Fuzzy Nonlinear Programming Research Articles

Fuzzy Non-Linear Programming for Fuzzy Inventory Model with Storage Space and Budget Constraint

Fuzzy Non-Linear Programming for Fuzzy Inventory Model with Storage Space and Budget Constraint

An interior penalty function method for solving fuzzy nonlinear programming problems

In this article, we investigate fuzzy interior penalty function method for solving fuzzy nonlinear programming problems (FNLPP) based on a new fuzzy arith-metic, unconstrained optimization, and fuzzy ranking on the parametric form of triangular fuzzy numbers (TFN). The main objective of this paper is to solve constrained fuzzy nonlinear programming problems using interior penalty func-tions (IPF) by converting it into unconstrained optimization problems. We prove an important lemma and a convergence theorem for the interior penalty functions method. Interior penalty function techniques favor sites near the boundary of the feasible region in the interior. We present a numerical example of the suggested method and compare the results to those produced by existing methods.

Delivering Goods Sustainably: A Fuzzy Nonlinear Multi-Objective Programming Approach for E-Commerce Logistics in Taiwan

With the booming development of e-commerce, the importance of controlling carbon emissions has become increasingly prominent in Taiwan. This study explores the trade-offs among time, cost, quality, and carbon emissions (TCQCE) in e-commerce logistics. Will carbon emissions mitigation lead to decreased logistics efficiency and increased costs? This article differs from other studies that use precise numbers and linear model situations. This study adopts fuzzy theory, nonlinear methods, and multi-objective programming models closer to the actual situation to study the decision-making between delayed logistics delivery times and reduced carbon emissions. This article also uses Project D as a case to enhance readers’ understanding of decision-making methods in real-life e-commerce logistics cases. The results show that extended delivery times could significantly reduce carbon emissions, ranging from 5259.31 to 419,199.60 tons, and reduce delivery quality under the 90.00% threshold and even under 75.25%. Extending delivery times is a viable business strategy, particularly by extending delivery to push carbon reduction policies to minimize environmental impact. However, consumer acceptance is crucial, as consumers willing to embrace longer wait times can significantly contribute to emission mitigation and support businesses committed to sustainability. This research uses a fuzzy nonlinear multi-objective programming model (FNMOPM) to contribute novel time management to mitigate carbon emissions. Moreover, this study uses a fuzzy and nonlinear approach to fill in the gaps of previous research to balance the efficiency and carbon emission mitigation goals of ESG (environmental, social, and governance) principles. The framework presented in this article solves the complex trade-off situations in the TCQCE issues. This article provides practical, actionable guidance for decision-making regarding sustainable e-commerce logistics, instilling confidence in its implementation.

SOLVING FUZZY NONLINEAR PROGRAMMING PROBLEMS WITH EXTERIOR PENALTY FUZZY VALUED FUNCTIONS

In this article, we explore the exterior penalty fuzzy valued function method for Fuzzy Nonlinear Programming Problems (FNLPP). We present methods of penalty fuzzy valued function for solving constrained optimization problems by converting to unconstrained optimization problems. Triangular fuzzy numbers are used to represent the problem’s decision variables and coefficients. Using a new fuzzy arithmetic and fuzzy ranking method on the parametric form of triangular fuzzy numbers, the optimal solution of the FNLPP is found by applying the exterior penalty fuzzy valued function method without changing to its equivalent crisp form. We present a numerical example of the suggested method and compare the results to those produced by existing methods

An optimization model for fuzzy nonlinear programming with Beale's conditions using trapezoidal membership functions

Non-linear Programming (NLP) is an optimization technique for determining the optimum solution to a broad range of research issues. Many times, the objective function is non-linear, owing to various economic behaviors such as demand, cost, and many others. Since the appearance of Kuhn and Tucker's fundamental theoretical work, a general NLP problem can be resolved using many methods to find the optimum solution. In this chapter, a fuzzy mathematical model based on Beale's condition is proposed to address NLP with inequality constraints in terms of fuzziness. Furthermore, the model demonstrates how quadratic programming problems can be solved using membership functions. The model also describes three stages: that is, mathematical formulation, computational procedures, and numerical illustration with comparative analysis. Likewise, the model illustrates the considered problem using two distinct approaches, namely membership functions (MF) and robust ranking index. Finally, the comparison analysis provides detailed results and discussion that justify the optimal outcome in order to address the vagueness of certain NLPPs.

Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty

This study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing problem in an uncertain environment where the capacities and carbon emission factors of the travel process and the transfer process in the multimodal network are considered fuzzy. Taking triangular fuzzy numbers to describe the uncertainty, this study proposes a fuzzy nonlinear programming model to deal with the specific routing problem. To make the problem solvable, this study adopts the fuzzy chance-constrained programming approach based on the possibility measure to remove the fuzziness of the proposed model. Furthermore, we use linear inequality constraints to reformulate the nonlinear equality constraints represented by the continuous piecewise linear functions and realize the linearization of the nonlinear programming model to improve the computational efficiency of problem solving. After model processing, we can utilize mathematical programming software to run exact solution algorithms to solve the specific routing problem. A numerical experiment is given to show the feasibility of the proposed model. The sensitivity analysis of the numerical experiment further clarifies how improving the confidence level of the chance constraints to enhance the possibility that the multimodal route planned in advance satisfies the real-time capacity constraint in the actual transportation, i.e., the reliability of the routing, increases both the total costs and carbon emissions of the route. The numerical experiment also finds that charging carbon emissions is not absolutely effective in emission reduction. In this condition, bi-objective analysis indicates the conflicting relationship between lowering transportation activity costs and reducing carbon emissions in routing optimization. The sensitivity of the Pareto solutions concerning the confidence level reveals that reliability, economy, and environmental sustainability are in conflict with each other. Based on the findings of this study, the customer and the multimodal transport operator can organize efficient multimodal transportation, balancing the above objectives using the proposed model.

A Pivotal Operation on Triangular Fuzzy Number for Solving Fuzzy Nonlinear Programming Problems

A Pivotal Operation on Triangular Fuzzy Number for Solving Fuzzy Nonlinear Programming Problems

Non-linear fuzzy programming - a case study

Non-linear fuzzy programming - a case study

Image reconstruction of ECT based on second-order hybrid sensitivity matrix and fuzzy nonlinear programming

In the derivation of the sensitivity matrix of electrical capacitance tomography, only the linear portion of the sensitivity coefficient is usually retained, while the neglected nonlinear part also contains important imaging information. In order to improve the accuracy of image reconstruction, a second-order hybrid sensitivity matrix is presented based on the capacitance normalization model and second-order item of sensitivity coefficients in this paper. Then, a fuzzy nonlinear programming algorithm based on the second-order hybrid sensitivity matrix (SHS-FNP) is proposed. Simulation and experiments are carried out. Reconstructed images using the presented method are compared with those of the Tikhonov algorithm, first-order hybrid Landweber algorithm, second-order hybrid Landweber algorithm, and fuzzy linear programming algorithm. The experimental results show that the SHS-FNP algorithm considerably enhances the quality of the reconstructed image.

An optimization method to solve a fully intuitionistic fuzzy non-linear separable programming problem

This paper presents an optimization method to solve a non-linear separable programming problem with coefficients and variables as generalized trapezoidal intuitionistic fuzzy numbers. Such optimization problems are known as fully intuitionistic fuzzy non-linear separable programming problems. The optimization method is based on the linear approximation of fully intuitionistic fuzzy non-linear separable functions. The concept of an intuitionistic fuzzy line segment between two intuitionistic fuzzy points is introduced to find the required linear approximation. In this way, a fully intuitionistic fuzzy non-linear programming problem is converted into an intuitionistic fuzzy linear programming problem. The defuzzification and component-wise comparison techniques are then used to convert the fully intuitionistic fuzzy linear programming problem to a linear programming problem with crisp coefficients which can then be solved by using traditional optimization techniques. The application of the proposed approach in an investment problem faced by a businessman has been presented.

