• Title/Summary/Keyword: Optimal Path Problem

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Optimal Straight Line Path of a Moving Facility (이동설비의 최적 직선 경로)

  • Sherali, Hanif D.
    • Journal of the Korean Operations Research and Management Science Society
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    • v.14 no.1
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    • pp.72-79
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    • 1989
  • In this paper we consider the problem of finding an optimal straight line path of moving facility which interacts with a set of existing facilities fixed within a given rectangular area. We present a simple algorithm for rectilinear metric which greatly improves the pervious method and also propose algorithms for Euclidean and squared Euclidean distances.

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A Study On Bi-Criteria Shortest Path Model Development Using Genetic Algorithm (유전 알고리즘을 이용한 이중목적 최단경로 모형개발에 관한 연구)

  • 이승재;장인성;박민희
    • Journal of Korean Society of Transportation
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    • v.18 no.3
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    • pp.77-86
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    • 2000
  • The shortest path problem is one of the mathematical Programming models that can be conveniently solved through the use of networks. The common shortest Path Problem is to minimize a single objective function such as distance, time or cost between two specified nodes in a transportation network. The sing1e objective model is not sufficient to reflect any Practical Problem with multiple conflicting objectives in the real world applications. In this paper, we consider the shortest Path Problem under multiple objective environment. Wile the shortest path problem with single objective is solvable in Polynomial time, the shortest Path Problem with multiple objectives is NP-complete. A genetic a1gorithm approach is developed to deal with this Problem. The results of the experimental investigation of the effectiveness of the algorithm are also Presented.

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OPTIMAL IMPACT ANGLE CONTROL GUIDANCE LAWS AGAINST A MANEUVERING TARGET

  • RYOO, CHANG-KYUNG
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.3
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    • pp.235-252
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    • 2015
  • Optimal impact angle control guidance law and its variants for intercepting a maneuvering target are introduced in this paper. The linear quadratic(LQ) optimal control theory is reviewed first to setup framework of guidance law derivation, called the sweep method. As an example, the inversely weighted time-to-go energy optimal control problem to obtain the optimal impact angle control guidance law for a fixed target is solved via the sweep method. Since this optimal guidance law is not applicable for a moving target due to the angle mismatch at the impact instant, the law is modified to three different biased proportional navigation(PN) laws: the flight path angle control law, the line-of-sight(LOS) angle control law, and the relative flight path angle control law. Effectiveness of the guidance laws are verified via numerical simulations.

Rough Cut Tool Path Planning in Fewer-axis CNC Machinig (저축 CNC 환경에서의 황삭가공)

  • 강지훈;서석환;이정재
    • Korean Journal of Computational Design and Engineering
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    • v.2 no.1
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    • pp.19-27
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    • 1997
  • This paper presents rough cut tool path planning for the fewer-axis machine consisting of a three-axis CNC machine and a rotary indexing table. In the problem dealt with in this paper, the tool orientation is "intermediately" changed, distinguished from the conventional problem where the tool orientation is assumed to be fixed. The developed rough cut path planning algorithm tries to minimize the number of tool orientation (setup) changes together with tool changes and the machining time for the rough cut by the four procedures: a) decomposition of the machining area based on the possibility of tool interference (via convex hull operation), b) determination of the optimal tool size and orientation (via network graph theory and branch-and bound algorithm), c) generation of tool path for the tool and orientation (based on zig-zag pattern), and d) feedrate adjustment to maintain the cutting force at an operation level (based on average cutting force). The developed algorithms are validated via computer simulations, and can be also used in pure fiveaxis machining environment without modification.

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AN APPROACH FOR SOLVING OF A MOVING BOUNDARY PROBLEM

  • Basirzadeh, H.;Kamyad, A.V.
    • Journal of applied mathematics & informatics
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    • v.14 no.1_2
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    • pp.97-113
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    • 2004
  • In this paper we shall study moving boundary problems, and we introduce an approach for solving a wide range of them by using calculus of variations and optimization. First, we transform the problem equivalently into an optimal control problem by defining an objective function and artificial control functions. By using measure theory, the new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; then we obtain an optimal measure which is then approximated by a finite combination of atomic measures and the problem converted to an infinite-dimensional linear programming. We approximate the infinite linear programming to a finite-dimensional linear programming. Then by using the solution of the latter problem we obtain an approximate solution for moving boundary function on specific time. Furthermore, we show the path of moving boundary from initial state to final state.

