Fuzzy Satisficing Method Research Articles

Multi-Objetive Dispatching in Multi-Area Power Systems Using the Fuzzy Satisficing Method

The traditional mathematical models for solving the economic dispatch problem at the generation level primarily focus on minimizing overall operational costs while ensuring demand is met across various periods. However, contemporary power systems integrate a diverse mix of generators from both conventional and renewable energy sources, contributing to economically efficient energy production and playing a pivotal role in reducing greenhouse gas emissions. As the complexity of power systems increases, the scope of economic dispatch must expand to address demand across multiple regions, incorporating a range of objective functions that optimize energy resource utilization, reduce costs, and achieve superior economic and technical outcomes. This paper, therefore, proposes an advanced optimization model designed to determine the hourly power output of various generation units distributed across multiple areas within the power system. The model satisfies the dual objective functions and adheres to stringent technical constraints, effectively framing the problem as a nonlinear programming challenge. Furthermore, an in-depth analysis of the resulting and exchanged energy quantities demonstrates that the model guarantees the hourly demand. Significantly, the system’s efficiency can be further enhanced by increasing the capacity of the interconnection links between areas, thereby generating additional savings that can be reinvested into expanding the links’ capacity. Moreover, the multi-objective model excels not only in meeting the proposed objective functions but also in optimizing energy exchange across the system. This optimization is applicable to various types of energy, including thermal and renewable sources, even those characterized by uncertainty in their primary resources. The model’s ability to effectively manage such uncertainties underscores its robustness, instilling confidence in its applicability and reliability across diverse energy scenarios. This adaptability makes the model a significant contribution to the field, offering a sophisticated tool for optimizing multi-area power systems in a way that balances economic, technical, and environmental considerations.

Optimal shared mobility planning for electric vehicles in the distribution network

Shared electric vehicle (EV) is an emerging component across interdependent power and transportation networks that affect economic, environmental and societal benefits. Studies on how to collaboratively enable the optimal planning of these interacted networks is less explored. In this work, a joint distribution network expansion planning framework integrated with a shared EV charging station is proposed. One of the objectives is to minimise overall investment cost considering operational waiting cost of shared EV charging service and power loss, while the other aims to maximise the utilisation of charging infrastructures. To overcome the difficulties in solving the multi-objective mixed-integer non-linear problem, Tchebycheff decomposition based evolutionary algorithm is modified to find the Pareto front showing the trade-offs between goals above. Besides, stochastic traffic assignment model is used to obtain traffic distribution and travel demand. The final optimal solution is decided by the fuzzy satisficing method. The performance of the proposed approach is evaluated on a 54-node test system. Sensitivity analysis is performed to assess the impact of key parameters from the perspectives of transportation and distribution network sectors. The numerical results demonstrate the capability and feasibility of the proposed method.

A carbon emission optimization model with reduction method of type-2 zigzag uncertain variable

The main investigation of the paper is to propose a reduction method of type-2 zigzag uncertain variables. We have also proposed an innovative, dynamic solid transportation problem (STP) considering maximization of profit and minimization of emission. The model has been presented to show an awareness among the drivers or managers of firms to emit less amount of carbon particles. The transportation parameters of the model have been taken as type-2 zigzag uncertain variables. The proposed expected value-based reduction method has been used to convert the transportation parameters into deterministic form. A real-life study has been presented here to show the use of the proposed reduction method and proposed STP. LINGO 13.0 optimization software has been used to solve the multi-objective STP using fuzzy satisficing method and intuitionistic fuzzy programming technique. The transportation parameters of the model are also presented in type-2 triangular fuzzy variables to show a comparison with the type-2 zigzag uncertain variable. A sensitivity analysis is presented with respect to different credibility levels of profit, emission, source, demand and conveyance.

Interactive fuzzy stochastic multiobjective purchase and transportation planning for food retailing

This paper considers purchase and transportation planning for food retailing in Japan where the food retailer deals with vegetables and fruits which are purchased at the central wholesale markets in several cities, and transports them by truck from each of the central wholesaler markets to the food retailer's storehouse. From a stochastic perspective, by carefully reviewing parameters in our original problem formulation, through the introduction of stochastic parameters, multiobjective linear stochastic programming problems are introduced. By using the typical stochastic models including the expectation model, the fractile model, the probability model together with chance constrained programming, the formulated multiobjective linear stochastic programming problems are transformed into deterministic ones. Assuming the decision maker has the fuzzy goal for each of the objective functions, several interactive fuzzy satisficing methods are presented for deriving a satisficing solution for the decision maker by updating the reference membership levels.

