In this paper, we establish a proof for a necessary condition for multiple objective fractional pro-gramming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we present the related semi parametric model.

This paper deals with day-ahead programming under uncertainties in microgrids (MGs). A two-stage stochastic programming with the fixed recourse approach was adopted. The studied MG was considered in the grid-connected mode with the capability of power exchange with the upstream network. Uncertain electricity market prices, unpredictable load demand, and uncertain wind and solar power values, due to intrinsically stochastic weather changes, were also considered in the proposed method. To cope with uncertainties, the scenario-based stochastic approach was utilized, and the reduction of the environmental emissions generated by the power resources was regarded as the second objective, besides the cost of units’ operation. The ɛ-constraint method was employed to deal with the presented multi-objective optimization problem, and the simulations were performed on a sample MG with one month of real data. The results demonstrated the applicability and effectiveness of the proposed techniques in real-world conditions.

This paper focused on locating ATMs problem. At first, this paper aims to identify effective factors in selecting ATMs appropriate locations. After selecting potential locations, optimal locations are determined through mathematical modeling. In this paper, effective factors to determine potential locations are weighted through Fuzzy AHP. Finally, linear allocation technique with multi-objective approach is used to determine ATMs locations at Bushehr city. After literature review, 46 effective factors are identified and then, based on experts' opinion are categorized in 6 groups of demographic, economic - social factors, competitive – commercial factors, public utility (infrastructure and proximity) factors, investment factors and political - legal factors. Results from Fuzzy AHP show that demographic factors are the most important factors among others. Final results show that each of these six categories, can have different effects on decision makers.

Multi objective quadratic fractional programming (MOQFP) problem involves optimization of several objective functions in the form of a ratio of numerator and denominator functions which involve both contains linear and quadratic forms with the assumption that the set of feasible solutions is a convex polyhedral with a finite number of extreme points and the denominator part of each of the objective functions is non-zero in the constraint set. In this paper, we extend the procedure as suggested by Lachhwani (Proc. Nat. Acad. Sci. India, 82 (4), 317-322) based on fuzzy goal programming approach for the solution of multi objective quadratic fractional programming (MOQFP) problem.The proposed technique is simple, efficient and requires less computational work. In the proposed FGP model formulation, corresponding objectives of equivalent multi objective programming problem are transformed into fuzzy goals (membership functions) by means of assigning an aspiration level to each of them and suitable membership function is de fined for each objectives. Then achievement of the highest membership value of each of fuzzy goals is formulated by minimizing the sum of negative deviational variables. The proposed methodology is illustrated with numerical example in order to support the proposed methodology.

In sciences and industries such as signal optimization, traffic assignment, economic market and etc, many problems have been modeled by bilevel programming (BLP) problems, where in each level one must optimize some objective functions. There are so many algorithms in order to find the global optimum of the linear version of BLP problems. This paper addresses multi-objective linear bilevel multi-follower programming (MOLBMFP) problems in which there is no sharing information among followers. It presents a new method for solving these problems.

Multiple objective programming (MOP) problems have become famous among many researchers due to more practical and realistic implementations. There have been a lot of methods proposed especially during the past four decades. In this paper, we develop a new algorithm based on a new approach to solve MOP problems by starting from a utopian point (which is usually infeasible) and moving towards the feasible region via stepwise movements and a plain continuous interaction with Decision Maker (DM). We consider the case where all objective functions and constraints are linear. The implementation of the proposed algorithm is demonstrated with two numerical examples.

In this paper, a multi- objective quadratic programming (Poss- MOQP) problem with possibilistic variables coefficients matrix in the objective functions is studied. Through the use of b-level sets the Poss- MOQP problem is converted into the corresponding deterministic multi- objective quadratic programming (b-MOQP) problem and hence into the single parametric quadratic programming problem using the weighting method. An extended b-possibly efficient solution is specified. A necessary and sufficient condition for finding such a solution is established. A relationship between the solutions of possibilistic levels is constructed. Numerical example is given to clarify the obtained results.