Solving Fuzzy Problems in Operations Research

1999 ◽  
Vol 3 (3) ◽  
pp. 171-176
Author(s):  
James J. Buckley ◽  
◽  
Thomas Feuring ◽  
Yoichi Hayashi ◽  
◽  
...  
Keyword(s):  
Operations Research ◽  
Flow Problem ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Approximate Solutions ◽  
Fuzzy Regression ◽  
Neural Net ◽  
Hierarchical Analysis ◽  
Route Problem ◽  
Shortest Route

Fuzzy optimization problems to which traditional methods - calculus and crisp algorithms - are not directly applicable have not been completely solved. We used evolutionary algorithms to produce good approximate solutions to fuzzy optimization problems including fully fuzzified linear programming, nonlinear fuzzy regression, neural net training, and fuzzy hierarchical analysis. We applied our evolutionary algorithm package to generating good approximate solutions to fuzzy optimization problems in operations research including the fuzzy shortest route problem and the fuzzy min-cost capacitated flow problem.

scholarly journals Conflict-free dynamic route multi-AGV using dijkstra floyd-warshall hybrid algorithm with time windows

2020 ◽  
Vol 10 (4) ◽  
pp. 3596
Author(s):  
Solichudin Solichudin ◽  
Aris Triwiyatno ◽  
Munawar A. Riyadi
Keyword(s):  
Optimization Problems ◽  
Time Window ◽  
Time Windows ◽  
Outdoor Environment ◽  
Route Problem ◽  
Shortest Route ◽  
Autonomous Guided Vehicle ◽  
Dynamic Route ◽  
Free Dynamic

Autonomous Guided Vehicle is a mobile robot that can move autonomously on a route or lane in an indoor or outdoor environment while performing a series of tasks. Determination of the shortest route on an autonomous guided vehicle is one of the optimization problems in handling conflict-free routes that have an influence on the distribution of goods in the manufacturing industry's warehouse. Pickup and delivery processes in the distribution on AGV goods such as scheduling, shipping, and determining the route of vehicle with short mileage characteristics, is very possible to do simulations with three AGV units. There is a windows time limit on workstations that limits shipping. The problem of determining the route in this study is considered necessary as a multi-vehicle route problem with a time window. This study aims to describe the combination of algorithms written based on dynamic programming to overcome the problem of conflict-free AGV routes using time windows. The combined approach of the Dijkstra and Floyd-Warshall algorithm results in the optimization of the closest distance in overcoming conflict-free routes.

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.

Solutions of the Shortest-Route Problem—A Review

1960 ◽  
Vol 8 (2) ◽  
pp. 224-230 ◽  
Author(s):  
Maurice Pollack ◽  
Walter Wiebenson
Keyword(s):  
Route Problem ◽  
Shortest Route

scholarly journals An Extensive Operational Law for Monotone Functions of LR Fuzzy Intervals with Applications to Fuzzy Optimization

2021 ◽  
Author(s):  
Mingxuan Zhao ◽  
Yulin Han ◽  
Jian Zhou
Keyword(s):  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Fuzzy Programming ◽  
Planning Problem ◽  
Monotone Functions ◽  
Solution Strategy ◽  
Deterministic Equivalent ◽  
The One ◽  
Short Time

Abstract The operational law put forward by Zhou et al. on strictly monotone functions with regard to regular LR fuzzy numbers makes a valuable push to the development of fuzzy set theory. However, its applicable conditions are confined to strictly monotone functions and regular LR fuzzy numbers, which restricts its application in practice to a certain degree. In this paper, we propose an extensive operational law that generalizes the one proposed by Zhou et al. to apply to monotone (but not necessarily strictly monotone) functions with regard to regular LR fuzzy intervals (LR-FIs), of which regular fuzzy numbers can be regarded as particular cases. By means of the extensive operational law, the inverse credibility distributions (ICDs) of monotone functions regarding regular LR-FIs can be calculated efficiently and effectively. Moreover, the extensive operational law has a wider range of applications, which can deal with the situations hard to be handled by the original operational law. Subsequently, based on the extensive operational law, the computational formulae for expected values (EVs) of LR-FIs and monotone functions with regard to regular LR-FIs are presented. Furthermore, the proposed operational law is also applied to dispose fuzzy optimization problems with regular LR-FIs, for which a solution strategy is provided, where the fuzzy programming is converted to a deterministic equivalent first and then a newly-devised solution algorithm is utilized. Finally, the proposed solution strategy is applied to a purchasing planning problem, whose performances are evaluated by comparing with the traditional fuzzy simulation-based genetic algorithm. Experimental results indicate that our method is much more efficient, yielding high-quality solutions within a short time.

scholarly journals A Dai-Liao Hybrid Hestenes-Stiefel and Fletcher-Revees Methods for Unconstrained Optimization

2021 ◽  
Vol 2 (1) ◽  
pp. 33
Author(s):  
Nasiru Salihu ◽  
Mathew Remilekun Odekunle ◽  
Also Mohammed Saleh ◽  
Suraj Salihu
Keyword(s):  
Unconstrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Convex Combination ◽  
Gradient Methods ◽  
Approximate Solutions ◽  
Step Size ◽  
Conjugacy Condition ◽  
Inexact Line Search ◽  
Wolfe Line Search

Some problems have no analytical solution or too difficult to solve by scientists, engineers, and mathematicians, so the development of numerical methods to obtain approximate solutions became necessary. Gradient methods are more efficient when the function to be minimized continuously in its first derivative. Therefore, this article presents a new hybrid Conjugate Gradient (CG) method to solve unconstrained optimization problems. The method requires the first-order derivatives but overcomes the steepest descent method’s shortcoming of slow convergence and needs not to save or compute the second-order derivatives needed by the Newton method. The CG update parameter is suggested from the Dai-Liao conjugacy condition as a convex combination of Hestenes-Stiefel and Fletcher-Revees algorithms by employing an optimal modulating choice parameterto avoid matrix storage. Numerical computation adopts an inexact line search to obtain the step-size that generates a decent property, showing that the algorithm is robust and efficient. The scheme converges globally under Wolfe line search, and it’s like is suitable in compressive sensing problems and M-tensor systems.

On quasi approximate solutions for nonsmooth robust semi-infinite optimization problems

2019 ◽  
Vol 35 (3) ◽  
pp. 417-426 ◽  
Author(s):  
CHANOKSUDA KHANTREE ◽  
RABIAN WANGKEEREE ◽  
◽  
Keyword(s):  
Constraint Qualification ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
Data Uncertainty ◽  
Necessary Condition ◽  
Duality Theorems ◽  
Approximate Form ◽  
Locally Lipschitz ◽  
Approximate Duality

This paper devotes to the quasi ε-solution for robust semi-infinite optimization problems (RSIP) involving a locally Lipschitz objective function and infinitely many locally Lipschitz constraint functions with data uncertainty. Under the fulfillment of robust type Guignard constraint qualification and robust type Kuhn-Tucker constraint qualification, a necessary condition for a quasi ε-solution to problem (RSIP). After introducing the generalized convexity, we give a sufficient optimality for such a quasi ε-solution to problem (RSIP). Finally, we also establish approximate duality theorems in term of Wolfe type which is formulated in approximate form.

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