A novel semi-supervised fuzzy clustering method based on interactive fuzzy satisficing for dental x-ray image segmentation

Dental X-ray image segmentation has an important role in practical dentistry and is widely used in the discovery of odontological diseases, tooth archeology and in automated dental identification systems. Enhancing the accuracy of dental segmentation is the main focus of researchers, involving various machine learning methods to be applied in order to gain the best performance. However, most of the currently used methods are facing problems of threshold, curve functions, choosing suitable parameters and detecting common boundaries among clusters. In this paper, we will present a new semi-supervised fuzzy clustering algorithm named as SSFC-FS based on Interactive Fuzzy Satisficing for the dental X-ray image segmentation problem. Firstly, features of a dental X-Ray image are modeled into a spatial objective function, which are then to be integrated into a new semi-supervised fuzzy clustering model. Secondly, the Interactive Fuzzy Satisficing method, which is considered as a useful tool to solve linear and nonlinear multi-objective problems in mixed fuzzy-stochastic environment, is applied to get the cluster centers and the membership matrix of the model. Thirdly, theoretically validation of the solutions including the convergence rate, bounds of parameters, and the comparison with solutions of other relevant methods is performed. Lastly, a new semi-supervised fuzzy clustering algorithm that uses an iterative strategy from the formulae of solutions is designed. This new algorithm was experimentally validated and compared with the relevant ones in terms of clustering quality on a real dataset including 56 dental X-ray images in the period 2014–2015 of Hanoi Medial University, Vietnam. The results revealed that the new algorithm has better clustering quality than other methods such as Fuzzy C-Means, Otsu, eSFCM, SSCMOO, FMMBIS and another version of SSFC-FS with the local Lagrange method named SSFC-SC. We also suggest the most appropriate values of parameters for the new algorithm.

Profit Maximization Solid Transportation Problem with Trapezoidal Interval Type-2 Fuzzy Numbers

This paper proposes a new concept on transportation problem in which, we maximize the profit and minimize the transportation time while transporting an amount of quantity from a source to the destination. Here, we design two transportation models, in both the models; we maximize the profit and minimize the time of transportation. Here model-I having the unit purchase cost, unit selling price, unit transportation cost and transportation time as trapezoidal interval type-2 fuzzy number, while in model-II all the parameters are trapezoidal interval type-2 fuzzy number. To reduce these model-I and model-II into crisp equivalent, we use the expected value of a trapezoidal interval type-2 fuzzy number. Then the crisp equivalent problems are solved by employing the Interactive fuzzy satisficing method and LINGO 13.0 software to get the optimal solution. A numerical example is provided to demonstrate the models.

An Interactive Fuzzy Satisficing Method for Multiobjective Linear Programming Problems with Random Fuzzy Variables Using Possibility-based Probability Model

This paper formulates multiobjective linear programming problems where each coefficient of the objective functions is expressed by a random fuzzy variable. Assuming that the decision maker concerns about the probability that each of the objective function values is smaller than or equal to a certain target value, the fuzzy goals of the decision maker for the probabilities are introduced. Then, the possibility-based probability model to maximize the degrees of possibility with respect to the attained probability is considered. For solving transformed deterministic problems efficiently, particle swarm optimization for nonlinear programming problems is introduced. An interactive fuzzy satisficing method is presented for deriving a satisficing solution for a decision maker efficiently by updating the reference probability levels. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.

An interactive fuzzy satisficing method for random fuzzy multiobjective linear programming problems through fractile criteria optimization with possibility

This paper considers multiobjective linear programming problems where each coefficient of the objective functions isexpressed by a random fuzzy variable. A new decision making model is proposed by incorporating the concept of fractilecriteria optimization into a possibilistic programming model. An interactive fuzzy satisficing method is presented forderiving a satisficing solution for a decision maker efficiently by updating the reference membership levels. In theproposed method, it is shown that the transformed deterministic problems for obtaining Pareto optimal solutions can besolved by using some convex programming techniques. An illustrative numerical example is provided to clarify theproposed method.

An Interactive Fuzzy Satisficing Method for Random Fuzzy Multiobjective Integer Programming Problems through Probability Maximization with Possibility

This paper considers multiobjective integer programming problems where each coefficient of the objective functions is expressed by a random fuzzy variable. A new decision making model is proposed by incorporating the concept of probability maximization into a possibilistic programming model. For solving transformed deterministic problems, genetic algorithms with double strings for nonlinear integer programming problems are introduced. An interactive fuzzy satisficing method is presented for deriving a satisficing solution to a decision maker by updating the reference probability levels. An illustrative numerical example is provided to clarify the proposed method.