SOLVING A SYSTEM OF THE NONLINEAR EQUATIONS BY ITERATIVE DYNAMIC PROGRAMMING

  • Effati, S.;Roohparvar, H.
    • Journal of applied mathematics & informatics
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    • v.24 no.1_2
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    • pp.399-409
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    • 2007
  • In this paper we use iterative dynamic programming in the discrete case to solve a wide range of the nonlinear equations systems. First, by defining an error function, we transform the problem to an optimal control problem in discrete case. In using iterative dynamic programming to solve optimal control problems up to now, we have broken up the problem into a number of stages and assumed that the performance index could always be expressed explicitly in terms of the state variables at the last stage. This provided a scheme where we could proceed backwards in a systematic way, carrying out optimization at each stage. Suppose that the performance index can not be expressed in terms of the variables at the last stage only. In other words, suppose the performance index is also a function of controls and variables at the other stages. Then we have a nonseparable optimal control problem. Furthermore, we obtain the path from the initial point up to the approximate solution.

An Optimal Path Generation Method considering the Safe Maneuvering of UGV (무인지상차량의 안전주행을 고려한 최적경로 생성 방법)

  • Kwak, Kyung-Woon;Jeong, Hae-Kwan;Choe, Tok-Son;Park, Yong-Woon;Kwak, Yoon-Keun;Kim, Soo-Hyun
    • Journal of the Korea Institute of Military Science and Technology
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    • v.13 no.6
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    • pp.951-957
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    • 2010
  • An optimal path generation method considering the safety of UGV(Unmanned Ground Vehicle) is proposed and demonstrated through examples. Among various functions of UGV, real-time obstacle avoidance is a key issue to realize realistic scenario in FCS(Future Combat Systems). A two-dimensional narrow corridor environment is considered as a test field. For each step of UGV movement, two objectives are considered: One is to minimize the distance to the target and the other to maximize the distance to the nearest point of an obstacle. A weighted objective function is used in the optimization problem. Equality and inequality constraints are taken to secure the UGV's dynamics and safety. The weighting factors are controlled by a fuzzy controller which is constructed by a fuzzy rule set and membership functions. Simulations are performed for two cases. First the weighting factors are considered as constant values to understand the characteristics of the corresponding solutions and then as variables that are adjusted by the fuzzy controller. The results are satisfactory for realistic situations considered. The proposed optimal path generation with the fuzzy control is expected to be well applicable to real environment.

A NEW METHOD FOR SOLVING FUZZY SHORTEST PATH PROBLEMS

  • Kumar, Amit;Kaur, Manjot
    • Journal of applied mathematics & informatics
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    • v.30 no.3_4
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    • pp.571-591
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    • 2012
  • To the best of our knowledge, there is no method, in the literature, to find the fuzzy optimal solution of fully fuzzy shortest path (FFSP) problems i.e., shortest path (SP) problems in which all the parameters are represented by fuzzy numbers. In this paper, a new method is proposed to find the fuzzy optimal solution of FFSP problems. Kumar and Kaur [Methods for solving unbalanced fuzzy transportation problems, Operational Research-An International Journal, 2010 (DOI 10.1007/s 12351-010-0101-3)] proposed a new method with new representation, named as JMD representation, of trapezoidal fuzzy numbers for solving fully fuzzy transportation problems and shown that it is better to solve fully fuzzy transportation problems by using proposed method with JMD representation as compare to proposed method with the existing representation. On the same direction in this paper a new method is proposed to find the solution of FFSP problems and it is shown that it is also better to solve FFSP problems with JMD representation as compare to existing representation. To show the advantages of proposed method with this representation over proposed method with other existing representations. A FFSP problem solved by using proposed method with JMD representation as well as proposed method with other existing representations and the obtained results are compared.

Intelligent Optimal Route Planning Based on Context Awareness (상황인식 기반 지능형 최적 경로계획)