Application of a Modified Gauss Elimination Technique for Separable Fuzzy Nonlinear Programming Problems

Application of a Modified Gauss Elimination Technique for Separable Fuzzy Nonlinear Programming Problems

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.

Optimum Route and Transport Mode Selection of Multimodal Transport with Time Window under Uncertain Conditions

Aiming at the problem of multimodal transport path planning under uncertain environments, this paper establishes a multi-objective fuzzy nonlinear programming model considering mixed-time window constraints by taking cost, time, and carbon emission as optimization objectives. To solve the model, the model is de-fuzzified by the fuzzy expectation value method and fuzzy chance-constrained planning method. Combining the game theory method with the weighted sum method, a cooperative game theory-based multi-objective optimization method is proposed. Finally, the effectiveness of the algorithm is verified in a real intermodal network. The experimental results show that the proposed method can effectively improve the performance of the weighted sum method and obtain the optimal multimodal transport path that satisfies the time window requirement, and the path optimization results are better than MOPSO and NSGA-II, effectively reducing transportation costs and carbon emissions. Meanwhile, the influence of uncertainty factors on the multimodal transport route planning results is analyzed. The results show that the uncertain factors will significantly increase the transportation cost and carbon emissions and affect the choice of route and transportation mode. Considering uncertainty factors can increase the reliability of route planning results and provide a more robust and effective solution for multimodal transportation.

Multi-Objective Reliability Optimization using Fuzzy Nonlinear Programming with Interval Membership Functions and Bias Functions: A Comparison of Particle Swarm Optimization and Genetic Algorithm

Multi-objective reliability optimization is a complex problem that involves simultaneously optimizing multiple objectives while ensuring that the system meets certain reliability requirements. In this paper, we present a methodology for solving multi-objective reliability optimization problems using fuzzy nonlinear programming. The methodology involves representing the reliability of each component as a triangular interval number and each objective function as an interval membership function. Conflicts between objectives are resolved using linear and nonlinear membership functions, and exponential and quadratic membership functions are used to obtain definite biases towards the objective. The proposed methodology employs Particle Swarm Optimization (PSO) or Genetic Algorithm (GA) to solve the problem, and the approach is compared with GA for linear and nonlinear membership functions. The results indicate the effectiveness of the methodology in addressing multi-objective reliability optimization problems

PSO vs GA: A Comparative Study of Multi-Objective Reliability Optimization using Fuzzy Nonlinear Programming Functions

Abstract— Multi-objective reliability optimization is a complex problem that involves simultaneously optimizing multiple objectives while ensuring that the system meets certain reliability requirements. In this paper, we present a methodology for solving multi-objective reliability optimization problems using fuzzy nonlinear programming. The methodology involves representing the reliability of each component as a triangular interval number and each objective function as an interval membership function. Conflicts between objectives are resolved using linear and nonlinear membership functions, and exponential and quadratic membership functions are used to obtain definite biases towards the objective. The proposed methodology employs Particle Swarm Optimization (PSO) or Genetic Algorithm (GA) to solve the problem, and the approach is compared with GA for linear and nonlinear membership functions. The results indicate the effectiveness of the methodology in addressing multi-objective reliability optimization problems.

A Multi Objective Epq Model with Uniform Demand and Productıon Rate Along Wıth Shortages Under Intuitioistic Fuzzy Programmıng Approach

In this paper we have described a multi-objective economic production quantity (EPQ) model with uniform demand rate as well as shortages. In this model we have considered the production rate as finite. Due to uncertainty in the various cost parameters, most of the costs parameters are taken as pentagonal fuzzy number. The model has been solved by Fuzzy Non-Linear Programming Problem (FNLP), Fuzzy Additive Goal Programming Problem (FAGP) and Intuitionistic fuzzy programming approach (IFP).To demonstrate the validity of this model some numerical examples have been given lastly. The sensitivity analysis for some cost parameters has also been given.

