scholarly journals Selected Multicriteria Shortest Path Problems: An Analysis of Complexity, Models and Adaptation of Standard Algorithms

2007 ◽  
Vol 17 (2) ◽  
pp. 269-287 ◽  
Author(s):  
Zbigniew Tarapata
Keyword(s):  
Mathematical Programming ◽  
Shortest Path ◽  
Optimization Problems ◽  
Weighted Graph ◽  
Path Selection ◽  
Shortest Path Problems ◽  
Grid Network ◽  
Graph Problems ◽  
Mathematical Programming Problems

Selected Multicriteria Shortest Path Problems: An Analysis of Complexity, Models and Adaptation of Standard AlgorithmsThe paper presents selected multicriteria (multiobjective) approaches to shortest path problems. A classification of multi-objective shortest path (MOSP) problems is given. Different models of MOSP problems are discussed in detail. Methods of solving the formulated optimization problems are presented. An analysis of the complexity of the presented methods and ways of adapting of classical algorithms for solving multiobjective shortest path problems are described. A comparison of the effectiveness of solving selected MOSP problems defined as mathematical programming problems (using the CPLEX 7.0 solver) and multi-weighted graph problems (using modified Dijkstra's algorithm) is given. Experimental results of using the presented methods for multicriteria path selection in a terrain-based grid network are given.

Note on “Optimal path selection approach for fuzzy reliable shortest path problem”

2020 ◽  
Vol 39 (5) ◽  
pp. 7653-7656
Author(s):  
Ranjan Kumar ◽  
SA Edalatpanah ◽  
Hitesh Mohapatra
Keyword(s):  
Shortest Path ◽  
Fuzzy Systems ◽  
Optimal Path ◽  
Vital Role ◽  
Path Selection ◽  
Shortest Path Problem ◽  
Shortest Path Problems ◽  
Fuzzy Environment ◽  
Selection Approach ◽  
Arc Lengths

There are different conditions where SPP play a vital role. However, there are various conditions, where we have to face with uncertain parameters such as variation of cost, time and so on. So to remove this uncertainty, Yang et al. [1] “[Journal of Intelligent & Fuzzy Systems, 32(1), 197-205”] have proposed the fuzzy reliable shortest path problem under mixed fuzzy environment and claimed that it is better to use their proposed method as compared to the existing method i.e., “[Hassanzadeh et al.; A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths, Mathematical and Computer Modeling, 57(2013) 84-99” [2]]. The aim of this note is, to highlight the shortcoming that is carried out in Yang et al. [1] article. They have used some mathematical incorrect assumptions under the mixed fuzzy domain, which is not true in a fuzzy environment.

scholarly journals Lagrange duality and saddle point optimality conditions for semi-infinite mathematical programming problems with equilibrium constraints

2019 ◽  
Vol 29 (4) ◽  
pp. 433-448
Author(s):  
Kunwar Singh ◽  
J.K. Maurya ◽  
S.K. Mishra
Keyword(s):  
Mathematical Programming ◽  
Saddle Point ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Mathematical Programming Problem ◽  
Dual Model ◽  
Equilibrium Constraints ◽  
Convexity Assumptions ◽  
Mathematical Programming Problems

In this paper, we consider a special class of optimization problems which contains infinitely many inequality constraints and finitely many complementarity constraints known as the semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC). We propose Lagrange type dual model for the SIMPEC and obtain their duality results using convexity assumptions. Further, we discuss the saddle point optimality conditions for the SIMPEC. Some examples are given to illustrate the obtained results.

scholarly journals Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1272
Author(s):  
Bogdana Stanojević ◽  
Milan Stanojević ◽  
Sorin Nădăban
Keyword(s):  
Mathematical Programming ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
Advantages And Disadvantages ◽  
Fuzzy Environment ◽  
Basic Ideas ◽  
Mathematical Programming Problems

Optimization problems in the fuzzy environment are widely studied in the literature. We restrict our attention to mathematical programming problems with coefficients and/or decision variables expressed by fuzzy numbers. Since the review of the recent literature on mathematical programming in the fuzzy environment shows that the extension principle is widely present through the fuzzy arithmetic but much less involved in the foundations of the solution concepts, we believe that efforts to rehabilitate the idea of following the extension principle when deriving relevant fuzzy descriptions to optimal solutions are highly needed. This paper identifies the current position and role of the extension principle in solving mathematical programming problems that involve fuzzy numbers in their models, highlighting the indispensability of the extension principle in approaching this class of problems. After presenting the basic ideas in fuzzy optimization, underlying the advantages and disadvantages of different solution approaches, we review the main methodologies yielding solutions that elude the extension principle, and then compare them to those that follow it. We also suggest research directions focusing on using the extension principle in all stages of the optimization process.

scholarly journals An Alternative Approach for Solving Extreme Point Linear and Linear Fractional Programming Problems

