Fuzzy Optimization Model Research Articles

Fuzzy optimal solution of electric tomography imaging: Modelling and application

In this paper, efforts are made to find the fuzzy optimal solutions for electric tomography imaging (ETI) process. Most of the conventional ETI methods depend on an optimization process with a deterministic objective function and constraint conditions. The effective application of these methods requires the availability of measured data. However, in practical ETI possess, the assessable data are uncertain, imprecise, incomplete, and characterized by fuzziness. In this paper, the fuzzy characteristics hidden in the ETI process are extracted, and a new model of fuzzy optimization is built up, whose optimal solution is obtained by using fuzzy linear programming (FLP). The FLP model can provide a robust methodology to boost the ETI spatial resolution. Thus it creates a new and promising research direction for the optimization of the ETI process. Experimental results prove that compared with other existing ETI algorithms, the proposed method is more effective in reconstructing complex and discretely distributed objects.

Credibilistic multi-period portfolio optimization based on scenario tree

In this paper, we consider a multi-period fuzzy portfolio optimization model with considering transaction costs and the possibility of risk-free investment. We formulate a bi-objective mean-VaR portfolio selection model based on the integration of fuzzy credibility theory and scenario tree in order to dealing with the markets uncertainty. The scenario tree is also a proper method for modeling multi-period portfolio problems since the length and continuity of their horizon. We take the return and risk as well cardinality, threshold, class, and liquidity constraints into consideration for further compliance of the model with reality. Then, an interactive dynamic programming method, which is based on a two-phase fuzzy interactive approach, is employed to solve the proposed model. In order to verify the proposed model, we present an empirical application in NYSE under different circumstances. The results show that the consideration of data uncertainty and other real-world assumptions lead to more practical and efficient solutions.

Fuzzy optimization to improve mobile health and wellness recommendation systems

In this article, we focus on mobile wellness and health-related applications from the perspective of the level of imprecision present in the data used in the recommendation systems. We propose a general fuzzy optimization model based on chanced constrained optimization to design recommendation systems that can take into consideration (i) the imprecision in the data and (ii) the imprecision by which one can estimate the effect of a recommendation on the user of the system. Our proposal is one of the first to use fuzzy optimization models in health-related decision making problems and the first to define a chance constrained optimization problem for interval-valued fuzzy numbers. The proposed approach identifies a set of actions to be taken by the users in order to optimize general health-related and/or wellness condition of the user from various perspectives. The model is illustrated through the example of walking speed optimization, with an additional numerical experiment offering a comparison with traditional methods.

AIS Data-based Decision Model for Navigation Risk in Sea Areas

The safety of maritime transportation has become increasingly important in recent decades. In this paper, a decision model (a multi-objective and multi-layer fuzzy optimisation model) for navigation risk in different sea areas is established. This is done according to the evaluation index system based on relative data extracted and analysed from Automatic Identification Systems (AIS) information and the multi-objective and multi-layer fuzzy optimisation theory. Then, sorted by an optimal relative membership degree vector and calculated from lower layer to higher layer, the sea areas which have higher navigation risk are selected. Finally, the decision model is shown to be scientific and practical since the results from it are basically consistent with real traffic in Chengshantou waters and the results from the fuzzy comprehensive evaluation model. With the decision model, navigation risk judgments in different sea areas can be offered. It can also provide decision making references to the design of ship routing systems, the layout of search and rescue sites, the configuration of rescue forces and the administration of navigation safety.

Multi-period mean–variance fuzzy portfolio optimization model with transaction costs

This paper examines the multi-period portfolio optimization problem with transaction costs and fuzzy variables to count for the uncertainty of future returns and liquidities on assets. The portfolio risk is quantified by using the variance of fuzzy returns. Two conflicting optimization objectives, namely, maximizing the terminal wealth and minimizing the cumulative risk of portfolios over the entire investment horizon, are taken into consideration. For solving the proposed model we introduce a new multi-objective evolutionary algorithm. Finally the performance of the proposed algorithm is compared with the NSGAII and MOEA/D with the assistance of real data from FTSE-100 in London.

