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Fuzzy Stochastic Capacitated Vehicle Routing Problem and Its Applications

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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MULTIPLE algorithm SOLUTION TO THE ARTIFICIAL-INTELLIGENCE DESIGN CHALLENGE

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1988年第5期11卷 397-402页

作者： DOTY, KW The Aerospace Corporation El Segundo California

This paper responds to the Artificial Intelligence Design Challenge at the 1987 AIAA Guidance, Navigation, and Control Conference. It describes a computer program that solves a variation of the classical traveling salesman problem that is representative of problems encountered in complex guidance and control systems. The problem is to find a tour connecting some or all of 11 cities that maximizes the total value of the cities visited while meeting a travel budget constraint. The solution procedure used was to construct several candidate tours using a variety of approaches, then adjust the highest-value tour found by solving the traveling salesman problem to find the optimal city ordering. An efficient bounding procedure was used to reduce the number of computations required to evaluate the stochastic budget constraint. The program consistently produced in a small amount of time the best answers known on 25 data sets designed to test the program's robustness.

关键词： Artificial Intelligence Computer Programs Control Systems Perturbation Method Computing Probability Distribution 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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Worst-case analysis of the X-38 crew return vehicle flight control system

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2001年第2期24卷 261-269页

作者： Shin, JY Balas, GJ Packard, AK Univ Minnesota Dept Aerosp Engn & Mech Minneapolis MN 55455 USA Univ Calif Berkeley Dept Mech Engn Berkeley CA 94704 USA

A linear fractional transformation (LFT model of the linearized equation of the lateral-directional axes of the X-38 crew return vehicle is developed to facilitate the analysis of flight control systems. The LFT model represents uncertainty in nine aerodynamic stability derivatives at a given flight condition with frequency-domain performance specifications. The X-38 LFT model combined with a controller at specific Right conditions is used to determine the aerodynamic coefficients that result in the worst-case performance and gain/phase margin of the closed-loop system. The,objective is to verify that a given controller remains stable and achieves desired performance objectives for all predefined aerodynamic variations at select operating conditions along its flight trajectory.

关键词： Crew Return Vehicle Flight Control System Aerodynamic Stability Closed Loop System Digital to Analog Converters Control Systems Ailerons International Space Station branch and bound algorithm Johnson Space Center

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Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2014年 59卷 22-44页

作者： Yang, Lixing Zhou, Xuesong Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China Arizona State Univ Sch Sustainable Engn & Built Environm Tempe AZ 85287 USA

Using a sample-based representation scheme to capture spatial and temporal travel time correlations, this article constructs an integer programming model for finding the a priori least expected time paths. We explicitly consider the non-anticipativity constraint associated with the a priori path in a time-dependent and stochastic network, and propose a number of reformulations to establish linear inequalities that can be easily dualized by a Lagrangian relaxation solution approach. The relaxed model is further decomposed into two sub-problems, which can be solved directly by using a modified label-correcting algorithm and a simple single-value linear programming method. Several solution algorithms, including a sub-gradient method, a branch and bound method, and heuristics with additional constraints on Lagrangian multipliers, are proposed to improve solution quality and find approximate optimal solutions. The numerical experiments investigate the quality and computational efficiency of the proposed solution approach. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： A priori least expected time path Time-dependent traffic network Lagrangian relaxation branch and bound algorithm

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The design of capacitated facility networks for long term care service

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COMPUTERS & INDUSTRIAL ENGINEERING 2015年 89卷 177-185页

作者： Song, Byung Duk Ko, Young Dae Hwang, Hark Korea Adv Inst Sci & Technol Dept Ind & Syst Engn Daejeon 305701 South Korea Deloitte Touche Tohmatsu Ltd Deloitte Consulting Data Analyt Grp Seoul 150945 South Korea

Life expectancy is going up and the demand of long term care facilities is increasing in most countries. This study deals with designing problem of facility networks for long-term care services in a city consisting of a number of regions. Assuming that in each region a candidate site for long-term care facility exists, we seek to identify regions where opening of a long-term care facility is desirable and also determine the type of new facility. For the problem, an integer programming model is formulated with the objective of minimizing the total construction cost. The closest assignment rule is adopted to reflect the preference of patient in choosing long term care facility by assigning patient to an open facility closest from his home. To solve the model, we develop a branch and bound algorithm for exact solution and a genetic algorithm to solve large sized problem. The validity of the mathematical model and the proposed algorithms are illustrated through a number of problem instances. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Long term care services Closest assignment rule branch and bound algorithm Genetic algorithm

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Improved generation of minimal addition chains

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COMPUTING 2006年第2期78卷 161-172页

作者： Bahig, Hatem M. Ain Shams Univ Fac Sci Dept Math Comp Sci Cairo Egypt

An addition chain for a natural number n is a sequence 1 = a(0) < a(1) <. . . a(r) = n of numbers such that for each 0 < i <= r, a(i) = a(j) + a(k) for some 0 <= k <= j < i. An improvement by a fa... 详细信息

An addition chain for a natural number n is a sequence 1 = a(0) < a(1) <. . . a(r) = n of numbers such that for each 0 < i <= r, a(i) = a(j) + a(k) for some 0 <= k <= j < i. An improvement by a factor of 2 in the generation of all minimal (or one) addition chains is achieved by finding sufficient conditions for star steps, computing what we will call nonstar lower bound in a minimal addition chain and omitting the sorting step.

