Modified artificial bee colony algorithm for solving mixed interval-valued fuzzy shortest path problem

Ali Ebrahimnejad,Harish Garg,Mohammad Enayattabr,Homayun Motameni

doi:10.1007/s40747-021-00278-0

Abstract

In recent years, numerous researchers examined and analyzed several different types of uncertainty in shortest path (SP) problems. However, those SP problems in which the costs of arcs are expressed in terms of mixed interval-valued fuzzy numbers are less addressed. Here, for solving such uncertain SP problems, first a new procedure is extended to approximate the summation of mixed interval-valued fuzzy numbers using alpha cuts. Then, an extended distance function is introduced for comparing the path weights. Finally, we intend to use a modified artificial bee colony (MABC) algorithm to find the interval-valued membership function of SP in such mixed interval-valued fuzzy network. The proposed algorithm is illustrated via two applications of SP problems in wireless sensor networks and then the results are compared with those derived from genetic and particle swarm optimization (PSO) algorithms, based on three indexes convergence iteration, convergence time and run time. The obtained results confirm that the MABC algorithm has less convergence iteration, convergence time and implementation time compared to GA and PSO algorithm.

Highlights

One of the practical applications of network theory in solving real-world problems is to solve the problem of the shortest path in the network
The main contributions of this study are summarized as follows: (1) to the best of our knowledge, this study is the first attempt for formulating the SP problem in a mixed interval-valued fuzzy environment, (2) a new approach is proposed to compare mixed intervalvalued fuzzy numbers, (3) a Modified Artificial Bee Colony (ABC) (MABC) algorithm is extended for finding the mixed interval-valued fuzzy shortest path, (4) in contrast to genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, the MABC algorithm has less convergence iteration, convergence time and implementation time, (5) two simulations on WSNs confirm that that the MABC algorithm is quite robust to recognize the shortest path among all paths of networks in terms of energy consummation
We investigated a kind of the SP problem in a network in which arc weights are represented in terms of mixed interval-valued fuzzy numbers (MIVFN) and proposed a modified version of the ABC algorithm for solving it

Summary

Introduction

One of the practical applications of network theory in solving real-world problems is to solve the problem of the shortest path in the network. In this study, we present the imprecision in data of WSN by means of mixed interval-valued fuzzy data On such motivation basis, the main contributions of this study are summarized as follows: (1) to the best of our knowledge, this study is the first attempt for formulating the SP problem in a mixed interval-valued fuzzy environment, (2) a new approach is proposed to compare mixed intervalvalued fuzzy numbers, (3) a MABC algorithm is extended for finding the mixed interval-valued fuzzy shortest path, (4) in contrast to GA and PSO algorithm, the MABC algorithm has less convergence iteration, convergence time and implementation time, (5) two simulations on WSNs confirm that that the MABC algorithm is quite robust to recognize the shortest path among all paths of networks in terms of energy consummation.

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Experiments and results

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