Multiobjective Fractional Programming Research Articles

Second-order strong optimality and duality for nonsmooth multiobjective fractional programming with constraints

Second-order strong optimality and duality for nonsmooth multiobjective fractional programming with constraints

An ordered multi-objective fuzzy stochastic approach to sustainable water resources management: a case study from Taiyuan City, China

Abstract The uncertainty of socioeconomic development and climate change poses challenges to the sustainable management of water resources in Taiyuan, China. The study proposes a type-2 fuzzy chance-constrained ordered multi-objective fractional programming (T2FCC-ORMOFP) model to address the allocation of water under uncertainties. The model incorporates type-2 fuzzy programming and chance-constrained programming into an overall framework to handle multiple uncertainties under multi-level and multi-objective conflicts, while using fractional programming to reflect the marginal benefits of the system. It prioritizes the principles of optimal, fair, and stable distribution by the upper-level governing authorities, while considering the social and economic environmental benefits of lower-level decision-making. The optimal water allocation scenarios were obtained under different hydrological guarantee rates, violation levels of water supply constraints, and net economic benefits of type-2 fuzzy numbers for 2030. Additionally, groundwater is replaced by reclaimed water in varying proportions for flexible water supply. The results show that the water demand in Taiyuan cannot be ignored, and the risk of water shortage is more sensitive for the agricultural and industrial sectors. The recycled water substitution strategy can optimize the water supply structure and improve social and economic benefits (9–12%). Also T2FCC-ORMOFP can improve overall efficiency (20%) compared with a single-level model.

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

Managing irrigation water resources with economic benefit and energy consumption: an interval linear multi-objective fractional optimization model under multiple uncertainties

At present, water shortage has increasingly become one of the key factors restricting the sustainable development of agriculture. And during the process of agricultural production, the energy consumption has also been paid more and more attention. Therefore, in order to deal with the above problems, an improved interval linear multi-objective fractional programming model (ILMOFPM) was developed, which has the characteristic is that it not only focuses on the optimal allocation of the amount of irrigation water resources, but also on improving irrigation water resources use efficiency. To demonstrate its effectiveness and applicability, ILMOFPM was applied to a case study in Jinghuiqu irrigation district, Shaanxi Province, China. Maximum economic benefit per unit of water resource and minimum energy consumption per unit of water resource were selected as the planning objectives. A series of irrigation water resources optimal allocation schemes were obtained, which could give the decision makers the desired optimal scheme according to the actual situation. Based on the results of the established model, economic benefit and energy consumption generally decreased as the representative hydrological years changed from wet to dry, and the total crop planting area also showed a decreased trend. Moreover, a lot of water resources was saved by introducing crop evapotranspiration and effective precipitation in the developed model, 57.45%, 44.17%, 39.33% of total water resources consumption were saved under different representative hydrological years, respectively.

On Quasidifferentiable Multiobjective Fractional Programming

On Quasidifferentiable Multiobjective Fractional Programming

Optimality Conditions for Generalized Convex Nonsmooth Uncertain Multi-objective Fractional Programming

Optimality Conditions for Generalized Convex Nonsmooth Uncertain Multi-objective Fractional Programming

A parametric approach to fuzzy multi-objective linear fractional program: An alpha cut based method

In the multi-objective programming problem (MOPP), finding an efficient solution is challenging and partially encompasses some difficulties in practice. This paper presents an approach to address the multi-objective linear fractional programing problem with fuzzy coefficients (FMOLFPP). In the method, at first, the concept of α - cuts is used to change the fuzzy numbers into intervals. Therefore, the fuzzy problem is further changed into an interval-valued linear fractional programming problem (IVLFPP). Afterward, this problem is transformed into a linear programming problem (LPP) using a parametric approach and the weighted sum method. It is proven that the solution resulted from the LPP is at least a weakly ɛ - efficient solution. Two examples are given to illustrate the method.

A Multiobjective Fractional Programming for a CHP System Operation Optimization Based on Energy Intensity

The objective of this research is to establish a multiobjective fractional programming (MOFP) model for supporting the operational management of a combined heat and power (CHP) system. Compared with the traditional operational optimization model of the CHP system, the importance of the energy intensity (i.e., the ratio of energy consumption and energy production) was emphasized in the MOFP model, which is considered as the system objective for replacing the common objective of minimizing the economic cost. This innovative transformation effectively reduces excessive energy consumption, accompanied by improvement in the system revenue. The CHP system of an industrial park in the City of Jinan, China, was used as a study case for demonstration. The obtained results reflected that the combination of two gas turbines (GTs) ensured safe, efficient, and stable output for meeting daily power requirements in various seasons. As for the steam load, during the summer, two heat recovery steam generators (HRSGs) play a major role, where the insufficient part is supplemented by two gas-fired boilers (SBs); conversely, the steam load in winter is mainly satisfied by the aid of two SBs. The successful application of the MOFP model in the park could provide a good demonstration for CHP management in many other districts and cities.

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.