Bi-level fuzzy optimization model of an algae-sugarcane-based eco-industrial park

Eco-industrial parks (EIPs) are designed to serve as effective measures in mitigating resource depletion and improving the environmental footprint of industrial processes. The system implements the concept of industrial symbiosis wherein an exchange of resources is conducted among the plants to achieve mutual economic and environmental benefit. The park authority has an objective of minimizing the environmental footprints of the EIP, and each respective plant aims to maximize its annual net profit while satisfying product demand. Thus, the design of the multiple resource type exchange network within the EIP can be adopted as a bi-level fuzzy optimization model, with the park authority designated as the upper-level decision-maker. The study investigates the impact of environmental footprint limits set by the park authority in the optimal design of the resource exchange networks between the plants in the EIP. A case study involving an algae-sugarcane-based eco-industrial park is considered to demonstrate the model. The results indicate that a compromise can be achieved between the levels of decision-makers at an overall degree of satisfaction of 0.189. This suggests the feasibility of the proposed EIP model accounting for the objectives of both levels of decision-makers.

A fuzzy hybrid integrated framework for portfolio optimization in private banking

Decision-making processes in private banking must comply with standards for risk management and transparency enforced by banking regulations. Therefore, investors must be supported throughout a risk-informed decision process. This paper contributes to the literature by presenting a hybrid integrated framework that considers personal features of the investor and additional characteristics imposed by regulations, for which linguistic evaluations are used with regard to risk exposure. The proposed approach for personal investment portfolios considers legal aspects and investor’s preferences as an input to the novel fuzzy multiple-attribute decision making approach for sorting problems proposed in this paper, called FTOPSIS-Class. Then, the next step of the proposed framework uses the sorting results for a fuzzy multi-objective optimization model that considers the risk and return associated with the investor’s profile over three objectives. The contributions of this paper are illustrated and validated by using a numerical application in line with a new trend for modern portfolio theory which enables a real world investor’s characteristics to be considered throughout the decision-making process.

Taguchi-factorial type-2 fuzzy random optimization model for planning conjunctive water management with compound uncertainties

In this study, a type-2 fuzzy random optimization (TFRO) method is developed for planning conjunctive water management system associated with compound uncertainties. TFRO can effectively address compound uncertainties expressed as type-2 fuzzy sets, probability distributions, and type-2 fuzzy random variables. Solution algorithm based on the degree of probability and the information of plausibility is proposed to transform nonlinear objective function and constraints into their linear equivalents. A real case of water-resources allocation problem in Zhangweinan River Basin (China) is employed to demonstrate the applicability of the proposed method. A Taguchi-factorial type-2 fuzzy random model is also formulated through introducing Taguchi design and ANOVA technique into the TFRO framework. Results obtained can help reveal the relationship among multiple impact factors of economic, environmental and resource (water conveyance efficiency, water delivery cost, and system violation risk), as well as quantify their contributions to the variability of system benefit and water allocation schemes.

A sustainable manufacturing system design: A fuzzy multi-objective optimization model.

In the past decade, there has been a growing concern about the environmental protection in public society as governments almost all over the world have initiated certain rules and regulations to promote energy saving and minimize the production of carbon dioxide (CO2) emissions in many manufacturing industries. The development of sustainable manufacturing systems is considered as one of the effective solutions to minimize the environmental impact. Lean approach is also considered as a proper method for achieving sustainability as it can reduce manufacturing wastes and increase the system efficiency and productivity. However, the lean approach does not include environmental waste of such as energy consumption and CO2 emissions when designing a lean manufacturing system. This paper addresses these issues by evaluating a sustainable manufacturing system design considering a measurement of energy consumption and CO2 emissions using different sources of energy (oil as direct energy source to generate thermal energy and oil or solar as indirect energy source to generate electricity). To this aim, a multi-objective mathematical model is developed incorporating the economic and ecological constraints aimed for minimization of the total cost, energy consumption, and CO2 emissions for a manufacturing system design. For the real worldscenario, the uncertainty in a number of input parameters was handled through the development of a fuzzy multi-objective model. The study also addresses decision-making in the number of machines, the number of air-conditioning units, and the number of bulbs involved in each process of a manufacturing system in conjunction with a quantity of material flow forprocessed products. A real case study was used for examining the validation and applicability of the developed sustainable manufacturing system model using the fuzzy multi-objective approach.

