Multiobjective Nonlinear Fractional Programming Research Articles

An Investigation of Linear Diophantine Fuzzy Nonlinear Fractional Programming Problems

The linear Diophantine fuzzy set notion is the main foundation of the interactive method of tackling nonlinear fractional programming problems that is presented in this research. When the decision maker (DM) defines the degree α of α level sets, the max-min problem is solved in this interactive technique using Zimmermann’s min operator method. By using the updating technique of degree α, we can solve DM from the set of α-cut optimal solutions based on the membership function and non-membership function. Fuzzy numbers based on α-cut analysis bestowing the degree α given by DM can first be used to classify fuzzy Diophantine inside the coefficients. After this, a crisp multi-objective non-linear fractional programming problem (MONLFPP) is created from a Diophantine fuzzy nonlinear programming problem (DFNLFPP). Additionally, the MONLFPP can be reduced to a single-objective nonlinear programming problem (NLPP) using the idea of fuzzy mathematical programming, which can then be solved using any suitable NLPP algorithm. The suggested approach is demonstrated using a numerical example.

An approach of fuzzy and TOPSIS to bi-level multi-objective nonlinear fractional programming problem

This paper proposes a solution technique to bi-level multi-objective nonlinear fractional programming problem which is based on the concept of TOPSIS (technique for order preference by similarity to ideal solution) and fuzzy goal programming approach. Nonlinear polynomial functions are considered as the numerators as well as denominators of the fractional objectives at each level. The concept used implements simultaneous minimization and maximization of the functions (numerators and denominators of fractional objectives, decision variables controlled by the upper level decision makers) from their respective aspired (ideal) and acceptable (anti-ideal) values. Distance functions and their corresponding fuzzy membership functions are constructed at both levels for the objectives. Aspired and acceptable values of the decision variables of upper level are ascertained using a certain process. The sum of only under deviational variables obtained from the fuzzy membership goals of the distance functions and the decision variables controlled by upper level decision maker is minimized to obtain the best compromise solution of the concerned bi-level problem. Some comparative discussions with an existing approach are incorporated, and two illustrative numerical examples are discussed to demonstrate the effectiveness of the proposed method.

On minimum expected search time for a multiplicative random search problem

In this paper, we obtain the minimum expected search time for a multiplicative random search problem from a viewpoint of computational optimisation. The target is drifting in one of m-disjoint bounded regions. Each region has a one searcher. We get a probabilistic multi-objective nonlinear fractional programming problem and we focus on a new method for solving it to obtain the minimum expected search time for detecting the target. An illustrative example has been given to demonstrate the applicability of this method.

On minimum expected search time for a multiplicative random search problem

In this paper, we obtain the minimum expected search time for a multiplicative random search problem from a viewpoint of computational optimisation. The target is drifting in one of m-disjoint bounded regions. Each region has a one searcher. We get a probabilistic multi-objective nonlinear fractional programming problem and we focus on a new method for solving it to obtain the minimum expected search time for detecting the target. An illustrative example has been given to demonstrate the applicability of this method.

Saddle Point Criteria in Multiobjective Fractional Programming Involving Exponential Invexity

Consider a system of nondifferentiable multiobjective nonlinear fractional programming problem involving exponential $$(p,\,r)$$ -invex functions with respect to $$\eta .$$ A new concept of saddle point for a mixed Lagrange function is introduced. We establish the equivalence between the saddle point and an efficient solution of the minimization multiobjective fractional problem involving exponential $$(p,\,r)$$ -invexity assumptions.

