Multiobjective Fractional Programming Problem Research Articles

Local isolated efficiency in non-smooth robust semi-infinite multi-objective fractional programming problems

Local isolated efficiency in non-smooth robust semi-infinite multi-objective fractional programming problems

Sequential Henig proper optimality conditions for multiobjective fractional programming problems via sequential proper subdifferential calculus

Sequential Henig proper optimality conditions for multiobjective fractional programming problems via sequential proper subdifferential calculus

Pareto Efficiency Criteria and Duality for Multiobjective Fractional Programming Problems with Equilibrium Constraints on Hadamard Manifolds

This article deals with multiobjective fractional programming problems with equilibrium constraints in the setting of Hadamard manifolds (abbreviated as MFPPEC). The generalized Guignard constraint qualification (abbreviated as GGCQ) for MFPPEC is presented. Furthermore, the Karush–Kuhn–Tucker (abbreviated as KKT) type necessary criteria of Pareto efficiency for MFPPEC are derived using GGCQ. Sufficient criteria of Pareto efficiency for MFPPEC are deduced under some geodesic convexity hypotheses. Subsequently, Mond–Weir and Wolfe type dual models related to MFPPEC are formulated. The weak, strong, and strict converse duality results are derived relating MFPPEC and the respective dual models. Suitable nontrivial examples have been furnished to demonstrate the significance of the results established in this article. The results derived in the article extend and generalize several notable results previously existing in the literature. To the best of our knowledge, optimality conditions and duality for MFPPEC have not yet been studied in the framework of manifolds.

Approximate Subdifferential of the Difference of Two Vector Convex Mappings

This paper deals with the strong approximate subdifferential formula for the difference of two vector convex mappings in terms of the star difference. This formula is obtained via a scalarization process by using the approximate subdifferential of the difference of two real convex functions established by Martinez-Legaz and Seeger, and the concept of regular subdifferentiability. This formula allows us to establish approximate optimality conditions characterizing the approximate strong efficient solution for a general DC problem and for a multiobjective fractional programming problem.

An efficient fuzzy mathematical approach to solve multi-objective fractional programming problem under fuzzy environment

An efficient fuzzy mathematical approach to solve multi-objective fractional programming problem under fuzzy environment

An Approach to Compute the Multi-Objective Programming Problem Under Triangular Fuzzy Numbers

The most important one advantages of the operation research (OR) theory is displayed of this paper for tackling multi-objective function programming problems (MOFPP). In this study, we present an approach for multi-objective fractional programming problems (MOFrPP) using fuzzy numbers (FN) coefficients in the objective functions (OF). The objective functions' (OF) parameters are all considered to be fuzzy triangular fuzzy numbers (FTrFN). This problem's multi-objective function (MOF) case was resolved by transforming the MOF to a linear programming problem (LnPP) that could be resolved using the simplex method (SM). The problem is being solved using algorithms. Then the value is compared with a result, which obtained by simplex method (SM). These techniques are illustrated with numerical examples (NE). This study shows the reliability of our methods and their utility to this specific set of multi-objective functions (MOF).

Sequential optimality conditions of approximate proper efficiency for a multiobjective fractional programming problem

Sequential optimality conditions of approximate proper efficiency for a multiobjective fractional programming problem

Robust optimality conditions and duality for nonsmooth multiobjective fractional semi-infinite programming problems with uncertain data

In this article, some Karush-Kuhn-Tucker type robust optimality conditions and duality for an uncertain nonsmooth multiobjective fractional semi-infinite programming problem ((UMFP), for short) are established. First, we provide, by combining robust optimization and the robust limiting constraint qualification, robust necessary optimality conditions in terms of Mordukhovich's subdifferentials. Under suitable assumptions on the generalized convexity/the strictly generalized convexity, robust necessary optimality condition becomes robust sufficient optimality condition. Second, we formulate types of Mond-Weir and Wolfe robust dual problem for (UMFP) via the Mordukhovich subdifferentials. Finally, as an application, we establish weak/strong/converse robust duality theorems for the problem (UMFP) and its Mond-Weir and Wolfe types dual problem. Some illustrative examples are also provided for our findings.

