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A Genetic algorithm with New Local Operators for Multiple Traveling Salesman Problems

INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2018年第1期11卷 692-705页

作者： Lo, Kin-Ming Yi, Wei-Ying Wong, Pak-Kan Leung, Kwong-Sak Leung, Yee Mak, Sui-Tung Chinese Univ Hong Kong Dept Comp Sci & Engn Hong Kong Hong Kong Peoples R China Chinese Univ Hong Kong Inst Future Cities Hong Kong Hong Kong Peoples R China Univ Southampton Dept Elect & Comp Sci Univ Rd Southampton SO17 1BJ Hants England

Multiple Traveling Salesman Problem (MTSP) is able to model and solve various real-life applications such as multiple scheduling, multiple vehicle routing and multiple path planning problems, etc. While Traveling Salesman Problem (TSP) focuses on searching a path of minimum traveling distance to visit all cities exactly once by one salesman, the objective of the MTSP is to find m paths for m salesmen with a minimized total cost - the sum of traveling distances of all salesmen through all of the respective cities covered. They have to start from a designated depot which is the departing and returning location of all salesmen. Since the MTSP is a NP-hard problem, a new effective Genetic algorithm with Local operators (GAL) is proposed in this paper to solve the MTSP and generate high quality solution within a reasonable amount of time for real-life applications. Two new local operators, branch and bound (BaB) and Cross Elimination (CE), are designed to speed up the convergence of the search process and improve the solution quality. Results demonstrate that GAL finds a better set of paths with a 9.62% saving on average in cost comparing to two existing MTSP algorithms.

关键词： Multiple Traveling Salesman Problem Genetic algorithm branch and bound algorithm Local operators

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Rebalancing the assembly lines: exact solution approaches

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2017年第20期55卷 5991-6010页

作者： Sanci, Ece Azizoglu, Meral Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA Middle East Tech Univ Dept Ind Engn Ankara Turkey

In this study, we consider an assembly line rebalancing problem with disruptions caused by workstation breakdowns or shutdowns. After the disruption, we aim to find a rebalance so as to catch the trade-off between the efficiency measure of cycle time and stability measure of number of tasks assigned to different workstations in the original and new balances. Our aim is to generate all nondominated objective vectors with respect to the efficiency and stability measures. We develop two optimisation algorithms: a Mixed Integer Linear Programming-based algorithm and a branch and bound algorithm. The results of our experiments have shown the favourable performances of both algorithms and the superiority of the branch and bound algorithm.

关键词： assembly lines rebalancing mixed integer linear programming branch and bound algorithm nondominated objective vectors

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Signed Clique Search in Signed Networks: Concepts and algorithms

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2021年第2期33卷 710-727页

作者： Li, Ronghua Dai, Qiangqiang Qin, Lu Wang, Guoren Xiao, Xiaokui Yu, Jeffrey Xu Qiao, Shaojie Beijing Inst Technol Beijing 100081 Peoples R China Univ Technol Sydney Ultimo NSW 2007 Australia Natl Univ Singapore Singapore 119077 Singapore Chinese Univ Hong Kong Shatin Hong Kong Peoples R China Chengdu Univ Informat Technol Chengdu 610225 Sichuan Peoples R China

Mining cohesive subgraphs from a network is a fundamental problem in network analysis. Most existing cohesive subgraph models are mainly tailored to unsigned networks. In this paper, we study the problem of seeking cohesive subgraphs in a signed network, in which each edge can be positive or negative, denoting friendship or conflict, respectively. We propose a novel model, called maximal (alpha, k)-clique, that represents a cohesive subgraph in signed networks. Specifically, a maximal (alpha, k)-clique is a clique in which every node has at most k negative neighbors and at least inverted right perpendicular alpha kinverted left perpendicular positive neighbors (alpha >= 1). We show that the problem of enumerating all maximal (alpha, k)-cliques in a signed network is NP-hard. To enumerate all maximal (alpha, k)-cliques efficiently, we first develop an elegant signed network reduction technique to significantly prune the signed network. Then, we present an efficient branch and bound enumeration algorithm with several carefully-designed pruning rules to enumerate all maximal (alpha, k)-cliques in the reduced signed network. In addition, we also propose an efficient algorithm with three novel upper-bounding techniques to find the maximum (alpha, k)-clique in a signed network. The results of extensive experiments on five large real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms.

