-integer linear program (MILP) that can be solved using available software. The logical constraints can also be used to express the configuration requirements for maneuvers where only the final relative alignment of the vehicles is important and the assignment of spacecraft within the fleet is not specified. The collision avoidance, trajectory optimization, and fleet assignment problems can be combined into a single MILE to obtain the optimal solution for these maneuvers. The MILE problem formulation, including these various avoidance constraints, is presented, and then several examples of their application to spacecraft maneuvers, including reconfiguration of a satellite formation and close inspection of the International Space Station by a microsatellite, are shown. These examples clearly show that the trajectory design methods presented are particularly well suited to proposed formation flying missions that involve multiple vehicles operating in close proximity.

关键词： Mixed Integer Linear Programming Monolithic Satellite ISS Trajectory Optimization Linear Programming Spacecraft Trajectories Spacecraft Maneuvers Thruster Plumes Path Planning branch and bound algorithm

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