Life Cycle Network Modeling Framework and Solution Algorithms for Systems Analysis and Optimization of the Water-Energy Nexus

The water footprint of energy systems must be considered, as future water scarcity has been identified as a major concern. This work presents a general life cycle network modeling and optimization framework for energy-based products and processes using a functional unit of liters of water consumed in the processing pathway. We analyze and optimize the water-energy nexus over the objectives of water footprint minimization, maximization of economic output per liter of water consumed (economic efficiency of water), and maximization of energy output per liter of water consumed (energy efficiency of water). A mixed integer, multiobjective nonlinear fractional programming (MINLFP) model is formulated. A mixed integer linear programing (MILP)-based branch and refine algorithm that incorporates both the parametric algorithm and nonlinear programming (NLP) subproblems is developed to boost solving efficiency. A case study in bioenergy is presented, and the water footprint is considered from biomass cultivation to biofuel production, providing a novel perspective into the consumption of water throughout the value chain. The case study, optimized successively over the three aforementioned objectives, utilizes a variety of candidate biomass feedstocks to meet primary fuel products demand (ethanol, diesel, and gasoline). A minimum water footprint of 55.1 ML/year was found, economic efficiencies of water range from −$1.31/L to $0.76/L, and energy efficiencies of water ranged from 15.32 MJ/L to 27.98 MJ/L. These results show optimization provides avenues for process improvement, as reported values for the energy efficiency of bioethanol range from 0.62 MJ/L to 3.18 MJ/L. Furthermore, the proposed solution approach was shown to be an order of magnitude more efficient than directly solving the original MINLFP problem with general purpose solvers.

Multiobjective integer nonlinear fractional programming problem: A cutting plane approach

The present paper discusses a multiobjective integer nonlinear fractional programming problem based on cutting plane technique. The methodology discussed is such that it finds all the nondominated t-tuples of the multiobjective nonlinear fractional programming problem by exploiting the quasimonotone character of the nonlinear fractional functions involved. The cut discussed in the present paper scans and truncates a portion of the feasible region in such way that once truncated, it does not reappear, thereby leading to the convergence of the proposed algorithm in finite number of steps. Further, the quasimonotone character of the objective functions involved enables us to find all the nondominated t-tuples at extreme points of the truncated feasible region obtained after repeated applications of the cut developed in the paper.

Duality for multiobjective fractional programming problems involving d -type-I n-set functions

We establish duality results under generalized convexity assumptions for a multiobjective nonlinear fractional programming problem involving d -type-I n -set functions. Our results generalize the results obtained by Preda and Stancu-Minasian [24], [25].

An interactive fuzzy satisficing method based on the fractile optimization model using possibility and necessity measures for a fuzzy random multiobjective linear programming problem

This paper treats a multiobjective linear programming problem in which the coefficients contained in the objective function of the problem are fuzzy random variables. First, in order to take into account ambiguities of judgment by a human decision maker, fuzzy objectives are introduced. Subsequently, we consider a problem of maximizing the possibility and necessity of the objective function value to satisfy the fuzzy objectives. Since these degrees vary stochastically, a formulation is based on the fractile optimization model in a stochastic programming method. A process is presented for equivalent transformation to a deterministic multiobjective nonlinear fractional programming method. For the transformed multiobjective programming problem, an interactive fuzzy satisficing method that derives a satisfactory solution of the decision maker through interactions with the decision maker is proposed. It is shown that the global optimum solution of problems solved iteratively by an interactive process can be derived by means of an extended Dinkelbach-type algorithm. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(5): 20–28, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20136

On some basic notions of fuzzy parametric nonsmooth multiobjective nonlinear fractional programming problems

Different basic notions like the solvability set, the stability set of the first and of the second kind for the smooth fuzzy parametric multiobjective NLP programs have been discussed in several papers. In this paper, these notions have been defined and qualitatively analyzed for a general class of nonsmooth multiobjective nonlinear fractional programming problems with fuzzy parameters under the concept of α-pareto optimality. The stability sets of the third and of the fourth kinds have also been defined and analyzed for this problem. A determination of the stability sets of the third and of the fourth kinds will be given.

Duality in multiobjective nonlinear fractional programs using augmented Lagrangian functions

A vector-valued generalized Lagrangian is constructed for a multiobjective nonlinear fractional programming problem. A multiobjective dual is considered using the Lagrangian. Using Pareto efficiency, duality theorems are proved, without assuming differentiability.