2015 ◽  
Vol 63 (2) ◽  
pp. 77-84
Author(s):  
Touhid Hossain ◽  
Md Rajib Arefin ◽  
Md Ainul Islam
Keyword(s):  
Mathematical Programming ◽  
Extreme Point ◽  
Fractional Programming ◽  
Optimization Problems ◽  
Computational Effort ◽  
Linear Fractional Programming ◽  
Alternative Approach ◽  
Alternative Algorithm ◽  
Mathematical Programming Problems

The paper considers a class of optimization problems known as extreme point mathematical programming problems. The objective of this paper is to improve the established methods for solving extreme point linear and linear fractional programming problems. To overcome the cumbersome and time consuming procedures of these existing methods, we propose an alternative algorithm to solve such types of problems which is simple and need less computational effort. Two simple examples are given to elucidate our proposed algorithm.Dhaka Univ. J. Sci. 63(2):77-84, 2015 (July)

scholarly journals Lagrangian Decomposition for Classical Planning (Extended Abstract)

2020 ◽  
Author(s):  
Florian Pommerening ◽  
Gabriele Röger ◽  
Malte Helmert ◽  
Hadrien Cambazad ◽  
Louis-Martin Rousseau ◽  
...  
Keyword(s):  
Mathematical Programming ◽  
Shortest Path ◽  
Iterative Process ◽  
Lagrangian Decomposition ◽  
Optimal Cost ◽  
Shortest Path Problems ◽  
Over Time

Optimal cost partitioning of classical planning heuristics has been shown to lead to excellent heuristic values but is often prohibitively expensive to compute. We analyze the application of Lagrangian decomposition, a classical tool in mathematical programming, to cost partitioning of operator-counting heuristics. This allows us to view the computation as an iterative process that can be seeded with any cost partitioning and that improves over time. In the case of non-negative cost partitioning of abstraction heuristics the computation reduces to independent shortest path problems and does not require an LP solver.

scholarly journals SHAKEDOWN LOADING OPTIMIZATION UNDER CONSTRAINED RESIDUAL DISPLACEMENTS—FORMULATION AND SOLUTION FOR CIRCULAR PLATES

2002 ◽  
Vol 8 (1) ◽  
pp. 54-67 ◽  
Author(s):  
Ela Jarmolajeva ◽  
Juozas Atkočiūnas
Keyword(s):  
Mathematical Programming ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Stress And Strain ◽  
Load Optimization ◽  
Residual Displacements ◽  
Non Linear ◽  
Mechanical Interpretation ◽  
Strength And Stiffness ◽  
Mathematical Programming Problems

The adapted plate load optimization problem is formulated applying the non-linear mathematical programming methods. The load variation bounds satisfying the optimality criterion in concert with the strength and stiffness requirements are to be identified. The stiffness constraints are realized via residual displacements. The dual mathematical programming problems cannot be applied directly when determining actual stress and strain fields of plate: the strained state depends upon the loading history. Thus the load optimization problem at shakedown is to be stated as a couple of problems solved in parallel: the shakedown state analysis problem and the verification of residual deflections bounds. The Rozen project gradient method is applied to solve the cyclically loaded non-linear shakedown plate stress and strain evaluation and that of the load optimization problems. The mechanical interpretation of Rozen optimality criterions allows to simplify the shakedown plate optimization mathematical model and solution algorithm formulations.

The Map-Based Shortest Route Selection by Using Ant Colony Optimization Algorithm

2018 ◽  
Vol 1 (1) ◽  
pp. 15
Author(s):  
Achmad Fanany Onnilita Gaffar ◽  
Agusma Wajiansyah ◽  
Supriadi Supriadi
Keyword(s):  
Ant Colony Optimization ◽  
Shortest Path ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Google Earth ◽  
Ant Colony ◽  
Food Sources ◽  
Shortest Route ◽  
Study Results ◽  
Destination Point

The shortest path problem is one of the optimization problems where the optimization value is a distance. In general, solving the problem of the shortest route search can be done using two methods, namely conventional methods and heuristic methods. The Ant Colony Optimization (ACO) is the one of the optimization algorithm based on heuristic method. ACO is adopted from the behavior of ant colonies which naturally able to find the shortest route on the way from the nest to the food sources. In this study, ACO is used to determine the shortest route from Bumi Senyiur Hotel (origin point) to East Kalimantan Governor's Office (destination point). The selection of the origin and destination points is based on a large number of possible major roads connecting the two points. The data source used is the base map of Samarinda City which is cropped on certain coordinates by using Google Earth app which covers the origin and destination points selected. The data pre-processing is performed on the base map image of the acquisition results to obtain its numerical data. ACO is implemented on the data to obtain the shortest path from the origin and destination point that has been determined. From the study results obtained that the number of ants that have been used has an effect on the increase of possible solutions to optimal. The number of tours effect on the number of pheromones that are left on each edge passed ant. With the global pheromone update on each tour then there is a possibility that the path that has passed the ant will run out of pheromone at the end of the tour. This causes the possibility of inconsistent results when using the number of ants smaller than the number of tours.

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