  • Lee, Hyun-Jung;Chang, Yong-Sik
    • Asia pacific journal of information systems
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    • v.19 no.2
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    • pp.117-137
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    • 2009
  • Recently, intelligent traffic information systems have enabled people to forecast traffic conditions before hitting the road. These convenient systems operate on the basis of data reflecting current road and traffic conditions as well as distance-based data between locations. Thanks to the rapid development of ubiquitous computing, tremendous context data have become readily available making vehicle route planning easier than ever. Previous research in relation to optimization of vehicle route planning merely focused on finding the optimal distance between locations. Contexts reflecting the road and traffic conditions were then not seriously treated as a way to resolve the optimal routing problems based on distance-based route planning, because this kind of information does not have much significant impact on traffic routing until a a complex traffic situation arises. Further, it was also not easy to take into full account the traffic contexts for resolving optimal routing problems because predicting the dynamic traffic situations was regarded a daunting task. However, with rapid increase in traffic complexity the importance of developing contexts reflecting data related to moving costs has emerged. Hence, this research proposes a framework designed to resolve an optimal route planning problem by taking full account of additional moving cost such as road traffic cost and weather cost, among others. Recent technological development particularly in the ubiquitous computing environment has facilitated the collection of such data. This framework is based on the contexts of time, traffic, and environment, which addresses the following issues. First, we clarify and classify the diverse contexts that affect a vehicle's velocity and estimates the optimization of moving cost based on dynamic programming that accounts for the context cost according to the variance of contexts. Second, the velocity reduction rate is applied to find the optimal route (shortest path) using the context data on the current traffic condition. The velocity reduction rate infers to the degree of possible velocity including moving vehicles' considerable road and traffic contexts, indicating the statistical or experimental data. Knowledge generated in this papercan be referenced by several organizations which deal with road and traffic data. Third, in experimentation, we evaluate the effectiveness of the proposed context-based optimal route (shortest path) between locations by comparing it to the previously used distance-based shortest path. A vehicles' optimal route might change due to its diverse velocity caused by unexpected but potential dynamic situations depending on the road condition. This study includes such context variables as 'road congestion', 'work', 'accident', and 'weather' which can alter the traffic condition. The contexts can affect moving vehicle's velocity on the road. Since these context variables except for 'weather' are related to road conditions, relevant data were provided by the Korea Expressway Corporation. The 'weather'-related data were attained from the Korea Meteorological Administration. The aware contexts are classified contexts causing reduction of vehicles' velocity which determines the velocity reduction rate. To find the optimal route (shortest path), we introduced the velocity reduction rate in the context for calculating a vehicle's velocity reflecting composite contexts when one event synchronizes with another. We then proposed a context-based optimal route (shortest path) algorithm based on the dynamic programming. The algorithm is composed of three steps. In the first initialization step, departure and destination locations are given, and the path step is initialized as 0. In the second step, moving costs including composite contexts into account between locations on path are estimated using the velocity reduction rate by context as increasing path steps. In the third step, the optimal route (shortest path) is retrieved through back-tracking. In the provided research model, we designed a framework to account for context awareness, moving cost estimation (taking both composite and single contexts into account), and optimal route (shortest path) algorithm (based on dynamic programming). Through illustrative experimentation using the Wilcoxon signed rank test, we proved that context-based route planning is much more effective than distance-based route planning., In addition, we found that the optimal solution (shortest paths) through the distance-based route planning might not be optimized in real situation because road condition is very dynamic and unpredictable while affecting most vehicles' moving costs. For further study, while more information is needed for a more accurate estimation of moving vehicles' costs, this study still stands viable in the applications to reduce moving costs by effective route planning. For instance, it could be applied to deliverers' decision making to enhance their decision satisfaction when they meet unpredictable dynamic situations in moving vehicles on the road. Overall, we conclude that taking into account the contexts as a part of costs is a meaningful and sensible approach to in resolving the optimal route problem.

Multiple Path Based Vehicle Routing in Dynamic and Stochastic Transportation Networks

  • Park, Dong-joo
    • Proceedings of the KOR-KST Conference
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    • 2000.02a
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    • pp.25-47
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    • 2000
  • In route guidance systems fastest-path routing has typically been adopted because of its simplicity. However, empirical studies on route choice behavior have shown that drivers use numerous criteria in choosing a route. The objective of this study is to develop computationally efficient algorithms for identifying a manageable subset of the nondominated (i.e. Pareto optimal) paths for real-time vehicle routing which reflect the drivers' preferences and route choice behaviors. We propose two pruning algorithms that reduce the search area based on a context-dependent linear utility function and thus reduce the computation time. The basic notion of the proposed approach is that ⅰ) enumerating all nondominated paths is computationally too expensive, ⅱ) obtaining a stable mathematical representation of the drivers' utility function is theoretically difficult and impractical, and ⅲ) obtaining optimal path given a nonlinear utility function is a NP-hard problem. Consequently, a heuristic two-stage strategy which identifies multiple routes and then select the near-optimal path may be effective and practical. As the first stage, we utilize the relaxation based pruning technique based on an entropy model to recognize and discard most of the nondominated paths that do not reflect the drivers' preference and/or the context-dependency of the preference. In addition, to make sure that paths identified are dissimilar in terms of links used, the number of shared links between routes is limited. We test the proposed algorithms in a large real-life traffic network and show that the algorithms reduce CPU time significantly compared with conventional multi-criteria shortest path algorithms while the attributes of the routes identified reflect drivers' preferences and generic route choice behaviors well.

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