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A comparative study of suboptimal branch and bound algorithms

INFORMATION SCIENCES 2014年 278卷 545-554页

作者： Nakariyakul, Songyot Thammasat Univ Dept Elect & Comp Engn Amphur Klongluang 12120 Pathumthani Thailand

The branch and bound algorithm is widely known as an efficient approach for selecting optimal feature subsets. If the optimality of the solution is allowed to be compromised, it is possible to further improve the search speed of the branch and bound algorithm. This paper studies the look-ahead search strategy which can eliminate many solutions deemed to be suboptimal early in the branch and bound search. We propose ways to incorporate the look-ahead search scheme into four major branch and bound algorithms, namely the basic branch and bound algorithm, the ordered branch and bound algorithm, the fast branch and bound algorithm, and the adaptive branch and bound algorithm. A comparative study of the look-ahead scheme in terms of the computational cost and the solution quality on these suboptimal branch and bound algorithms is carried out on real data sets. Furthermore, we test the feasible use of suboptimal branch and bound algorithms on a high-dimensional data set and compare its performance with other well-known suboptimal feature selection algorithms. (C) 2014 Elsevier Inc. All rights reserved.

关键词： branch and bound algorithm Dimensionality reduction Feature selection High dimensionality Look-ahead search strategy Suboptimal solution

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Multi-objective optimization in a finite time thermodynamic method for dish-Stirling by branch and bound method and MOPSO algorithm

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Frontiers in Energy 2020年第3期14卷 649-665页

作者： Mohammad Reza NAZEMZADEGAN Alibakhsh KASAEIAN Somayeh TOGHYANI Mohammad Hossein AHMADI R.SAIDUR Tingzhen MING Department of Renewable Energies Faculty of New Science and TechnologiesUniversity of TehranTehran***Iran Faculty of Mechanical Engineering and Mechatronic Shahrood University of TechnologyShahrood ***Iran Faculty of Science and Technology Sunway UniversityNo.5Jalan UniversitiBandar Sunway47500 Petaling JayaMalaysia Department of Engineering Lancaster UniversityLancasterLAI 4YWUK School of Civil Engineering and Architecture Wuhan University of TechnologyWuhan 430070China

There are various analyses for a solar system with the dish-Stirling *** of those analyses is the finite time thermodynamic analysis by which the total power of the system can be obtained by calculating the process *** this study,the convection and radiation heat transfer losses from collector surface,the conduction heat transfer between hot and cold cylinders,and cold side heat exchanger have been *** this investigation,four objective functions have been optimized simultaneously,including power,efficiency,entropy,and economic *** addition to the fourobjective optimization,three-objective,two-objective,and single-objective optimizations have been done on the dish-Stirling *** algorithm of multi-objective particle swarm optimization(MO P S O)with post-expression of preferences is used for multi-objective optimizations while the branch and bound algorithm with pre-expression of preferences is used for single-objective and multi-objective *** the case of multi-objective optimizations with post-expression of preferences,Pareto optimal front are obtained,afterward by implementing the fuzzy,LINMAP,and TOPSIS decision making algorithms,the single optimum results can be *** comparison of the results shows the benefits of MOPSO in optimizing dish Stirling finite time thermodynamic equations.

关键词： dish-Stirling finite time model branch and bound algorithm multi-objective particle swann optimization(MOPSO)

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A branch-and-bound-based solution method for solving vehicle routing problem with fuzzy stochastic demands

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SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2021年第4期46卷 1-17页

作者： Singh, V. P. Sharma, Kirti Chakraborty, Debjani VNIT Nagpur Dept Math Nagpur Maharashtra India IIT Kharagpur Dept Math Kharagpur W Bengal India

In this paper, a capacitated vehicle routing problem (CVRP) with fuzzy stochastic demands has been presented. Discrete fuzzy random variables have been used to represent the demands of the customers. The objective of CVRP with fuzzy stochastic demands is to obtain a set of routes that originates as well as terminates at the source node and while traversing the route, the demands of all the customers present in the network are satisfied. The task here is to carry out all these operations with minimum cost. CVRP in imprecise and random environment has been considered here, and an a priori route construction technique has been adopted for which branch and bound algorithm has been used. The recourse policy used in this work is reactive, i.e. recourse to depot is done only upon the occurrence of the failure. The delivery policy considered here is unsplit delivery. Demands of the customers are the only source of impreciseness and randomness in the problem under construction. Parametric graded mean integration representation (PGMIR) method has been used for the comparison purposes, whenever required. A numerical example with four customers has been solved to present the proposed methodology.

