Fuzzy Integer Linear Programming Research Articles

Enhancing the Efficiency of Electric Vehicles Charging Stations Based on Novel Fuzzy Integer Linear Programming

The electric vehicles (EVs) charging stations (CSs) at public premises have higher installation and power consumption costs. The potential benefits of public CSs rely on their efficient utilization. However, the conventional charging methods obligate a long waiting time and thereby deteriorate their efficiency with low utilization. This paper suggests a novel fuzzy integer linear programming and a heuristic fuzzy inference approach (FIA) for CSs utilization. The model introduces the underlying fuzzy inference system and a detailed formulation for obtaining the optimal solution. The developed fuzzy inference incorporates the uncertain and independent available power, required state-of-charge, and dwell time from the power grid and EVs domains and correlates them into weighted control variables. The FIA automates the service provision for the EVs with the most urgent requirements by resolving the objective function utilizing the weighted control variables, thereby optimizing the waiting time and the CSs utilization. To evaluate the effectiveness of the proposed FIA, several case studies were conducted, corresponding to different parking capacities and installations of CSs. Moreover, the simulations were conducted on EVs with varying battery capacities, and their performance was evaluated based on several metrics, including average waiting time, utilization of CSs, fairness, and execution time. The simulation results have confirmed that the effectiveness of the proposed FIA scheduling method is considerably higher than that of the other methods discussed.

Optimization of Waiting Time for Electric Vehicles Using a Fuzzy Inference System

Electric vehicles (EVs) need to be recharged at intermediate locations, such as shopping malls, restaurants, and parking lots, to meet the daily commute requirements of their users. Currently, public electric vehicle supply equipment (EVSE) serve EVs by conventional methods, which can result in long waiting time for users. This issue reduces the travel efficiency of EVs and thus affects user comfort. Most previous research has studied energy consumption and charging cost optimization; however, comparatively less work has focused on waiting time optimization despite its great importance from the EV user’s perspective. In this paper, we formulate the waiting time optimization as a fuzzy integer linear programming problem and propose a novel heuristic fuzzy inference system-based algorithm (FISA) that resolves the objective function and minimizes the waiting time of EVs at public EVSE installations. We developed the underlying fuzzy inference system by defining the membership functions, expert rules, and formulation for obtaining the optimal solution. The novel FISA automates the correlations of the uncertain and independent input parameters into weighted control variables and resolves the objective function in each sampling period to optimize the waiting time for EVs with the most urgent service requirements. A java language-based simulator is developed for a parking lot to evaluate the effectiveness of the proposed FISA. The simulation results indicate higher efficiency of the proposed FISA compared with state-of-art scheduling algorithms.

A two-layer decentralized charging approach for residential electric vehicles based on fuzzy data fusion

This work presents a two-layer decentralized charging approach (TLDCA) based on fuzzy data fusion concerning the economic and power layers for optimizing the charging cost of residential electric vehicles (EVs). We defined the problem with the fuzzy objective function of minimizing the charging costs and presented a detailed fuzzy integer linear programming formulation for obtaining the optimal solution set. The optimal solution set relies on the decision control variable which is obtained through the fuzzy fusion mechanism that incorporates multiple independent and uncertain day-ahead price patterns and state-of-charge inputs from the utility grid and EV domains. The developed TLDCA reduces the charging cost for EVs while guaranteeing their required energy by determining the optimal charging schedule. We conduct two case studies to investigate the TLDCA behavior, where the first case explores the optimization of charging costs and the changing needs of individual EVs. The second case examines the charging cost, impact on load profile, and peak-to-average ratio against the summer and winter load profiles for the aggregated EVs. The simulation results verify that the developed TLDCA optimizes the charging cost and peak-to-average ratio compared to the uncoordinated charging, standard-rate charging, and time-of-use charging schemes.

A mathematical model for solving fuzzy integer linear programming problems with fully rough intervals

A suggested algorithm to solve triangular fuzzy rough integer linear programming (TFRILP) problems with α-level is introduced in this paper in order to find rough value optimal solutions and decision rough integer variables, where all parameters and decision variables in the constraints and the objective function are triangular fuzzy rough numbers. In real-life situations, the parameters of a linear programming problem model may not be defined precisely, because of the current market globalization and some other uncontrollable factors. In order to solve this problem, a proper methodology is adopted to solve the TFRILP problems by the slice-sum method with the branch-and-bound technique, through which two fuzzy integers linear programming (FILP) problems with triangular fuzzy interval coefficients and variables were constructed. One of these problems is an FILP problem, where all of its coefficients are the upper approximation interval and represent rather satisfactory solutions; the other is an FILP problem, where all of its coefficients are the lower approximation interval and represent completely satisfactory solutions. Moreover, α-level at α = 0.5 is adopted to find some other rough value optimal solutions and decision rough integer variables. Integer programming is used, since a lot of the linear programming problems require that the decision variables be integers. In addition, the motivation behind this study is to enable the decision makers to make the right decision considering the proposed solutions, while dealing with the uncertain and imprecise data. A flowchart is also provided to illustrate the problem-solving steps. Finally, two numerical examples are given to clarify the obtained results.