Fuzzy multi-objective approach for optimal selection of suppliers and transportation decisions in an eco-efficient closed loop supply chain network

Establishment of a closed loop supply chain (CLSC) network has attracted immense significance due to government policies and societal demand for environmental consciousness. However, to enhance the financial and ecological impact of the network, the forward and reverse supply chain networks must integrate well so that decisions taken in both areas complement each other. In this study, we propose an eco-efficient CLSC design for extending the existing supply chain of an Indian firm that assembles inkjet printers. The network design is configured as a multi-objective model in a multi-period setting and is mathematically formulated into a mixed integer programming problem with fuzzy objectives. Fuzziness provides flexibility to the decision makers because they must accommodate the conflicting nature of the objectives. The fuzzy multi-objective model incorporates the firm's economic and environmental concerns into the decision making process by selecting environmentally responsible suppliers to procure components based on sustainable criteria, choosing appropriate recovery options for end-of-use (EOU) inkjet printers, and planning an efficient transportation network design for reducing the carbon emission of the distribution and collection activities. The uniqueness of the proposed fuzzy CLSC optimization model lies in providing an integrated decision making framework that can aid the manufacturer in making crucial strategic, tactical, and operational decisions of optimal selection of suppliers, component order allocation, recovery flow allocation, and vehicle routing planning. The novelty of the model also lies in simultaneously minimising the overall cost of the activities undertaken, maximizing the performance of the component suppliers and minimising the carbon emissions of the associated transportation activities. A weighted fuzzy mathematical programming approach is utilised for generating a fuzzy, properly efficient solution as the desired compromised solution for the CLSC network problem configuration. The relevance of the model is justified using a real data set derived from a case study of the firm based in the northern capital region (NCR) of India. The findings indicate that the proposed integrated CLSC network model enables the firm in gaining sustainably from the numerous electronic product reuse opportunities in the Indian market. Further, while costly to begin with, choosing suppliers with higher sustainable performance and vehicles with lesser emission rate could substantially enhance firm's sustainable image and result in higher profits in the future.

Fuzzy vulnerability mapping of urban groundwater systems to nitrate contamination

The aim of this study is to develop a new fuzzy optimization model to find the optimal factor weights of modified DRASTIC index for groundwater vulnerability mapping an urban aquifer to nitrate contamination. Eight factors including water table depth, recharge, aquifer media, soil media, topography, impact of vadose zone, hydraulic conductivity, and land use are considered and rated. A fuzzy linear regression is formulated between the values of eight factors and corresponding nitrate concentration in groundwater. An optimization model based on real code genetic algorithm with objective of minimizing the sum of the fuzzy spread of the regression coefficients is implemented. Aquifer of Mashhad metropolis (northeast of Iran) is chosen to evaluate the proposed model. The results show the proposed model is a promising tool for weighting the factors with avoiding the subjectivity and also ambiguities accompanied by parameters to produce an accurate specific vulnerability mapping of an urban aquifer.

Novel numerical methods for reliability analysis and optimization in engineering fuzzy heat conduction problem

Engineering fuzzy heat conduction problem with subjective uncertainties in input parameters constitutes a significant challenge. Based on fuzzy and interval theory, this paper presents novel numerical methods to efficiently identify the effect of fuzzy uncertainty on the system reliability analysis and optimization design. Firstly using the interval ranking strategy, the interval safety possibility in the transition state can be precisely quantified, and the eventual fuzzy safety possibility is calculated by integral operation. Then a fuzzy reliability-based optimization model is established with considerable computational cost caused by the two-layer nested loop. In order to improve the computational efficiency, a subinterval perturbation method based on the first-order Taylor series is presented to replace the inner loop. Comparing numerical results with traditional reliability model, two numerical examples are provided to evidence the superiority of proposed model and method for fuzzy reliability analysis and optimization in practical engineering.

The utility based non-linear fuzzy AHP optimization model for network selection in heterogeneous wireless networks

Next generation wireless networks will integrate various heterogeneous technologies like WLAN, WiMax and cellular technologies etc., to support multimedia services with higher bandwidth and guaranteed quality of service (QoS). In order to keep the mobile user always connected to the best wireless network in terms of QoS parameters and user preferences, an optimal network selection technique in heterogeneous networks is required. This paper proposes a novel fuzzy-Analytic Hierarchy Process (AHP) based network selection in heterogeneous wireless networks. Triangular fuzzy numbers are used to represent the elements in the comparison matrices for voice, video and best effort applications. Deriving crisp weights from these fuzzy comparison matrices is a challenging task. When extent analysis method is applied, irrational zero weights are obtained for some attributes. Due to this, many important criteria are not considered in the decision making process. To overcome this problem, a new non-linear fuzzy optimization model for deriving crisp weights from fuzzy comparison matrices for network selection is presented. The weights obtained from this model are more consistent than the existing optimization models. Also, parameterized utility functions are used to model the different Quality of Service (QoS) attributes (bandwidth, delay, jitter, bit error rate) and user preferences (cost) for three different types of applications. Finally, scores are calculated exclusively for each network by three MADM (Multiple Attribute Decision Making) methods Simple Additive Weighting (SAW), TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution) and MEW (Multiplicative Exponential Weighting). Results show that the MEW method gives more appropriate scores with utility functions than the SAW and TOPSIS methods.

