Genetic Algorithm for FGP Model of a Multiobjective Bilevel Programming Problem in Uncertain Environment

In this paper, we propose an alternate modified solution procedure based on fuzzy goal programming (FGP) approach for solving bi-level multiobjective linear fractional programming problems (BL-MOLFPPs) with some major modifications in the algorithm suggested by Abo-Sinna and Baky (2010). The proposed modified technique is simpler and requires less computational works than that of earlier technique. In the formulation of FGP models, each objective function (at both the levels - leader's level and follower's level) as well as control variables (of leader's level) are transformed into fuzzy goals with modified membership functions. Then FGP approach is used for achieving the highest degree of each of membership goals. To avoid decision deadlock situations and difficulties associated with bi-level programming problems, solution preferences by decision makers (at leader's and follower's levels) are not taken into account in proposed algorithm. A comparative analysis is also carried out with numerical example in order to show efficiency of proposed algorithm over earlier technique.

This paper explores the application of fuzzy goal programming (FGP) for modeling and solving land allocation problems with chance constraints, aimed at optimizing the production of seasonal crops within agricultural systems in uncertain environments. The decision-making environment in agricultural systems is often characterized by imprecision, particularly due to unpredictable rainfall patterns and limited availability of irrigation water, which are influenced by socio-economic factors. These uncertainties pose significant challenges in real-world agricultural scenarios. The proposed model incorporates fuzzy descriptions for the utilization of cultivable land, farming resources, and the achievement of production goals for seasonal crops. Water supply, as a critical resource, and socio-economic constraints are represented probabilistically within this uncertain decision-making framework. The model addresses land-use planning for the cultivation of five major crops—Paddy, Wheat, Mustard, Potato, and Pulses—across three crop cycles: Pre-Kharif, Kharif, and Rabi, throughout the planning year for the Bardhaman district of West Bengal, India. The solution process focuses on maximizing the membership value (unity) of the fuzzy goals, reflecting the aspirations of the decision maker (DM) as closely as possible, based on their needs and objectives. The potential of this approach is demonstrated through a case study of Bardhaman district, West Bengal, India, illustrating how FGP can be used to address agricultural planning challenges under uncertain conditions.

This article presents a fuzzy goal programming (FGP) procedure for modeling and solving multilevel programming (MLP) problems by using genetic algorithm (GA) in a large hierarchical decision making system. In the proposed approach, an GA scheme is introduced first for searching of solutions at different stages and thereby solving the problem and making decision in the order of hierarchy of execution of decision powers of the decision makers (DMs) located at different hierarchical levels. In the proposed GA scheme, Roulette-wheel selection scheme, single point crossover and random mutation are adopted to search a satisfactory solution in the hierarchical decision system. To illustrate the potential use of the approach, a numerical example is solved.

A hybrid genetic algorithm model for transshipment management decisions

This is a summary of the Ph.D. thesis defended by the author in December 2009 at Ecole des Mines de Nantes and Universidad de los Andes in Bogota. The thesis was advised by Christelle Gueret and Andres L. Medaglia and co-advised by Bruno Castanier and Nubia Velasco. The manuscript is written in English and it is available from the author upon request. The focus of the dissertation is to study real-world vehicle routing problems (VRPs) in uncertain environments. First, the thesis proposes a set of new methods for the VRP faced by a public utility and reports how these methods were embedded into a decision support system. Second, the thesis introduces a stochastic VRP widely found in practice but never studied in the literature before: the multi-compartment VRP with stochastic demands (MC-VRPSD). To solve the problem the dissertation proposes a set of solution methods that offer different tradeoffs between accuracy, speed, simplicity and flexibility. Lastly, the thesis proposes two multiobjective approaches to address the risk behavior of decision makers towards the cost spread in stochastic routing problems and applies them to the MC-VRPSD.

Fuzzy goal programming has important applications in many areas of supply chain, logistics, transportation and shipping business. Business management has complications, and there exist many interactions between the factors of its components. The locomotive of world trade is maritime transport and approximately 90% of the products in the world are transported by sea. Optimization of maritime operations is a challenge in order to provide technical, operational and financial benefits. Fuzzy goal programming models attract interests of many scholars, therefore the objective of this paper is to investigate the problem of minimization of total cost and minimization of loss or damage of containers returned from destination port. There are various types of fuzzy goal programming problems based on models and solution methods. This paper employs fuzzy goal programming with triangular fuzzy numbers, membership functions, constraints, assumptions as well as the variables and parameters for optimizing the solution of the model problem. The proposed model presents the mathematical algorithm, and reveals the optimal solution according to satisfaction rank from 0 to 1. Providing a theoretical background, this study offers novel ideas to researchers, decision makers and authorities.

Fuzzy goal programming for health-care organization

In this paper, we present modified fuzzy goal programming (FGP) approach and generalized MATLAB program for solving multi-level linear fractional programming problems (ML-LFPPs) based on with some major modifications in earlier FGP algorithms. In proposed modified FGP approach, solution preferences by the decision makers at each level are not considered and fuzzy goal for the decision vectors is defined using individual best solutions. The proposed modified algorithm as well as MATLAB program simplifies the earlier algorithm on ML-LFPP by eliminating solution preferences by the decision makers at each level, thereby avoiding difficulties associate with multi-level programming problems and decision deadlock situation. The proposed modified technique is simple, efficient and requires less computational efforts in comparison of earlier FGP techniques. Also, the proposed coding of generalized MATLAB program based on this modified approach for solving ML-LFPPs is the unique programming tool toward dealing with such complex mathematical problems with MATLAB. This software based program is useful and user can directly obtain compromise optimal solution of ML-LFPPs with it. The aim of this paper is to present modified FGP technique and generalized MATLAB program to obtain compromise optimal solution of ML-LFP problems in simple and efficient manner. A comparative analysis is also carried out with numerical example in order to show efficiency of proposed modified approach and to demonstrate functionality of MATLAB program.