关键词： Vehicle routing problem branch and bound algorithm discrete fuzzy random variable fuzzy stochastic demands

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Design of space thrusters: a topology optimization problem solved via a branch and bound method

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JOURNAL OF GLOBAL OPTIMIZATION 2016年第2期64卷 273-288页

作者： Sanogo, Satafa Messine, Frederic Univ Toulouse Laplace CNRS UMR5213 Toulouse INP F-31071 Toulouse France

In this paper, an exact branch and bound algorithm has been developed to solve a difficult global optimization problem concerning the design of space thrusters. This optimization problem is hard to solve mainly because the objective function to be minimized is implicit and must be computed by using a Finite Element method code. In a previous paper, we implement a method based on local search algorithms and we then proved that this problem is non convex yielding a strong dependency between the obtained local solution and the starting points. In this paper, by taking into account a monotonicity hypothesis that we validated numerically, we provide properties making it possible the computation of bounds. This yields the development of a topology optimization branch and bound code. Some numerical examples show the efficiency of this new approach.

关键词： Maxwell equations Inverse problem PDE-constrained optimization Topology optimization SIMP method branch and bound algorithm

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Path-Planning with Avoidance Using Nonlinear branch-and-bound Optimization

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2009年第2期32卷 384-394页

作者： Eele, Alison Richards, Arthur Univ Bristol Dept Aerosp Engn Bristol BS8 1TR Avon England

This paper describes a novel method for finding optimal trajectories for a vehicle constrained to avoid fixed obstacles. The key property of the method is that it provides globally optimal solutions while retaining the full nonlinear dynamics model. Applications for the method include guidance of unmanned aerial vehicles, air traffic control,and robot path planning. The core concept is the direct application of branch-and-bound optimization to find guaranteed, globally optimal solutions to nonconvex problems. The method tailors the branch-and-bound approach specifically for avoidance problems by exploiting two new ideas: first, using a geometric branching strategy based on the decision between passing an obstacle clockwise or counterclockwise;and second, solving the resulting subproblems by constructing simple solutions on each chosen "side" and using them to initialize an interior-point optimization. The algorithm is refined by comparing nine geometric branching strategies. The solution time of the method depends on the choice of branching strategy, which determines how the solution tree is explored. A good strategy is one requiring fewer tree branches to be enumerated before the global optimal is found. The best of these branching strategies has been compared with an existing mixed-integer linear programming approach and demonstrated a significant improvement on mixed-integer linear programming solve times.

关键词： Path Planning Mixed Integer Linear Programming Nonlinear Dynamics Uninhabited Aerial Vehicle Obstacle Avoidance branch and bound algorithm Air Traffic Management Air Traffic Control Optimization algorithm Vehicle Trajectories

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bounding vertex coloring by truncated Multistage branch and bound

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NETWORKS 2004年第4期44卷 231-242页

作者： Caramia, M Dell'Olmo, P Ist Applicaz Calcolo M Picone I-00161 Rome Italy Univ Roma La Sapienza Diparimento Stat Probabil & Stat Applicate I-00185 Rome Italy

In this article we design a truncated enumerative algorithm based on branch and bound rules embedded in a multistage scheme that allows iterative visits of subgraphs. The algorithm is designed to find lower bounds on the chromatic number of graphs, and, by means of simple coloring extension rules, it is often capable of finding optimal solutions. In this issue we obtain a very promising result: our algorithm was able to solve benchmarks DSJC125_5, DSJC125_9, DSJC250_1, DSJR500_1c, and DSJR500_5, which had not previously been solved. Furthermore, we show how our method can be employed in finding upper bounds on the chromatic number, and thus, we compare the upper bound-lower bound gaps so obtained with those achieved by known exact algorithms. The comparison highlights that in more than half of the tested benchmarks the gap obtained by our algorithm was lower than that obtained by a recent branch and cut method and by the well-known DSATUR algorithm. To provide a deeper analysis we finally compare the upper bounds found by the proposed algorithm on the same benchmarks with the best heuristic solutions known in the open literature. Also, in this case, the proposed truncated branch and bound was often able to outperform these heuristic solutions. (C) 2004 Wiley Periodicals, Inc.