Application of multi-objective probabilistic fractional programming problem in production planning

This paper presents the application of multi-objective probabilistic fractional programming problem in production planning. The production planning model for a manufacturing company that produce multiple products with a specified period is formulated by considering some of the parameters in the right hand sides of the constraints as random variables following continuous distribution namely gamma distribution. The formulated mathematical model is a multi-objective probabilistic fractional programming problem. In the solution procedure, the deterministic equivalent of the probabilistic programming problem has not been obtained. The analytical method for multi-objective fractional programming problem has also not been applied to solve the proposed model. A stochastic simulation-based genetic algorithm is applied to solve the proposed model directly. A set of Pareto optimal solutions is obtained for the formulated production planning problem.

Correction: On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty

Correction: On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty

A new Mean Deviation and Advanced Mean Deviation Techniques to Solve Multi-Objective Fractional Programming Problem Via Point-Slopes Formula

In this paper, we have proposed a new technique to find an efficient solution to fractional programming problems (FPP). The multi-objective fractional programming problem (MOFPP) is converted into multi-objective linear programming (MOLPP) utilizing the point-slopes formula for a plane, which has equivalent weights to the MOFPP. The MOLPP is diminished to a single objective linear programming problem (SOLPP) through using two new techniques for the values of the objective function and suggesting an algorithm for its solution. Finally, we obtained the optimal solution for MOFPP by solving the consequent linear programming problem (LPP). The proposed practicability is confirmed with the existing approaches, with some numerical examples and we indicated comparison with other techniques.

Fuzzy solution of fully fuzzy multi-objective linear fractional programming problems

In this study, we present a novel method for solving fully fuzzy multi-objective linear fractional programming problems without transforming to equivalent crisp problems. First, we calculate the fuzzy optimal value for each fractional objective function and then we convert the fully fuzzy multi-objective linear fractional programming problem to a single objective fuzzy linear fractional programming problem and find its fuzzy optimal solution which inturn yields a fuzzy Pareto optimal solution for the given fully fuzzy multi-objective linear fractional programming problem. To demonstrate the proposed strategy, a numerical example is provided.

Second-order optimality conditions in locally Lipschitz multiobjective fractional programming problem with inequality constraints

Our purpose, in this article, is to establish second-order optimality conditions for a second-order strict local Pareto minimum and a weak local Pareto minimum for a locally Lipschitz multiobjective fractional programming problem with inequality constraints. We do not require here the data to be second-order differentiable in any case. We first provide some basic calculus rules for the two extended-real-valued mappings defined on an open set of a Banach space. We second establish primal and dual Karush–Kuhn–Tucker second-order necessary optimality conditions to such problem. We third present second-order sufficient optimality conditions which are very near to a dual Karush–Kuhn–Tucker second-order necessary optimality condition. Some examples demonstrate the applicability of the obtained main results.

Solution procedure for multi-objective fractional programming problem under hesitant fuzzy decision environment

For the three last decades, the multi-objective fractional programming problem has attracted the attention of many researchers due to various applications in production planning, financial field, and inventory management, and so on. The main aim of this study is to introduce a new application of hesitant fuzzy sets in real-life modeling. We intend to model multi-objective linear fractional programming problems under a hesitant fuzzy environment and present a procedure to solve them. the increasing applications of multi-objective linear fractional programming problems and the lack of research papers in this field under a hesitant fuzzy environment are the main motivations of this study. In a hesitant fuzzy set, the membership degree of an element belongs to the set can be represented by several possible values in [0,1]. These values can be chosen by different experts that cannot reach a single opinion in determining a membership degree. so, in our model several evaluations for each of goals established by decision makers based on their attitudes. The generalization of the fuzzy decision-making principle and some new concepts provide an effective solution procedure for the problem. Finally, a practical example is extended to illustrate the applicability of the proposed method.

