A Metaheuristic Optimization Algorithm for Solving Higher-Order Boundary Value Problems

An effective metaheuristic algorithm to solve the higher-order boundary value problems, called a genetic programming technique is presented. In this paper, a genetic programming algorithm, which depends on the syntax tree representation, is employed to obtain the analytical solutions of higher- order differential equations with the boundary conditions. The proposed algorithm can be produce an exact or approximate solution when the classical methods lead to unsatisfactory results. To illustrate the efficiency and accuracy of the designed algorithm, several examples are tested. Finally, the obtained results are compared with the existing methods such as the homotopy analysis method, the B-Spline collocation method and the differential transform method.

NEW IMPROVED METHOD FOR SOLVING THE FUZZY LINEAR PROGRAMMING PROBLEMS WITH VARIABLES GIVEN AS FUZZY NUMBERS

The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fuzzy linear programming problem with variables given as fuzzy numbers with minimum uncertainty. In this paper, the fuzzy linear programming problems with variables given as fuzzy numbers is transformed into equivalent interval linear programming problems with variables given as interval numbers. The solutions to these interval linear programming problems with variables given as interval numbers are then obtained with the help of linear programming technique. A set of six random numerical examples has been solved using the proposed approach.

Multi-objective optimization of tensile properties of the corrugated composite sheet

Corrugated sheets with optimized mechanical properties are crucial for lightweight design in industrial applications. This study considered and optimized a corrugated sheet with a sinusoidal profile to enhance elastic modulus, tensile-bending coupling, and weight reduction. For this aim, first, flat specimens consisting of E-glass woven fiber and epoxy resin were made by hand lay-up method, following ASTM D3039. The tensile test determined young’s modulus of flat samples. Afterward, two molds with supports were fabricated. The corrugated specimens were constructed and exposed to a standard tensile test. The finite element analysis was used to simulate the tensile test of corrugated samples. The numerical force-displacement curve is derived from numerical analysis and verified by experimental results. After that, two multi-objective optimization problems, mass-constraint and global optimization, were implemented. Analytical formulations were verified by numerical and experimental results and utilized for optimization purposes. The genetic algorithm was used to examine and confirm trade-off behavior between objective functions. The Pareto fronts diagrams for mentioned two multi-objective optimization problem were obtained. Finally, the optimum parameters are calculated by using the LINMAP (Linear Programming Technique for Multi-dimensional Analysis of Preference) method.

Hesitant Fuzzy 2-Dimension Linguistic Programming Technique for Multidimensional Analysis of Preference for Multicriteria Group Decision Making

The hesitant fuzzy 2-dimension linguistic element (HF2DLE) allows decision makers to express the importance or reliability of each term included in a hesitant fuzzy linguistic element as a linguistic term. This paper investigates a programming technique for multidimensional analysis of preference for hesitant fuzzy 2-dimension linguistic multicriteria group decision making. Considering the flexibility of HF2DLEs in expressing hesitant qualitative preference information, we first adopt HF2DLEs to depict both the evaluation values of alternatives and the truth degrees of alternative comparisons. To calculate the relative closeness degrees (RCDs) of alternatives, the Euclidean distances between HF2DLEs are defined. Based on RCDs and preference relations on alternatives, the group consistency and inconsistency indices are constructed, and a bi-objective hesitant fuzzy 2-dimension linguistic programming model is established to derive the criteria weights and positive and negative ideal solutions. Since the objective functions and partial constraint coefficients of the established model are HF2DLEs, an effective solution is developed, through which the RCDs can be calculated to obtain the individual rankings of alternatives. Furthermore, a single-objective assignment model is constructed to determine the best alternative. Finally, a case study is conducted to illustrate the feasibility of the proposed method, and its effectiveness is demonstrated by comparison analyses.

Production Efficiency of Major Crops among Smallholders Farmers in Central Ethiopia

Agricultural production of most smallholders in Ethiopia is dependent with recurrent rainfall resulted in production variations. Limited input availability and precarious environmental conditions determine smallholders’ decisions on their production and the production efficiencies vary from farmer to farmer. This study was carried out with the aim of analyzing the technical, allocative and economic efficiencies of smallholder farmers in the production of major crops and their determinants in central Ethiopia, Oromia special zone surrounding Addis Ababa. Multistage sampling technique was employed to randomly and proportionally select 386 smallholders from ten PAs. Primary data were collected from smallholders through a semi structured questionnaire using face to face interview. Cross sectional data collected from sampled households in the study area were analyzed using mathematical and econometric methods. Mathematical programming technique selected for this study was Data Envelopment Analysis (DEA) using linear programming technique assuming multi-input and multi-outputs were handled. Tobit regression model was regressed against the socioeconomic, demographic, and institutional variables that are expected to affect the technical, allocative and economic efficiencies of sampled households. The results of estimated efficiency scores show the mean technical, allocative and economic efficiencies were 0.75, 0.60 and 0.45 respectively. The mean scores of efficiencies show underutilization of resources and the possibilities of smallholders to increase their agricultural production by 25%, and reduce cost of production by 40% and total cost by 55%. Marital status, level of education, farming experience, access to credit, cooperative membership, access to farming information, and off/non-farm income has positive influence on the technical, allocative and economic efficiencies. While age of the household head, access to training and livestock size has negative relations to efficiencies. Delivery of agricultural inputs and trainings on time by the government is the key policy implication to improve the efficiencies of smallholders.

Optimum Project Portfolio Selection for Developmental Plans Using Goal Programming

In vision-driven development plans, such as the Kuwait Mid-Range Development Plan 2015/2016–2019/2020, themes and pillars are derived from the plan's vision, and global indices are assigned by international organizations to accurately measure the performance against the vision's themes. This allows for comparison with other countries, and it also set targets for progression over time. One or more projects are assigned to the indicators of these global indices. A Multi-Criteria Mathematical Programming Technique (e.g., Goal Programming) is used with multiple goals and priorities where an Optimal Portfolio of Projects is found that satisfied the selection criteria.

Optimum Project Portfolio Selection for Developmental Plans Using Goal Programming

In vision-driven development plans, such as the Kuwait Mid-Range Development Plan 2015/2016–2019/2020, themes and pillars are derived from the plan's vision, and global indices are assigned by international organizations to accurately measure the performance against the vision's themes. This allows for comparison with other countries, and it also set targets for progression over time. One or more projects are assigned to the indicators of these global indices. A Multi-Criteria Mathematical Programming Technique (e.g., Goal Programming) is used with multiple goals and priorities where an Optimal Portfolio of Projects is found that satisfied the selection criteria.

Multi-Objective Capacitated Solid Transportation Problem with Uncertain Variables

This paper investigates a multi-objective capacitated solid transportation problem (MOCSTP) in an uncertain environment, where all the parameters are taken as zigzag uncertain variables. To deal with the uncertain MOCSTP model, the expected value model (EVM) and optimistic value model (OVM) are developed with the help of two different ranking criteria of uncertainty theory. Using the key fundamentals of uncertainty, these two models are transformed into their relevant deterministic forms which are further converted into a single-objective model using two solution approaches: minimizing distance method and fuzzy programming technique with linear membership function. Thereafter, the Lingo 18.0 optimization tool is used to solve the single-objective problem of both models to achieve the Pareto-optimal solution. Finally, numerical results are presented to demonstrate the application and algorithm of the models. To investigate the variation in the objective function, the sensitivity of the objective functions in the OVM model is also examined with respect to the confidence levels.