Optimal route selection based on Monte Carlo method and adaptive amoeba algorithm under uncertain environment

The fuzzy optimal path under uncertainty is one of the basic network optimization problems. Considering the uncertain environment, many fuzzy numbers are used to represent the edge weights, such as interval number and triangular fuzzy number. Then, these fuzzy numbers are converted to real numbers directly. This converting makes the optimal path the shortest path selection problem. However, much information of uncertainty get lost when converting fuzzy numbers to real numbers. In order to ensure all the origan data complete, in this paper, a fuzzy optimal path solving model based on the Monte Carlo method and adaptive amoeba algorithm is proposed. In Monte Carlo process, a random number which belongs to the fuzzy number is generated. Then, Physarum polycephalum algorithm is used to solve the shortest path every time and record the result. After many times calculation, many shortest paths have been found and recorded. At last, by analysing the characters of all the results, the optimal path can be selected. Several numerical examples are given to illustrate the effectiveness of the proposed method, the results show that the proposed method can deal with the fuzzy optimal path problems effectively.

A Me -based rough approximation approach for multi-period and multi-product fashion assortment planning problem with substitution

Develop a novel fuzzy model for fashion assortment planning with substitution.A new fuzzy measure is proposed to represent optimistic and pessimistic attitudes.The fuzzy measure proposed can avoid losing information in the conversion process.The results show that the model can offer better strategies for fashion retailers. Assortment planning is the process conducted by fashion retailers to determine the variety and quantity of products to sell at each sales period. As it has a great impact on the financial performance for retail stores, retailers take it as the crucial activity and the nucleus for an intelligent inventory control system. In this paper, we consider the assortment planning with substitution (a substitute product when the original choice is unavailable) under a fuzzy environment and then a fuzzy optimization model is built to obtain maximum benefits for retailers. For the fuzzy variables in the objective functions, we propose a fuzzy measure which can represent any attitudes between extremely optimistic and pessimistic to handle objective functions and get their expected value. For the constraints, a similarity relationship based on the fuzzy measure is defined, and the feasible region is addressed by the rough approximation based on this similarity relationship. Then, the lower approximation model (LAM) and the upper approximation model (UAM), which can avoid losing much information in the modeling process, are generated. To solve the model, a hybrid genetic algorithm with rough simulation is proposed. Finally, an application is used to demonstrate the practicality and effectiveness of the model and solution algorithm.

Random Fuzzy Optimization Model for Short-Term Hydropower Scheduling Considering Uncertainty of Power Load

This paper proposes a random fuzzy optimization (RFO) model for short-term hydropower scheduling, in order to avoid frequent unit switches owing to uncertainty of the power load. The cascade hydropower stations of Qing River in China are firstly introduced for research, and the power load error of the cascade is described. Defined as a random fuzzy variable, the error is analyzed and its distribution is derived to signify the uncertainty. Then random fuzzy programming is integrated into short-term hydropower scheduling to develop the RFO model, with more attention payed to unit spare capacity, while satisfying the demand of power grids. Meanwhile, an applicable solution searching strategy is proposed to solve the model. Simulation results of random fuzzy optimization of the cascade prove that the strategy is practical and the developed model is effective to avoid frequent unit switches. The method also can provide available references for other cascade dispatching center and hydropower stations with the same plight.

A systematic decision making approach for product conceptual design based on fuzzy morphological matrix