Robust-based interactive portfolio selection problems with an uncertainty set of returns

This paper considers a robust portfolio selection problem with an uncertainty set of future returns and satisfaction levels in terms of the total return and robustness parameter. Since the proposed model is formulated as an ill-defined problem due to uncertainty and is bi-objective, that is, to maximize both the abovementioned satisfaction levels, it is difficult to solve the model directly without introducing some criterion of optimality for the bi-objective functions. Therefore, by introducing fuzzy goals and an interactive fuzzy satisficing method, the proposed model is transformed into a deterministic equivalent problem. Furthermore, to obtain the exact optimal portfolio analytically, a solution method is developed by introducing the auxiliary problem and performing equivalent transformations. In order to compare the proposed model with previous useful models, numerical examples are provided, and the results show that it is important to maximize the robustness parameter and total return using the interactive process for adjusting investor's satisfaction levels.

Fuzzy and multiobjective purchase and transportation planning for food retailing: case study in Japan

This paper considers purchase and transportation planning for food retailing in Japan, and formulates a linear programming problem where the profit of a food retailer is maximised. The food retailer deals with vegetables and fruits which are purchased at the central wholesale markets in several cities, and transports them by truck from each of the central wholesaler markets to the food retailer’s storehouse. Having examined the optimal solution to the formulated linear programming problem, in view of the recent global warming issue, a single objective problem is reformulated as a multiobjective one. Furthermore, introducing the fuzzy goals of the decision maker, through an interactive fuzzy satisficing method, a satisficing solution for the decision maker is derived efficiently by updating the reference membership levels.

An Interactive Fuzzy Satisficing Method for Multiobjective Stochastic Integer Programming with Simple Recourse

This paper considers multiobjective integer programming problems involving random variables in constraints. Using the concept of simple recourse, the formulated multiobjective stochastic simple recourse problems are transformed into deterministic ones. For solving transformed deterministic problems efficiently, we also introduce genetic algorithms with double strings for nonlinear integer programming problems. Taking into account vagueness of judgments of the decision maker, an interactive fuzzy satisficing method is presented. In the proposed interactive method, after determineing the fuzzy goals of the decision maker, a satisficing solution for the decision maker is derived efficiently by updating the reference membership levels of the decision maker. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.

Fuzzy multiobjective nonlinear operation planning in district heating and cooling plants

This paper formulates an operation planning problem of an actual district heating and cooling plant as a multiobjective nonlinear programming problem. For the formulated multiobjective nonlinear programming problem, an interactive fuzzy satisficing method to derive a satisficing solution for the decision maker is presented. Observing the problem is nonconvex and involves hundreds of decision variables, an approximate solution method through particle swarm optimization for nonlinear programming is introduced. Using the operation planning problem of an actual district heating and cooling plant, the feasibility and effectiveness of the proposed method are investigated.

An interactive fuzzy satisficing method based on fractile criterion optimization for multiobjective stochastic integer programming problems

In this paper, we focus on multiobjective integer programming problems involving random variable coefficients in objective functions and constraints. Using the concept of chance constrained conditions, such multiobjective stochastic integer programming problems are transformed into deterministic ones based on the fractile criterion optimization model. As a fusion of stochastic programming and fuzzy one, we introduce fuzzy goals representing the ambiguity of the decision maker’s judgments into them and define M- θ -efficiency, a new concept of efficient solution, as a fusion of stochastic approaches and fuzzy ones. Then, we construct an interactive fuzzy satisficing method using genetic algorithms to derive a satisficing solution for the decision maker which is guaranteed to be M- θ -efficient by updating the reference membership levels. Finally, the efficiency of the proposed method is demonstrated through numerical experiments.

An interactive fuzzy satisficing method based on variance minimization under expectation constraints for multiobjective stochastic linear programming problems

In this paper, we focus on multiobjective linear programming problems involving random variable coefficients in objective functions and constraints. Using the concept of chance constrained conditions, such multiobjective stochastic linear programming problems are transformed into deterministic ones based on the variance minimization model under expectation constraints. After introducing fuzzy goals to reflect the ambiguity of the decision maker’s judgements for objective functions, we propose an interactive fuzzy satisficing method to derive a satisficing solution for them as a fusion of the stochastic programming and the fuzzy one. The application of the proposed method to an illustrative numerical example shows its usefulness.