关键词： branch and bound algorithm chromatic number combinatorial optimization heuristic lower bound

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Type-II transfer line Balancing problem - A branch and bound approach

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COMPUTERS & INDUSTRIAL ENGINEERING 2024年 198卷

作者： Telemeci, Yasin Ersin Azizoglu, Meral Middle East Tech Univ Dept Ind Eng TR-06800 Ankara Turkiye

In this study, we consider the Type II Transfer Line Balancing problem, aiming to minimize the cycle time by assigning operations to blocks and blocks to workstations. We develop a mixed integer programming model and propose a branch and bound algorithm for exact solutions. Our algorithm efficiency is enhanced through lower and upper bounds. Computational results demonstrate the satisfactory performance of the model and branch and bound algorithm for moderate-sized problem instances.

关键词： Transfer Lines Type-II Transfer Line Balancing Mathematical Model branch and bound algorithm

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A branch and bound method for the line balancing problem in U-shaped assembly lines with equipment requirements

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JOURNAL OF MANUFACTURING SYSTEMS 2015年 36卷 46-54页

作者： Ogan, Dilek Azizoglu, Meral ASELSAN Elect Co Ankara Turkey Middle E Tech Univ Dept Ind Engn TR-06800 Ankara Turkey

In this study we consider a U-shaped assembly line balancing problem where each task uses a specified set of equipments and each type of equipment has a specified cost. Our problem is to assign the tasks together with their equipments to the workstations so as to minimize the total equipment cost. We formulate the problem as a mixed integer linear programming model that is capable of solving small sized instances. We propose a branch and bound algorithm that uses efficient precedence relations and lower bounds. We find that the algorithm is able to solve moderate sized problem instances in reasonable times. (C) 2015 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

关键词： U-shaped assembly line Equipment requirement branch and bound algorithm

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branch-and-bound-Based Local Search Heuristics for Train Timetabling on Single-Track Railway Network

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NETWORKS & SPATIAL ECONOMICS 2017年第1期17卷 1-39页

作者： Karoonsoontawong, Ampol Taptana, Apisak King Mongkuts Univ Technol Thonburi Fac Engn Dept Civil Engn 126 Pracha Utid Rd Bangmodthung Khrubangkok 10140 Thailand

The modified formulation and two branch-and-bound-based local search heuristic algorithms for train timetabling in single-track railway network in the planning application are proposed. The original local search heuristic is modified such that when a neighbor of a currently tested resolved conflict for improvement is evaluated, the depth-first search branch-and-bound algorithm is employed with two branching rules: least-lower-bound and least-delay-time. The detailed implementation of the proposed heuristic algorithms are described, including the neighborhood definitions of overtaking and crossing conflicts, the procedure to detect overtaking and crossing conflicts, and a recursive procedure for the depth-first search branch-and-bound algorithm. The proposed heuristic algorithms, the original heuristic, the equivalent manual solution method and the exact solution method are compared using a toy problem and four problems (26-train, 50-train, 76-train and 108-train) in the Thailand Southern line railway network, which consisted of 266 single-track segments, 15 double-track segments, 282 stations/sidings, and total distance of 1577 km. The proposed heuristic algorithm with the least-lower-bound branching rule outperforms the other heuristics in terms of the solution quality with up to 2.827 % improvement over the equivalent manual solution method and less than 8 % optimality gap. The proposed heuristic algorithms require longer time to terminate than the original heuristic. The proposed heuristic algorithm with the least-lower-bound branching rule converges faster than that with the least-delay-time branching rule in all test problems. Based on the empirical results, the proposed heuristic algorithms are solvable in polynomial time. Furthermore, the proposed heuristic algorithm with the least-lower-bound branching rule is enhanced by embedding a uniform sampling strategy, and it is found that the total CPU time can be saved by about 50 % with marginally worse solution q

关键词： Train timetabling Local search heuristic branch and bound algorithm

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OPTIMAL MATERIAL SELECTION USING branch-AND-bound TECHNIQUES

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AIAA JOURNAL 1995年第2期33卷 340-347页

作者： SEPULVEDA, AE University of California Los Angeles Los Angeles California 90024

A methodology for structural synthesis is presented in which the optimal material selection for the truss structures is treated in terms of (0, 1) variables. Structural member sizes and material selection variables are treated simultaneously as design variables. Optimization is carried out by generating and solving a sequence of explicit approximate problems using a branch and bound strategy. Intermediate design variables and intermediate response quantities are used to enhance the quality of the approximate design problems. Numerical results for example problems are presented to illustrate the efficiency of the design procedure set forth.

关键词： Trusses Structural Members Structural Synthesis branch and bound algorithm Structural Element Nonlinear Programming Dynamic Displacements Young's Modulus Structural Optimization Compressive Stress

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