Sequential approximate weak optimality conditions for multiobjective fractional programming problems via sequential calculus rules for the Brøndsted-Rockafellar approximate subdifferential

Sequential approximate weak optimality conditions for multiobjective fractional programming problems via sequential calculus rules for the Brøndsted-Rockafellar approximate subdifferential

Solving multi-level multiobjective fractional programming problem with rough interval parameter in neutrosophic environment

In this study, a novel algorithm is developed to solve the multi-level multiobjective fractional programming problems, using the idea of a neutrosophic fuzzy set. The co-efficients in each objective functions is assumed to be rough intervals. Furthermore, the objective functions are transformed into two sub-problems based on lower and upper approximation intervals. The marginal evaluation of pre-determined neutrosophic fuzzy goals for all objective functions at each level is achieved by different membership functions, such as truth, indeterminacy/neutral, and falsity degrees in neutrosophic uncertainty. In addition, the neutrosophic fuzzy goal programming algorithm is proposed to attain the highest degrees of each marginal evaluation goals by reducing their deviational variables and consequently obtain the optimal solution for all the decision-makers at all levels. To verify and validate the proposed neutrosophic fuzzy goal programming techniques, a numerical example is adressed in a hierarchical decision-making environment along with the conclusions.

Multi-objective optimization modelling of sustainable green supply chain in inventory and production management

The ever increasing pressure to conserve the environment from global warming cannot be overemphasized. Emission from the inventory and production process contributes immensely to global warming and hence, the need to device a sustainable green inventory by the operational managers. In this paper, a multi-item multi-objective inventory model with back-ordered quantity incorporating green investment in order to save the environment is proposed. The model is formulated as a multi-objective fractional programming problem with four objectives: maximizing profit ratio to total back-ordered quantity, minimizing the holding cost in the system, minimizing total waste produced by the inventory system per cycle and minimizing the total penalty cost due to green investment. The constraints are included with budget limitation, space restrictions, a constraint on cost of ordering each item, environmental waste disposal restriction, cost of pollution control, electricity consumption cost during production and cost of greenhouse gas emission in the production process. The model effectiveness is illustrated numerically, and the solution obtained to give a useful suggestion to the decision-markers in the manufacturing sectors.

Parametric approach for approximate efficiency of robust multiobjective fractional programming problems

In this paper, a methodology is developed to solve an uncertain multiobjective fractional programming problem in the face of data uncertainty in the objective and constraint functions. We use the robust optimization approach (worst‐case approach) for finding ɛ‐efficient solutions of the associated robust multiobjective fractional programming problem defined as a robust (worst‐case) counterpart. For the robust multiobjective fractional programming problem constructed in the robust approach, In fact, in the parametric Dinkelbach approach. We define for the given multiobjective fractional programming problem its corresponding parametric robust vector optimization problem. Then, we establish both necessary and sufficient optimality conditions for a feasible solution to be an ‐efficient solution (an approximate efficient solution) of the parametric robust vector optimization problem. Also we prove the relationship between ɛ‐efficiency of the robust multiobjective fractional programming problem (and thus ɛ‐efficiency of the considered uncertain multiobjective fractional programming problem) and ‐efficiency of its corresponding parametric robust vector optimization problem constructed in the Dinkelbach approach. In order to prove this result, we also use a scalarization method. Thus, the equivalence between an approximate efficient solution of the parametric robust vector optimization problem and an approximate minimizer of its associated scalar optimization problem constructed in the used scalarization method is also established.

Solving the multi-objective stochastic interval-valued linear fractional integer programming problem

In this paper, we consider a Multi-Objective Stochastic Interval-Valued Linear Fractional Integer Programming problem (MOSIVLFIP). We especially deal with a multi-objective stochastic fractional problem involving an inequality type of constraints, where all quantities on the right side are log-normal random variables, and the objective functions coefficients are fractional intervals. The proposed solving procedure is divided in three steps. In the first one, the probabilistic constraints are converted into deterministic ones by using the chance constrained programming technique. Then, the second step consists of transforming the studied problem objectives on an optimization problem with an interval-valued objective functions. Finally, by introducing the concept of weighted sum method, the equivalent converted problem obtained from the two first steps is transformed into a single objective deterministic fractional problem. The effectiveness of the proposed procedure is illustrated through a numerical example.

Higher order symmetric duality for multiobjective fractional programming problems over cones

This article studies a pair of higher order nondifferentiable symmetric fractional programming problem over cones. First, higher order cone convex function is introduced. Then using the properties of this function, duality results are set up, which give the legitimacy of the pair of primal dual symmetric model.