关键词： addition chain branch and bound algorithm nonstar lower bound sorting

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An algorithm for the capacitated, multi-commodity multi-period facility location problem

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COMPUTERS & OPERATIONS RESEARCH 2001年第5期28卷 411-427页

作者： Canel, C Khumawala, BM Law, J Loh, A Univ N Carolina Dept Prod & Decis Sci Wilmington NC 28403 USA Univ Houston Dept Informat & Decis Sci Houston TX 77204 USA Chinese Univ Hong Kong Dept Decis Sci & Managerial Econ Shatin Hong Kong Peoples R China Univ Houston Dept Ind Engn Houston TX 77204 USA

There are substantial number of exact and heuristic solution methods proposed for solving the facilities location problems. This paper develops an algorithm to solve the capacitated, multi-commodity, multiperiod (dynamic), multi-stage facility location problem. The literature on such composite facility location problem is still sparse, The proposed algorithm consists of two parts: in the first part branch and bound is used to generate a list of candidate solutions for each period and then dynamic programming is used to find the optimal sequence of configurations over the multi-period planning horizon. bounds commonly known in the location literature as delta and omega are used extensively to effectively reduce the total number of transshipment subproblems needed to be solved. The proposed algorithm is particularly effective when the facility reopening and closing costs are relatively significant in the multi-period problem. An example problem is included to illustrate the proposed solution procedure.

关键词： facility location branch and bound algorithm

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Bilevel integer programming on a Boolean network for discovering critical genetic alterations in cancer development and therapy

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第2期300卷 743-754页

作者： Moon, Kyungduk Lee, Kangbok Chopra, Sunil Kwon, Steve Pohang Univ Sci & Technol Dept Ind & Management Engn Pohang 37673 South Korea Northwestern Univ Kellogg Sch Management Evanston IL 60208 USA Holy Name Med Ctr Teaneck NJ 07666 USA

Boolean network is a modeling tool that describes a dynamic system with binary variables and their logical transition formulas. Recent studies in precision medicine use a Boolean network to discover critical genetic alterations that may lead to cancer or target genes for effective therapies to individuals. In this paper, we study a logical inference problem in a Boolean network to find all such critical genetic alterations in a minimal (parsimonious) way. We propose a bilevel integer programming model to find a single minimal genetic alteration. Using the bilevel integer programming model, we develop a branch and bound algorithm that effectively finds all of the minimal alterations. Through a computational study with eleven Boolean networks from the literature, we show that the proposed algorithm finds solutions much faster than the state-of-the-art algorithms in large data sets. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Bioinformatics Boolean network Bilevel programming branch and bound algorithm

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Weapon-Target Assignment algorithm for Simultaneous and Sequenced Arrival

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2018年第11期41卷 2361-2373页

作者： Volle, Kyle Rogers, Jonathan Georgia Inst Technol Sch Mech Engn Atlanta GA 30332 USA

Weapon-target assignment is a multi-agent control problem in which each weapon is assigned to a target to minimize the expected survival value of the targets. In this work, a multi-objective version of the weapon-target assignment problem is considered in which the quality of an assignment is dependent on both the total effectiveness of the weapons assigned to each target and the relative timing of agents' arrival. Such timing constraints may be important in real-world scenarios in which a mission planner wishes to enforce an element of surprise on each target. Building on previous work, a new modified cost function is presented that couples weapon effectiveness and timing metrics into a combined cost. In cases where weapon-target closing speeds are limited to a certain range, this combined cost allows the inclusion of arrival time constraints in the assignment decision process. The performance of this new cost function is demonstrated through theoretical analysis and simulation. Results show that the proposed cost function balances the dual goals of optimizing effectiveness and arrival time considerations under closing speed limitations and that a user-defined tuning parameter can be used to adjust the priority of the dual goals of sequenced arrival and achieving the desired probability of kill.

关键词： Weapon Target Assignment algorithm Weapon Target Assignment branch and bound algorithm Monte Carlo Simulation algorithm Performance Optimization algorithm Mobile Robotic System Damage Assessment Annealing Computing

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