DOI: http://dx.doi.org/10.26483/ijarcs.v8i7.4267 Volume 8, No. 7, July – August 2017 International Journal of Advanced Research in Computer Science RESEARCH PAPER Available Online at www.ijarcs.info © 2015-19, IJARCS All Rights Reserved 470 ISSN No. 0976-5697 MULTI-OBJECTIVE FUZZY SHORTEST PATH SELECTION FOR GREEN ROUTING AND SCHEDULING PROBLEMS Gumpina Vakula Rani Reasearch Scholar, Dept. of Comp. Sc Rayalaseema University, Kurnool, AP, India Dr. Bhaskar Reddy Professor, Dept. of Comp. Sc S K University Ananthapur, AP, India Abstract: The Green Routing and Scheduling Problems deal with the models which relate to ecological issues. For modeling routing and transportation processes characterized by subjectivity, ambiguity, uncertainty and imprecision, fuzzy logic approach happens to be a very promising mathematical approach.The present investigation discusses about the multi objective fuzzy shortest path selection, where the arc lengths are expressed as trapezoidal fuzzy numbers. The shortest paths can be distinguished by using the highest degree of similarity measure. The optimal path selected depends on the different weights given to the MOFSP in the network. The decision maker can select the best one or the most satisfactory solution depending on the priority and nature of the problem. The algorithms are illustrated with a bi-objective optimization problem with crisp and trapezoidal fuzzy values. The numerical experimentation is used to evaluate the proposed model. The experiment results of the proposed model prove that the results lead to the selection of shortest path as a standard algorithm. Key Words: Fuzzy shortest path, Bellman’s Dynamic Programming, Fuzzy Triangular shortest path, Fuzzy Trapezoidal shortest path, Degree of Similarity, MOSPP(Multi Objective Shortest Path Problem), Green Routing and Scheduling Problems (GRSP). I. INTRODUCTION The Green Routing and Scheduling Problems (GRSP) deal with the models which relate to environmental issues. From the last few decades, these problems have been studied by the researchers with great interest. About three-quarters of the oil produced in the world is used for transportation purposes. There is a necessity to conserve and plan for sustainable transportation. The key components to achieve sustainable transportation are effective planning and efficiency of transportation process. Some of the problems like sustainable logistics, waste management [1] etc are dealt by GRSP. Some variants of Green routing and scheduling problems are : (i) the priority based routing, which is considered in public transportation, logistics and waste management, and ii) the time-dependent scheduling of vehicles , which helps to decrease in pollution by avoiding congested routes. Many practical problems may not be characterized by single objective functions completely. In a real time routing network, multiple objectives, for example, scheduling of a vehicle, time, cost, priority, distance, etc. can be assigned to each edge. The task of finding the shortest path with more than one objective is known as the multi-objective shortest path problem. Fuzzy logic could be used successfully to model situations in a highly complex environment where a suitable mathematical model could not be provided [3]. For modeling traffic and transportation processes characterized by subjectivity, ambiguity, uncertainty and imprecision, fuzzy logic approach happens to be a very promising mathematical approach. The use of fuzzy logic is advantageous in several situations especially in decision making processes where the description through algorithms is difficult and the associated criteria are multiplied. This paper presents the related work in section 2, preliminary definitions and concepts required for computation and analysis of fuzzy numbers in Section 3. The shortest path algorithms are demonstrated in Section 4. In Section 5, Experiments of these algorithms are conducted and results are compared and presented graphically. Section 6 presents conclusions and provides some pointers for future work. II. RELATED WORK Shortest path in fuzzy network was first introduced byauthors [2] in 1980. Floyd's algorithm and Ford’s algorithm was used to find the Shortest path in fuzzy network. Fuzzy shortest path algorithm using Dynamical programming technique was proposed by authors [4]. Authors [5,6,7] proposed Fuzzy shortest path algorithm using linear programming approach. Fuzzy Shortest Path Based on Degree of Similarity was studied by the authors[8,9] . Thus numerous papers have been published on the FSPP. The task of finding Fuzzy Shortest Path using different approaches is discussed and analyzed with a case study. III. PREREQUISITES Authors[4] were discussed about the fuzzy- number concepts and definitions in their research work is as follows: Definition 1: “A fuzzy number is a quantity whose value is imprecise, rather than exact as is the case with "ordinary" (single-valued) numbers “. Any fuzzy number can be thought of as a function whose domain is a specified set, usually the set of real numbers, and whose range is the span of non-negative real numbers between, and including, 0 and 1. Each numerical value in the domain is assigned a specific "grade of membership" where 0 represents the smallest possible grade, and 1 is the largest possible grade.