Optimal fuzzy solution for fully fuzzy integer linear programming problems

Optimal fuzzy solution for fully fuzzy integer linear programming problems

Secure and Optimum Fuel Distribution of Nato

ABSTRACTThe aim of the research is to optimize safe, secure, and cost-effective fuel distribution in Afghanistan. In the solving process of this decision-making optimization problem; first, the route and the total distribution cost of the outsourced third party logistics (3PL) company was calculated. Then the same cost calculations was done both with the suggested “Integer Linear Programming” and “Fuzzy Integer Linear Programmings” comparatively. Research has indicated that the Integer Linear Programming Model forecasts a cost savings of 7.2%, while the Fuzzy Integer Linear Programming forecasts 10.7%.

Branch-and-price algorithm for fuzzy integer programming problems with block angular structure

This paper deals with fuzzy integer linear programming problems with block angular structure in which the fuzzy constraints are simplified by using possibility and necessity relations. This main fuzzy problem is efficiently decomposed and is solved by a branch-and-price algorithm. In the nodes of the branch-and-price tree, the linear relaxation of the problem is solved by applying a column generation method. Also, the relationship between the optimal solutions of this problem under possibility and necessity relations is derived. To show the validation of the proposed algorithm, some results are proved. In addition, the application of this algorithm is illustrated on fuzzy multicommodity flow problem. For this case, a new branching scheme is proposed to preserve the network structure of the subproblems which are produced in the column generation method. Some examples are solved and their results are compared with the previous works. Also, the results of the proposed algorithm are reported on some large-scale benchmark instances.

Fuzzy network design of sustainable supply chains

The paper focuses on supply chain network design under uncertain conditions. In order to achieve a sustainable supply chain configuration, suitable indices such as CO2 emissions and energy consumption are considered. Uncertainty in such performance is addressed by a fuzzy possibility theory approach. In particular, this paper presents a technique employing fuzzy integer linear programming to design the optimally efficient and sustainable supply chain network. Closed loop solutions with reverse logistics are compared with traditional forward supply chain structures in order to obtain improved sustainability performance. A case study inspired from the related literature is presented to show the technique effectiveness.

Using Fuzzy Numbers in Network Design Optimization Problems

The fluctuations that have taken place in the worldwide economy over the past few years make it difficult to estimate the costs of the equipment that have to be used in order to design a telecommunications network. The literature is replete with prescriptive integer programming models for various network design problems that do not take into account the problems inherent vagueness due to equipment costs. This paper considers the real-world wavelength division multiplexing (WDM) network design problem. The vagueness that appears in this problem is assumed and handled by means of fuzzy-set-based methodologies. A fuzzy integer linear programming model is then proposed to be used as an auxiliary model to solve the former problem. With the purpose to obtain cost-effective network designs, this model is then solved using Cplex, which is a commercial high-performance optimization engine.

THE FUZZY EVALUATION OF THE ICT PROJECTS IN STRATEGIC ENVIRONMENT (CASE STUDY: IRAN TELECOMMUNICATION RESEARCH CENTER)

Many criteria should be considered for project selection in Information and Communication Technology (ICT) sectors; while, the resources are limited. Besides, the uncertainty of the selection and evaluation process increases the difficulty of ICT project selection. Therefore, a fuzzy system in combination with fuzzy integer linear programming, fuzzy entropy, and fuzzy numbers have been developed; it smoothes the process of ICT project selection. This fuzzy system is flexible in the project selection for Iran ICT sectors, especially in (Research and Development) R&D sectors. It enhances the accuracy of the evaluation process as it resolves the uncertainty of ICT project selection.

Fuzzy Optimization Models for the Design of WDM Networks

The wavelength-division multiplexing network design problem is considered in this paper. The literature is replete with prescriptive integer programming models for various versions of wavelength-division multiplexing network design problems, but in no case they consider the real situation of solving them taking into account their inherent vagueness. In this paper, this vagueness is assumed and handled by means of fuzzy sets based methodologies. In particular, two fuzzy integer linear programming models are proposed to be used as auxiliary models for solving the former problem. As an original way to effectively solve these models obtaining cost-effective network designs, we use three metaheuristic procedures that are compared among them.

Fuzzy integer linear programming problems

In this paper, the fuzzy integer linear programming problem (FILP) is considered. This problem is reduced to crisp integer linear programming problem. This transformation is performed by the related theorems and lemmas. The solution of FILP is obtained by the solutions of ILP’s. Finally the method is illustrated by two numerical examples.

PROMETHEE: an extension through fuzzy mathematical programming

PROMETHEE multi-criteria methods are based on fuzzy evaluations of the differences between pairs of alternatives for each criterion. PROMETHEE II associates a crisp number to each action. PROMETHEE III associates an interval to each action and two actions are considered indifferent when they are very close to each other. PROMETHEE V applies Integer Linear Programming in order to select the subset of alternatives that maximizes the sum of PROMETHEE II scorings, subject to a set of constraints. In order to make the model more realistic, this paper proposes that some constraints are soft and some coefficients are estimated by fuzzy numbers. Fuzzy Integer Linear Programming is applied, using the PROMETHEE III scorings as objective function coefficients, in order to find the subsets of non-outranked alternatives that best satisfy the soft constraints. The new model is more realistic and fits better the fuzzy philosophy of PROMETHEE. The method is illustrated with an example.

Three models of fuzzy integer linear programming

In this paper we study some models for dealing with Fuzzy Integer Linear Programming problems which have a certain lack of precision of a vague nature in their formulation. We present methods to solve them with either fuzzy constraints, or fuzzy numbers in the objective function or fuzzy numbers defining the set of constraints. These methods are based on the representation theorem and on fuzzy number ranking methods.