关键词： Signed clique signed network maximal clique enumeration branch and bound algorithm

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Mean-variance portfolio optimal problem under concave transaction cost

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期174卷 1-12页

作者： Xue, HG Xu, CX Feng, ZX Xi An Jiao Tong Univ Fac Sci Sch Econ & Finance Xian 710049 Peoples R China Xi An Jiao Tong Univ Fac Sci Xian 710049 Peoples R China Xi An Jiao Tong Univ JinHe Ctr Econ Res Xian 710049 Peoples R China

In this paper, the classical mean-variance portfolio model is modified for calculating a globally optimal portfolio under concave transaction costs. A non-decreasing concave function is employed to approximate origin transaction cost function. The resulting model is a. D-C (difference of two convex functions) programming and a branch and bound algorithm is designed to solve the problem. A series Of numerical experiments on the model is presented. The history data of nine stocks in Shan Xi province is used in experiments, and efficient frontiers generated from the resulting model with different limitations on investments are presented to show the effect of the model and the efficiency of the algorithm solving the model. (c) 2005 Elsevier Inc. All rights reserved.

关键词： mean-variance concave transaction cost globally optimal portfolio branch and bound algorithm efficient frontier

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Fuzzy Stochastic Capacitated Vehicle Routing Problem and Its Applications

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2022年第3期24卷 1478-1490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

This paper considers Capacitated Vehicle Routing Problem (CVRP) in an imprecise and random environment. The deterministic version of the problem deals with finding a set of routes in such a way that the demand of all the customers present in the network are satisfied and the cost incurred in performing these operations comes out to be a minimum. In practical life situations, problems are not always defined in crisp form. Phenomena like randomness and impreciseness are quite natural to arise in real life. This work presents CVRP in such a mixed environment, such type of CVRP may be called as Fuzzy Stochastic Capacitated Vehicle Routing Problem. In this work, the demands of the customers are assumed to be stochastic and are revealed only when a vehicle arrives at the customer location. Moreover, the edge weights represent time required to traverse the edge and hence are both imprecise and random in nature. Factors like traffic conditions, weather conditions, are responsible for the random nature of the edge weights and the varying speed of the vehicle is responsible for impreciseness. Thus, the work presents CVRP with stochastic demands and stochastic and imprecise travel times. In this paper, an expectation-based approach has been used to deal with the randomness of edge weights. A two-stage model is used to solve the problem where the first stage corresponds to finding an optimal tour and recourse actions are planned in the second stage. A procedure based on branch and bound algorithm has been used to find minimum cost route. A small numerical example is presented to explain the working of the method proposed and the proposed solution approach is further tested on modified fuzzy versions of some benchmarks datasets.

关键词： Transportation and logistics Capacitated vehicle routing problem branch and bound algorithm Network Triangular fuzzy number

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Optimization of a long-short portfolio under nonconvex transaction cost

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2005年第1-2期32卷 115-132页

作者： Konno, H Akishino, K Yamamoto, R Chuo Univ Dept Ind & Syst Engn Hachioji Tokyo Japan

The purpose of this paper is to propose a practical branch and bound algorithm for solving a class of long-short portfolio optimization problem with concave and d.c. transaction cost and complementarity conditions on the variables. We will show that this algorithm can solve a problem of practical size and that the long-short strategy leads to a portfolio with significantly better risk-return structure compared with standard purchase only portfolio both in terms of ex-ante and ex-post performance.