• Propose novel behavioral membership functions within the fuzzy goal programming approach. • Model decision-makers’ behavioral aspects and risk perceptions. • Develop a behavior-based fuzzy goal programming approach. • Enhance utility functions within the fuzzy goal programming methodology. • Demonstrate applicability and efficacy through a venture capital investment problem. A relevant extension of traditional goal programming (GP), fuzzy goal programming (FGP) can handle uncertainty and imprecision in multi-objective optimization problems. Based on fuzzy set theory, the notion of membership functions has been introduced to consider the fuzziness related to objectives and constraints. These membership functions are mainly intended for fuzziness in the GP rather than modeling the decision-maker's (DM's) preferences and his/her attitude toward risk in the decision-making process. In the satisfying philosophy of FGP, little attention has been given to how preferences evolve in terms of the behavior of the decision-maker (DM) and how these preferences may affect decisions in risky scenarios. To address this issue, we suggest novel behavioral-type utility functions for the FGP approach by introducing the concept of behavioral membership functions. This concept offers an innovative procedure for simulating the DM's behavioral preferences in the FGP approach. First, two main categories of objectives in relation to the DM's behavioral preferences are distinguished in this work. A risk aversion parameter is integrated into membership functions according to the nature of each objective type, obtaining the so-called behavioral membership functions. A behavioral FGP approach is subsequently formulated. Finally, an illustrative example of venture capital investments, a sensitivity analysis, and comparisons with other FGP approaches are provided to demonstrate the validity and practicality of our proposed approach.

Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models

In the present paper, genetic algorithms (GA) have been used to optimize the design of a generic expert system based on fuzzy logics. Using the classical branch-and-bound method, the latter performs a heuristic graph search to solve a decision-making problem under uncertain environment. After building this fuzzy expert system, we isolate a set of parameters which are important for the system efficiency, and we show how these parameters can be optimized automatically using Genetic Algorithms. This optimization brings significant improvement over the manual tuning of the parameters in the specific case of a fuzzy expert system developed for the automatic target recognition of armoured vehicles starting from short-range infra-red images. >

Defined as the fulfillment of nutritional requirements of people working at different places such as schools, hospitals etc., public food service’s one of the most important stage is menu planning. Menu planning is such a complex process that one should take not only many factors into consideration like cost, energy/nutrition units, taste, diversity etc., but also some aims which should be practiced simultaneously. One of the programs which can be used in programming for such a process is goal programming, a technic for multi-purpose decisions. In the goal programming as a data based technic, fuzzy goal programming models have also been advanced for the situations in which data are not certain. In this study, an example lunch meal menu planning is prepared for the workers between 19 and 30 years old. The menu is planned as non-optional. During the process of planning, fuzzy goal programming method was used in consequence of fuzziness in data.

Transportation problem is an integral part of this competitive world. Minimizing transportation cost of a product from sources to destinations is the main objective of traditional transportation problems. In the present context single objective transportation problem fails to meet the managerial decision making requirements which demands the multi objective transportation problems. Many real life problems can be formulated as multi objective transportation problem, and their solution requires consideration of conflicting objectives. Naturally, these problems have a number of potentially Pareto-optimal solutions. Multi-objective transportation problem refers to a special class of vector minimum linear programming problem, which usually involves multiple, conflicting, and incommensurable objective functions. Solving these complexities, the decision maker has to develop a utility function. In this paper, we develop a utility function to attain the targeted goal for a multi objective transportation problem. This utility function is developed using fuzzy membership functions considering deviations of objective function from the goal value where deviation variable has chosen as fuzzy type. Moreover, fuzzy max-min operator has been included for taking limiting value of the objective functions. Performance of the utility function to achieve proper goal is evaluated and justified by solving numerical examples using fuzzy goal programming.

Water allocation is an essential programming to support the sustainable development of Wuwei Basin, Gansu Province, China. To satisfy the demands of the decision makers (DMs) of each subarea and the total area, a bilevel multiobjective linear programming (BLMOLP) model is proposed. In the BLMOLP, DMs have a hierarchy of two levels—the upper level and the lower level DMs. In this paper, a fuzzy goal programming (FGP) approach is applied to solve the BLMOLP. Firstly, the upper level is solved and used as the tolerance for the lower level. Then the weights of each objective function in the lower level are evaluated. Finally, a satisfied optimization solution of the problem was calculated. The result suggests that the FGP is a simple and feasible approach to BLMOLP problems. The proposed method was applied to a case study for water resources allocation in Wuwei Basin. For four scenarios under consideration, the model can effectively balance the benefits among all regions and sections according to the priority of the upper level decision makers. The results indicate that comprehensive solutions have been obtained.

Application of fuzzy goal programming and genetic algorithm is considered in this paper. We extend a multi-objective model for integrated inventory-production-distribution planning in supply chain (SC). We consider a supply chain network which consists of a manufacture, with multiple plants, multiple distribution centers (DCs), multiple retailers and multiple customers. The manufacturer produces several items. Decision maker’s imprecise aspiration levels of goals are incorporated into model using fuzzy goal programming approach. Due to the complexity of problem in large size and in order to get a satisfactory near optimal solution with great speed, a new genetic algorithm is proposed to solve constrained problems. To show the efficiency of the used model and fuzzy goal programming approach and genetic algorithm for the collaborative inventory-production-distribution problem, computational experiments are performed on a hypothetically constructed case problem.