Multi-objtective predictive control based on fuzzy satisfactory goal programming

Optimizing sustainable and renewable energy portfolios using a fuzzy interval goal programming approach

In this paper, we propose an alternate modified solution procedure based on fuzzy goal programming (FGP) approach for solving bi-level multiobjective linear fractional programming problems (BL-MOLFPPs) with some major modifications in the algorithm suggested by Abo-Sinna and Baky (2010). The proposed modified technique is simpler and requires less computational works than that of earlier technique. In the formulation of FGP models, each objective function (at both the levels - leader's level and follower's level) as well as control variables (of leader's level) are transformed into fuzzy goals with modified membership functions. Then FGP approach is used for achieving the highest degree of each of membership goals. To avoid decision deadlock situations and difficulties associated with bi-level programming problems, solution preferences by decision makers (at leader's and follower's levels) are not taken into account in proposed algorithm. A comparative analysis is also carried out with numerical example in order to show efficiency of proposed algorithm over earlier technique.

In this paper, we present modified fuzzy goal programming (FGP) approach and generalized MATLAB program for solving multi-level linear fractional programming problems (ML-LFPPs) based on with some major modifications in earlier FGP algorithms. In proposed modified FGP approach, solution preferences by the decision makers at each level are not considered and fuzzy goal for the decision vectors is defined using individual best solutions. The proposed modified algorithm as well as MATLAB program simplifies the earlier algorithm on ML-LFPP by eliminating solution preferences by the decision makers at each level, thereby avoiding difficulties associate with multi-level programming problems and decision deadlock situation. The proposed modified technique is simple, efficient and requires less computational efforts in comparison of earlier FGP techniques. Also, the proposed coding of generalized MATLAB program based on this modified approach for solving ML-LFPPs is the unique programming tool toward dealing with such complex mathematical problems with MATLAB. This software based program is useful and user can directly obtain compromise optimal solution of ML-LFPPs with it. The aim of this paper is to present modified FGP technique and generalized MATLAB program to obtain compromise optimal solution of ML-LFP problems in simple and efficient manner. A comparative analysis is also carried out with numerical example in order to show efficiency of proposed modified approach and to demonstrate functionality of MATLAB program.

Production planning is one of the most important issues of managers in industry. Production managers face up with several goals that sometimes conflict with each other. Operations research techniques with considering the constraints, optimize organizational goals. Objectives of all these techniques are raising productivity in the organization. In this paper, the researchers present a multi-objective linear fractional model of production planning in wood and metal company. One of the difficulties in solving the multiple objective fractional problems is computational problem that arises from of variability, in the example of Charnes and Cooper (1961) methods. In this research, fuzzy approach issued to solve multiple objective fractional mathematical problems of Khavar-E-Miane Wood and Metal Company. First, with some assumptions, the fuzzy linear fractional goal programming method of Pal has been used to solve the problem of production planning. Then, the fuzzy method of Dutta is utilized to solve the problem. Comparison of results showed that both methods have identical solution. Key words: Production planning, fuzzy goal programming, productivity, fuzzy fractional programming, wood and metal company.

This paper deals with a fuzzy goal programming methodology for solving multiobjective linear fractional chance constrained programming problems containing fuzzy numbers and exponentially distributed fuzzy random variables associated with the system constraints. In model formulation process, the problem is converted into an equivalent fuzzy programming model by applying chance constrained programming technique in a fuzzily defined probabilistic decision making situation. Then using the concept of α-cut for fuzzy numbers and by considering the tolerance level of fuzzy numbers the problem reduces to an equivalent sub problem with interval coefficients. In this method the convex combination of each interval is used and the problem is reduced to a nonlinear programming problem. Finally the model is solved by converting nonlinear model into its equivalent multiobjective linear programming model by using Taylor series; and a priority based fuzzy goal programming method is used for achievement of the highest membership degree. To demonstrate the efficiency of the proposed technique an illustrative example, studied previously, is solved and the solution is compared with the existing methodology.

Fuzzy analytical hierarchy process and multi-segment goal programming applied to new product segmented under price strategy

This paper presents a fuzzy goal programming approach for modelling and solving multi-objective decision making problem having fuzzy random variables and fuzzy numbers associated with the system constraints. In the model formulation process, the problem is converted into an equivalent fuzzy programming problem by using chance constrained programming technique. The problem is then decomposed into sub problems by considering the tolerance limits of fuzzy numbers relating to the system constraints. The individual optimal solution of each objective is found to construct the membership goals. A two-phase fuzzy goal programming model is developed to achieve the highest degree of each of the defined membership goals of the objectives to the extent possible by minimising under deviational variables and thereby obtaining most satisfactory solution in the decision making environment. A numerical example is solved to illustrate the proposed approach and the achieved solutions are compared with other existing methodologies.

