Genetic Algorithm approach for Solving MultiObjective Fuzzy Stochastic Programming Problem and its applications

Abstract

Multi-Objective Fuzzy Stochastic Programming Problem involves fuzziness and randomness under one roof. It is the extension of multi-objective probabilistic programming problem where all or some of the parameters are fuzzy random variables. In order to solve such programming problems a deterministic equivalent of the problem is desired. So, the solution procedure to solve such programming problems without finding the deterministic equivalent model is an interesting problem. The traditional method is incapable in solving multi-objective fuzzy stochastic programming problem without deterministic equivalent model of the problem. Therefore, a non traditional method like Genetic Algorithm is vital to solve multiobjective fuzzy stochastic programming problem. This hindrance motivates to propose a solution procedure to solve multi-objective fuzzy stochastic programming problem without finding the deterministic equivalent model of the problem. In the thesis, a solution procedure is proposed to solve multi-objective fuzzy stochastic programming problem without finding the deterministic equivalent model of multi-objective fuzzy stochastic programming problem. The fuzzy random variables are generated using the fuzzy known parameter of the different continuous distributions. These parameters are taken as fuzzy triangular numbers. In order to solve multi-objective fuzzy stochastic programming problem, fuzziness is removed using and#945; cut technique. Then after fuzzy stochastic genetic algorithm based simulation is proposed to obtain the Pareto optimal solutions. In this thesis, a solution procedure has been developed to solve Routing and Sitting problem as a multi-objective fuzzy stochastic programming problem where supply and demand follows weibull distribution. The fuzzy programming method is used to obtain the ideal solution of each objective function using genetic algorithm and then a pay-off matrix is formulated to calculate membership function. The final model is solved again using genetic algorithm to obtain the Pareto optimal solution. newline newlineThe proposed solution procedure is applied to multi-objective fuzzy stochastic transportation with supplies and demand as fuzzy random variables which follows fuzzynormal and fuzzylognormal distributions. A case study of an oil company in North East India, is also presented. newline newlineThe problem of crops pattern and water balance of Balasore area of Odisha, India is studied with fuzzyuniform water requirement of the crops. Five crops are taken depending on the region and the total water required by the crops for the growing season are supplied from the rainfall and the runoff generated during rainfall from a given command area. A multi-objective fuzzy stochastic programming problem is formulated to obtain best crops pattern and also to maximize the production. Portfolio selection problem is very interesting problem. A multi-objective fuzzy stochastic two stage programming problem is formulated where stocks from various sectors under BSE 100 are studied to design a portfolio with minimum risk assets. To procure the minimum risk assets, a fuzzy stochastic price scenario method is developed, and with the selected assets maximum profit is calculated under different scenarios. newline newlineBilevel programming problem is difficult to solve and to obtain the global solution. A solution procedure is developed motivated from the real games to solve the multi-objective fuzzy stochastic bilevel programming problem. A case study of company s store and local vendor of a garment industries is studied. The expected return follows fuzzynormal distribution both in the upper and lower level of multi-objective fuzzy stochastic programming problem. newline newline newline