International Journal of Engineering and Advanced Technology (IJEAT) ISSN: 2249 – 8958, Volume-9 Issue-2, December, 2019 9 Published By: Blue Eyes Intelligence Engineering & Sciences Publication Retrieval Number: B3054129219/2019©BEIESP DOI: 10.35940/ijeat.B3054.129219 Abstract: In real-life situations, we human beings faced with multi-objective problems that are conflicting and non-commensurable with each other. Especially, when goods are transported from source to locations with a goal to keep exact relationships between a few parameters, those parameters of such problems might also arise in the form of fractions which are linear in nature such as; actual transportation fee/total transportation cost, delivery fee/desired path, total return/total investment, etc. Due to the uncertainty of nature, such a relationship is not deterministic. Mathematically such kinds of mathematical problems are characterized as a multi-objective linear fractional stochastic transportation problem. However, it is difficult to handle such types of mathematical problems. It can't be solved directly using mathematical programming approaches. In this paper, a solution procedure is proposed for the above problem using a stochastic Genetic Algorithm based simulation. The parameters in the constraint of the above problem follow a normal distribution. The probabilistic constraints are handled by stochastic simulation-based GA for the solution procedure of the proposed problem. The feasibility of probability constraints is checked by the stochastic programming through the Genetic Algorithm approach, without finding the equivalent deterministic model. The feasibility is maintained all-over the problem. The stochastic simulation-based Genetic Algorithm is considered to generate non-dominated solutions for the given problem. Then, a numerical case study is provided to illustrate the method. Keywords: Genetic Algorithm, multi-objective programming, stochastic fractional programming, transportation problem. I. INTRODUCTION Transportation problems with the ratio of optimization of parameters where the ratios are objective functions are known as fractional transportation problems. It is concerned with delivering the commodities from numerous assets to various locations along to keep up great connections among a couple of parameters. Those parameters of transportation problems may happen as a proportion of actual transportation cost/total standard transportation cost, shipping cost/desired path, total return/total investment, and so forth. In real-life, distributions of commodities are done on the minimization of the ratio of the total cost to total profit. The Revised Manuscript Received on December 08, 2019 * Correspondence Author Adane Abebaw Gessesse*, Department of Mathematics, KIIT, Deemed to be University, Bhubneswar 751024, India. Rajashree Mishra, Department of Mathematics, KIIT, Deemed to beUniversity, Bhubneswar 751024, India. Mitali Madhumita Acharya, Department of Mathematics, KIIT,Deemed to be University, Bhubaneswar 751024, India. problem derived by such type of two linear functions gets its name as a linear fractional transportation problem (LFTP). In many real-world situations, for LFTP, decisions are often made in the presence of multiple, non-commensurable, conflicting objectives. Such kinds of problems are called multi-objective linear fractional transportation problems (MOLFTP). It deals with the distribution of goods at a time by considering the ratio of several objective functions. The parameters associated with the MOLFTP are not deterministic or fixed value always. In a mathematical programming model, uncertainties are addressed using the fuzzy program set theory or probability theory. In the present paper, we deal with the parameters to address uncertainty using probability theory. The presence of probability in a mathematical programming problem leads to a stochastic programming (SP) problem. SP problem is one of the mathematical programming problems that involve randomness. It is concerned with the decision-making in which a few or all parameters traced as random variables for capturing uncertainty. In our proposed work, attention has been given to solve a stochastic transportation problem having more than one linear fractional objective function. The parameters of the constraints in the above problem are normal random variables. The mathematical model is known as a multi-objective linear fractional stochastic transportation problem (MOLFSTP). However, a set of optimal solutions known as Pareto-optimal (PO) solutions occurs due to the presence of conflicting objectives in a MOLFSTP. Finding these set of PO solutions is not practically possible, rather an approximation set to the true Pareto front (PF) is expected. Researchers have attempted various methods to tackle those types of MOLFSTP problems. Nowadays, due to the popularization of the evolutionary algorithm, many researches are going on solving the above problem using the said algorithm. One such popular algorithm is the Genetic Algorithm (GA) which is an efficient algorithm for tackling such type of problems. Because of its population-based nature, in a single simulation run, GA can obtain multiple PO solutions. GA is superior in comparison to the classical methods. Because it finds convergent solutions, finds a diversified set of solutions, and covers the entire PF [1]. The remainder of the paper is set up as follows. Following the introduction section, the literature survey has been provided in Section 2. Solving Multi-Objective Linear Fractional Stochastic Transportation Problems Involving Normal Distribution using Simulation-Based Genetic Algorithm Adane Abebaw Gessesse, Rajashree Mishra, Mitali Madhumita Acharya