Conceptual design plays an important role in development of new products and redesign of existing products. Morphological matrix is a popular tool for conceptual design. Although the morphological-matrix based conceptual design approaches are effective for generation of conceptual schemes, quantitative evaluation to each of the function solution principle is seldom considered, thus leading to the difficulty to identify the optimal conceptual design by combining these function solution principles. In addition, the uncertainties due to the subjective evaluations from engineers and customers in early design stage are not considered in these morphological-matrix based conceptual design approaches. To solve these problems, a systematic decision making approach is developed in this research for product conceptual design based on fuzzy morphological matrix to quantitatively evaluate function solution principles using knowledge and preferences of engineers and customers with subjective uncertainties. In this research, the morphological matrix is quantified by associating the properties of function solution principles with the information of customer preferences and product failures. Customer preferences for different function solution principles are obtained from multiple customers using fuzzy pairwise comparison (FPC). The fuzzy customer preference degree of each solution principle is then calculated by fuzzy logarithmic least square method (FLLSM). In addition, the product failure data are used to improve product reliability through fuzzy failure mode effects analysis (FMEA). Unlike the traditional FMEA, the causality relationships among failure modes of solution principles are analyzed to use failure information more effectively through constructing a directed failure causality relationship diagram (DFCRD). A fuzzy multi-objective optimization model is also developed to solve the conceptual design problem. The effectiveness of this new approach is demonstrated using a real-world application for conceptual design of a horizontal directional drilling machine (HDDM).

An improved heterogeneous multi-swarm PSO algorithm to generate an optimal T-S fuzzy model of a hydraulic process

In this paper, a new methodology to develop an Optimal Fuzzy model (OptiFel) using an improved Multi-swarm Particle Swarm Optimization (MsPSO) algorithm is proposed with a new adaptive inertia weight based on Grey relational analysis. Since the classical MsPSO suffers from premature convergence and can be trapped into local optima, which significantly affects the model accuracy, a modified MsPSO algorithm is presented here. The most important advantage of the proposed algorithm is the adjustment of fewer parameters in which the main parameter is the inertia weight. In fact, the control of this parameter could facilitate the convergence and prevent an explosion of the swarm. The performance of the proposed algorithm is evaluated by adopting standard tests and indicators which are reported in the specialized literature. The proposed Grey MsPSO is first applied to solve the optimization problems of six benchmark functions and then, compared with the other nine variants of particle swarm optimization. In order to demonstrate the higher search performance of the proposed algorithm, the comparison is then made via two performance tests such as the standard deviation and central processing unit time. To further validate the generalization ability of the Improved OptiFel approach, the proposed algorithm is secondly applied on the Box–Jenkins Gas Furnace system and on a irrigation station prototype. A comparative study based on Mean Square Error is then performed between the proposed approach and other existing methods. As a result, the improved Grey MsPSO is well adopted to find an optimal model for the real processes with high accuracy and strong generalization ability.

Deriving crisp and consistent priorities for fuzzy AHP-based multicriteria systems using non-linear constrained optimization

Fuzzy optimization models are used to derive crisp weights (priority vectors) for the fuzzy analytic hierarchy process (AHP) based multicriteria decision making systems. These optimization models deal with the imprecise judgements of decision makers by formulating the optimization problem as the system of constrained non linear equations. Firstly, a Genetic Algorithm based heuristic solution for this optimization problem is implemented in this paper. It has been found that the crisp weights derived from this solution for fuzzy-AHP system, sometimes lead to less consistent or inconsistent solutions. To deal with this problem, we have proposed a consistency based constraint for the optimization models. A decision maker can set the consistency threshold value and if the solution exists for that threshold value then crisp weights can be derived, otherwise it can be concluded that the fuzzy comparison matrix for AHP is not consistent for the given threshold. Three examples are considered to demonstrate the effectiveness of the proposed method. Results with the proposed constraint based fuzzy optimization model are more consistent than the existing optimization models.

Upgrading fuzzy logic by GA-PS to determine asphaltene stability in crude oil

Precipitation and deposition of asphaltene are undesirable phenomena that arise during petroleum production which give rise to a pronounced rate of increase in operational cost and adversely affect production rates as well. Hence, it is imperative to develop a mathematical model for the assessment of asphaltene stability in crude oil. In the present study, delta RI which constitutes the difference between refractive index of crude oil (RI) and refractive index of crude oil at the onset of asphaltene precipitation (PRI) is employed as the principal factor for determining the asphaltene stability of the region. Fuzzy logic is a potent tool capable of extracting the underlying dependency between SARA fractions (saturate, aromatic, resin, and asphaltene) data and delta RI for the inexpensive and rapid diagnosis of asphaltene stability. In this study a novel strategy known as hybrid genetic algorithm-pattern search (GA-PS) is suggested for the development of an optimal fuzzy logic model as a reliable alternative for the widely-applied subtractive clustering (SC) method. While SC solely optimizes mean of input Gaussian membership functions (GMFs), GA-PS tool optimizes both mean and variance of input GMFs. Comparison between GA-PS and SC methods confirmed the capability of GA-PS for developing an optimal fuzzy logic model.