Interactive fuzzy multiobjective reliability optimization using NSGA-II

In many practical situations where reliability enhancement is involved, the decision making is complicated because of the presence of several mutually conflicting objectives. Presence of multiple objectives in a problem, in principle, gives rise to a set of optimal solutions (largely known as Pareto-optimal solutions), instead of a single optimal solution. This type of problem is known as multiobjective optimization problem (MOOP). In general, a MOOP can be solved using weighted sums or decision-making schemes. An alternative way is to look for the Pareto-optimal front. Many evolutionary algorithms (EAs) like genetic algorithm (GA) have been suggested to solve MOOP, hence termed as multiobjective evolutionary algorithms (MOEAs). Nondominated sorting genetic algorithm (NSGA-II) is one such MOEA which demonstrates the ability to identify a Pareto-optimal front efficiently. Thus, it provides the decision maker (DM) a complete picture of the optimal solution space. This paper presents the reliability optimization of a life-support system in a space capsule where reliability of the system is maximized while minimizing the cost. An interactive fuzzy satisficing method for deriving a Pareto-optimal solution preferred by the DM is presented here. Prior preference of the DM has been taken into account here. Using the concept of fuzzy sets and convex fuzzy decision making a multiobjective fuzzy optimization problem is formulated from the original crisp optimization problem. Different nonlinear membership functions based on the DM’s preference have been employed for the fuzzification. Then, NSGA-II is applied to solve the resulting fuzzified MOOP. Resulting Pareto-optimal solution gives the DM variety of alternatives to seek an appropriate solution by modifying parameters interactively according to his/her preference again. Various Pareto-optimal fronts under different preferences of DM have been reported.

An Interactive Fuzzy Satisficing Method for Multiobjective Nonlinear Integer Programming Problems with Block-Angular Structures through Genetic Algorithms with Decomposition Procedures

We focus on multiobjective nonlinear integer programming problems with block-angular structures which are often seen as a mathematical model of large-scale discrete systems optimization. By considering the vague nature of the decision maker's judgments, fuzzy goals of the decision maker are introduced, and the problem is interpreted as maximizing an overall degree of satisfaction with the multiple fuzzy goals. For deriving a satisficing solution for the decision maker, we develop an interactive fuzzy satisficing method. Realizing the block-angular structures that can be exploited in solving problems, we also propose genetic algorithms with decomposition procedures. Illustrative numerical examples are provided to demonstrate the feasibility and efficiency of the proposed method.

A Fuzzy Model for the Multiobjective Emergency Facility Location Problem with A-Distance

This paper proposes a new multiobjective location problem for emergency facilities, e.g. ambulance service stations and fire stations. In the problem, one of the objectives is to minimize the maximal distance of the paths from the located emergency facilities to hospitals via accidents. The other is to maximize the frequency of accidents that the emergency facilities can respond quickly. An interactive fuzzy satisficing method with particle swarm optimization (PSO) method is proposed for finding a satisficing location for the problem. Computational results illustrate the method with numerical examples of the multiobjective location problem.

Decision process for multiobjective, multi-item production-inventory system via interactive fuzzy satisficing technique

Multiobjective and single-objective inventory models of stochastically deteriorating items are developed in which demand is a function of inventory level and selling price of the commodity. Production rate depends upon the quality level of the items produced and unit production cost is a function of production rate. Deterioration depends upon both the quality of the item and duration of time for storage. The time-related deterioration function follows a two-parameter Weibull distribution in time. In these models, results are derived for both without shortages and partially backlogged shortages. Here, objectives for profit maximization for each item are separately formulated with different goals and compromise solutions of the multiobjective production/inventory problems are obtained by goal programming method. The models are illustrated with numerical examples and results for different formulations are compared. The results for the models assuming them to be a single house integrated business are also obtained using a gradient-based optimization technique and compared with those obtained from the respective decentralized models. Taking man-machine interaction into consideration, interactive solutions are derived for one of the said models—multiobjective model with shortages using interactive fuzzy satisficing method. Pareto optimum and satisficing results are derived for some numerical data.

An Interactive Fuzzy Satisficing Method for Multiobjective Stochastic Integer Programming Problems through a Probability Maximization Model

In this paper, we deal with multiobjective integer programming problems involving random variable coefficients in objective functions and/or constraints. After reformulation of them on the basis of a probability maximization model for the chance constrained programming, incorporating fuzzy goals of the decision maker for the objective functions, we propose an interactive fuzzy satisficing method to derive a satisficing solution for the decision maker using genetic algorithms as a fusion of the stochastic programming and the fuzzy one.