关键词： portfolio theory long-short portfolio concave cost d.c. cost branch and bound algorithm global optimization

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SOLUTION APPROACHES TO LINEAR FRACTIONAL PROGRAMMING AND ITS STOCHASTIC GENERALIZATIONS USING SECOND ORDER CONE APPROXIMATIONS

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SIAM JOURNAL ON OPTIMIZATION 2021年第1期31卷 945-971页

作者： Kim, Cheolmin Mehrotra, Sanjay Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

We consider linear fractional programming problems in a form of which the linear fractional program and its stochastic and distributionally robust counterparts with finite support are special cases. We introduce a novel reformulation that involves differences of square terms in the constraint, subsequently using a piecewise linear approximation for the concave part. Using the resulting second order cone programs (SOCPs), we develop a solution algorithm in the branch and bound framework. Our method iteratively refines the piecewise linear approximations by dividing hyper-rectangles and solves SOCPs to obtain lower bounds for the sub-hyper-rectangles. We derive a bound on the optimality gap as a function of the approximation errors at the iterate and prove that the number of iterations to attain an epsilon-optimal solution is in the order of O(root epsilon). Numerical experiments show that the proposed algorithm scales better than state-of-the-art linear-programming-based algorithms and commercial solvers to solve linear fractional programs. Specifically, the proposed algorithm achieves two or more digits of accuracy in significantly less time than the time required by the known algorithms on medium to larger size problem instances. Experimental results with Wasserstein ambiguity sets reveal that our reformulation-based approach solves small size distributionally robust linear fractional programs, with the cardinality of support up to 25.

关键词： distributionally robust optimization linear fractional programming second order cone approximations branch and bound algorithm convergence analysis

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A simultaneous diagonalization based SOCP relaxation for portfolio optimization with an orthogonality constraint

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2023年第1期85卷 247-261页

作者： Xu, Zhijun Zhou, Jing Zhejiang Univ Technol Coll Sci Hangzhou 310023 Peoples R China

The portfolio rebalancing with transaction costs plays an important role in both theoretical analyses and commercial applications. This paper studies a standard portfolio problem that is subject to an additional orthogonality constraint guaranteeing that buying and selling a same security do not occur at the same time point. Incorporating the orthogonality constraint into the portfolio problem leads to a quadratic programming problem with linear complementarity constraints. We derive an enhanced simultaneous diagonalization based second order cone programming (ESDSOCP) relaxation by taking advantage of the feature that the objective and constraint matrices are commutative. The ESDSOCP relaxation has lower computational complexity than the semi-definite programming (SDP) relaxation, and it is proved to be as tight as the SDP relaxation. It is worth noting that the original simultaneous diagonalization based second order cone programming relaxation (SDSOCP) is only guaranteed to be as tight as the SDP relaxation on condition that the objective matrix is positive definite. Note that the objective matrix in this paper is positive semidefinite (while not positive definite), thus the ESDSOCP relaxation outperforms the original SDSOCP relaxation. We further design a branch and bound algorithm based on the ESDSOCP relaxation to find the global optimal solution and computational results illustrate the effectiveness of the proposed algorithm.

关键词： Portfolio optimization Second order cone programming relaxation Semi-definite programming relaxation branch and bound algorithm Simultaneous diagonalization Orthogonality constraint

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Optimal parallel machines scheduling with machine availability and eligibility constraints

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2008年第1-2期36卷 132-139页

作者： Sheen, Gwo-Ji Liao, Lu-Wen Lin, Cheng-Feng Natl Cent Univ Inst Ind Management Tao Yuan 32001 Taiwan

In reality, the machine might become unavailable due to machine breakdowns or various inevitable reasons, and machine might have different capability to processing job. Motivated by this, we consider the problem of scheduling n non-preemptive and independent jobs on m identical machines incorporating machine availability and eligibility constraints while minimizing the maximum lateness. Each machine is capable of processing at specific availability intervals. We develop a branch and bound algorithm applying several immediate selection rules for solving this scheduling problem.

关键词： parallel machine scheduling availability constraint eligibility constraint maximum lateness branch and bound algorithm

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On solving nonconvex optimization problems by reducing the duality gap

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JOURNAL OF GLOBAL OPTIMIZATION 2005年第3期32卷 349-365页

作者： Tuy, H Inst Math Hanoi 10307 Vietnam

Lagrangian bounds, i.e. bounds computed by Lagrangian relaxation, have been used successfully in branch and bound bound methods for solving certain classes of nonconvex optimization problems by reducing the duality gap. We discuss this method for the class of partly linear and partly convex optimization problems and, incidentally, point out incorrect results in the recent literature on this subject.

关键词： branch and bound algorithm convergence conditions dual bound Lagrangian bound partly convex programming partly linear

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