To comply with the effluent standards and growing demands for safety and reliability, the operation of wastewater treatment processes (WWTPs) has been considered as a multiobjective control problem. In this article, a data-driven multiobjective predictive control (MOPC) method is developed to deal with the conflicting control objectives to improve the operation performance of WWTPs. The main contributions of MOPC are three folds: first, a multiobjective control strategy is developed in the design of MOPC. And an adaptive fuzzy neural network identifier, using the relevant process data, is designed to catch the nonlinear behaviors of WWTPs. Second, a transfer multiobjective optimization algorithm (TMOOA) is developed to obtain the optimal solutions of the conflicting control objectives. The major advantage of TMOOA is its low computational cost, which is realized by avoiding the computation of Pareto fronts. Third, the stability of MOPC has been given in detail. Meanwhile, the benefits and feasibility of MOPC are confirmed on the benchmark simulation model no. 2. The results further demonstrate the effectiveness of the proposed control method.

In this study, a model representing military requirements as scenarios and capabilities is offered. Pair-wise comparisons of scenarios are made according to occurrence probabilities by using the Analytical Hierarchy Process (AHP). The weights calculated from AHP are used as the starting weights in a Quality Function Deployment (QFD) matrix. QFD is used to transfer war fighter requirements into the benefit values of projects. Two levels of QFD matrices are used to evaluate new capability areas versus capabilities and capabilities versus projects. The benefit values of the projects are used in a multi-objective problem (multi-objective multiple knapsack problem) that considers the project benefit, implementation risks and environmental impact as multiple objectives. Implementation risk and environmental impact values are also calculated using the same combined AHP and QFD methodology. Finally, the results of the fuzzy multi-objective goal programming suggest a list of projects that offers optimal benefit when carried out within multiple budgets.

Supplier selection is a strategic complex multi-criteria problem of selecting the appropriate supplier. The main objective of this paper is to propose a hybrid model including intuitionistic fuzzy AHP using triangular intuitionistic fuzzy numbers and goal programming for the supplier selection problem. Intuitionistic fuzzy AHP is a useful tool for handling the complex problems with hierarchical form under intuitionistic fuzzy environment. And the goal programming is a linear programming based method and deals with multiple conflicting objective measures effectively. In this study, we evaluated three suppliers according to five criteria by using intuitionistic fuzzy AHP which utilizes triangular intuitionistic fuzzy scale. By applying intuitionistic fuzzy AHP, the priority weights of the criteria and suppliers are calculated. Then, the weights are used in the goal programming model to find the best alternatives. The results point out that the supplier selection problem can be tackled with using the proposed hybrid method effectively.

A decision support system for fuzzy multi-objective multi-period sustainable project selection

Fuzzy goal programming – A parametric approach

This chapter presents two methodologies for solving quadratic programming problems with multiple objectives under fuzzy stochastic environments. The right side parameters of the chance constraints of both the models are chosen as fuzzy random variables (FRVs) following different probability distributions. Like the previous chapters, chance constrained programming (CCP) methodology is employed to the fuzzy chance constraints to develop fuzzy programming model. In the first model, cut of fuzzy sets and fuzzy partial order relations are incorporated to the fuzzy programming model to develop an equivalent deterministic model. For the second model, defuzzification method of fuzzy numbers (FNs), which are presented in Chapter 2, are taken into consideration to generate equivalent quadratic programming model in a crisp environment. As the objective functions are quadratic in nature, it is easy to understand that the membership functions obtained through methodological development process are also quadratic in nature. To linearize the quadratic membership functions, linearization techniques are employed in this chapter. Finally, for achieving the maximum degree of each of the membership goals of the objectives, a fuzzy goal programming (FGP) approach is developed for the linearized membership goals and solved by minimizing under-deviational variables and satisfying modified system constraints in fuzzy stochastic decision-making environments. To illustrate the acceptability of the developed methodology presented in this chapter, some numerical examples are included.

Fuzzy goal programming for health-care organization

Disasters are the unfortunate suddenly occurring events which collapse a living society within a moment. Facebook, the most trending social media have initiated an active role to response the crisis developing a safety check feature to know about the demand of victims in an area. Through this feature the Facebook authority can confirm the requirement of the affected people in a specific area. This research have introduced a mathematical model for multi-objective solid transportation problem to quick delivery of the relief products to the devastating society according to the most prior demand of an area acquiring the best information through safety check feature launched by Facebook with limited resources. The two main objectives of the model are to minimize the total cost and minimize the total time so that relief can be executed under a limited budget responding quickly to the affected area. In this paper, fuzzy goal programming is adopted to solve the multi-objective solid transportation problem. To contemplate the performance of the model, a numerical example is presented in this paper. The numerical example is solved with LINGO optimization solver.