Performance enhancement of parabolic trough collector solar thermal power plants with thermal energy storage capability

This paper proposes a fuzzy non-linear programming based optimisation approach using Genetic algorithm to enhance the performance of commercial parabolic trough collector concentrated solar thermal power plants with thermal energy storage capability. The proposed optimisation approach, unlike conventional methods, considers three plant performance parameters: capacity factor, plant efficiency, and levelized cost of energy for arriving at optimal plant performance. By properly sizing the PTC plant with respect to plant efficiency, thermal energy storage capacity, capacity factor, and levelized cost of electricity, even better performance levels can be achieved. For analysis purpose and to validate the efficiency of the proposed approach, three representative locations in Saudi Arabia: Yanbu, Abha, and Dawadmi were considered—wherein the design of a 100 MW commercial parabolic trough collector solar thermal power plant is optimised. The results showed that the proposed optimization approach when applied to commercial parabolic trough collector plants with thermal energy storage capability can achieve superior plant efficiency of the order of 16.53% and 17.42% and with a capacity factor greater than 60%. The findings of the study has been validated with the help of operational parameters of the commercially operated Andasol-1, La Florida, and Aste 1A parabolic trough collector concentrated solar power plants. The results confirm the efficacy of the proposed optimization approach as it achieved superior plant efficiency. This will put decision makers in better position while choosing the ideal solar thermal technology for a particular location. This research work will help augment the competitiveness and efficacy of parabolic trough collector concentrated solar power technology and prompt policymakers to increase their share in the global renewable energy mix.

A Fuzzy Multi Objective Inventory Model with Production Cost and Set-up-Cost Dependent on Population

AbstractIn this paper, I have developed a multi item production inventory model for the non-deteriorating items with constant demand rate under the limitation on set up cost. The production price and set-up price are the most vital problem within the inventory system of the marketplace in international. Here the production cost is dependent on the demand as well as populations. Set up cost is dependent on the average inventory level. Holding cost is the most challenging issue in the business world. In order to reduce the holding cost, the holding cost function has been considered as on the number of peoples. Due to uncertainty all the cost parameters are taken as the generalized triangular fuzzy number. Multi objective fuzzy inventory model has been solved by various techniques like Fuzzy programming technique with hyperbolic membership function, Fuzzy non-linear programming technique and Fuzzy additive goal programming technique. Numerical example is given to illustrate the inventory model. Sensitivity analysis and the graphical representations have been shown to illustrate the reality of the inventory model.

Evaluating the sustainability of smart technology applications in healthcare after the COVID-19 pandemic: A hybridising subjective and objective fuzzy group decision-making approach with explainable artificial intelligence.

During the COVID-19 pandemic, some smart technology applications were more effective than had been expected, whereas some others did not achieve satisfactory performance. Consequently, whether smart technology applications in healthcare are sustainable is a question that warrants investigation. To address this question, a hybridising subjective and objective fuzzy group decision-making approach with explainable artificial intelligence was proposed in this study and then used to evaluate the sustainability of smart technology applications in healthcare. The contribution of this research is its subjective evaluation of the sustainability of smart technology applications followed by correction of the evaluation outcome on the basis of the applications' objective performance during the COVID-19 pandemic. To this end, a fuzzy nonlinear programming model was formulated and optimised. In addition, the impact of several major global events that occurred during the pandemic on the sustainability of smart technology applications was considered. The proposed methodology was applied to evaluate the sustainability levels of eight smart technology applications in healthcare. According to the experimental results, three applications-namely healthcare apps, smartwatches, and remote temperature scanners-are expected to be highly sustainable in healthcare, whereas one application, namely smart clothing, is not.

Efficient road traffic anti-collision warning system based on fuzzy nonlinear programming

Efficient road traffic anti-collision warning system based on fuzzy nonlinear programming