Fuzzy Random Chance-constrained Programming Research Articles

Chance-constrained programming for drinking water quality management under fuzziness and randomness

ABSTRACT In this paper, an inexact fuzzy random chance-constrained programming (IFRCCP) model was proposed to deal with the randomness and fuzziness in the optimization of booster cost for the water distribution system (WDS). The IFRCCP model was applied to a WDS to analyze the effects of randomness and fuzziness on the booster costs. The booster cost intervals were obtained under various violation levels and confidence levels. The results indicated that the lower and upper booster costs increased with the confidence levels of the lower limits and decreased with the violation levels of the lower limits for both normal and log-normal distribution fuzzy random variables (FRVs). Moreover, the increased magnitude of lower and upper booster costs under normal distribution FRV is a little less than that under log-normal distribution FRV, while the decreased magnitude of lower and upper booster costs under normal distribution FRV is larger than that under log-normal distribution FRV. The same regulation can be found for the FVR with both triangular and trapezoidal distribution FRVs. With the increase of booster number, the increased magnitude of the lower and upper booster costs decreased for both normal and log-normal distribution FRVs.

Reliable hub-and-spoke network design problems under uncertainty through multi-objective programming

HLP (hub location problem) tries to find locations of hub facilities and assignment of nodes to extended facilities. Hubs are facilities to collect, arrange, and distribute commodities in telecommunication networks, cargo delivery systems, etc. Hubs are very crucial and their inaccessibility impresses on network whole levels. In this paper, first, total reliability of the network is defined based on considering the reliability values of nubs and arcs. Then, a reliable hub-and-spoke network design problem under uncertainty is introduced through the multi - objective programming method in which the parameters are random fuzzy variables. Indeed, we are making effort to either maximize the average reliability or minimize total cost. Then, the proposed reliable multi - objective hub-and-spoke network design problem under uncertainty is solved by a new method using Zimmermann fuzzy multi - objective programming and random fuzzy chance-constrained programming based on possibility theory. Finally, some benchmark problems are solved as numerical examples to clarify the described method and show its efficiency.

Fuzzy Random Chance-Constrained Programming Model for the Vehicle Routing Problem of Hazardous Materials Transportation

As an indispensable necessity in daily routine of citizens, hazardous materials (Hazmat) not only plays an increasingly important role, but also brings a series of transportation uncertainty phenomena, the most prominent of which is a safety problem. When it attempts to find the best vehicle route scheme that can possess the lowest risk attribute in a fuzzy random environment for a single warehouse, the influence of cost should also be taken into account. In this study, a new mathematical theory was conducted in the modeling process. To take a full consideration of uncertainty, vehicle travel distance and population density along the road segment were assumed to be fuzzy variables. Meanwhile, accident probability and vehicle speed were set to be stochastic. Furthermore, based on the assumptions, authors established three chance constrained programming models according to the uncertain theory. Model I was used to seek the achievement of minimum risk of the vehicle route scheme, using traditional risk model; the goal of Model II was to obtain the lowest total cost, including the green cost, and the main purpose of Model III was to establish a balance between cost and risk. To settle the above models, a hybrid intelligent algorithm was designed, which was a combination of genetic algorithm and fuzzy random simulation algorithm, which simultaneously proved its convergence. At last, two experiments were designed to illustrate the feasibility of the proposed models and algorithms.

Random-Fuzzy Chance-Constrained Programming Optimal Power Flow of Wind Integrated Power Considering Voltage Stability

Considering the random and fuzzy nature of wind speed, this paper proposes a multi-objective random-fuzzy chance-constrained programming optimal power flow (OPF) for wind integrated power systems. The proposed method is based on random-fuzzy chance-constrained programming. The optimization model aims at minimizing generation cost, carbon dioxide (CO2) emission, and system functional power loss, and P-Q-V steady-state voltage stability is included in the constraints. Based on random-fuzzy chance-constrained programming, the corresponding solution process of the proposed multi-objective OPF is proposed, which is a hybrid of random-fuzzy simulation, non-dominated sorting genetic algorithm-II (NSGA-II), and fuzzy satisfaction-maximizing decision-making method. The proposed approach is simulated on the IEEE 30-bus system to provide an example of its application. The simulation results demonstrate that the proposed random-fuzzy chance-constrained programming OPF has higher security and more economy than dynamic stochastic optimal power flow (DSOPF) and dynamic fuzzy optimal power flow (DFOPF).

An extended multi-objective mixed integer programming for water resources management through possibility theory

AbstractIn this study, we develop an extended multi-objective mixed integer programming (EMOMIP) approach for water resources management under uncertainty, in which the parameters are fuzzy random variables while the decision variables are interval variables. Furthermore, some alternatives are considered to retrieve the difference between the quantities of promised water-allocation targets and the actual allocated water. Then, the proposed EMOMIP for the problem is solved by a new method using fuzzy random chance-constrained programming based on the idea of possibility theory. This method can satisfy both optimistic and pessimistic decision makers simultaneously. Finally, a real example is given to explain the proposed method.

Novel Reliable Uncapacitated P-Hub Location Problems Under Uncertainty

Hubs are facilities to collect, arrange and distribute commodities in telecommunication networks, cargo delivery systems, etc. In this article, it will study two popular hub location problems (p-hub center and p-hub maximal covering problems) under uncertainty. First, novel reliable uncapacitated p-hub location problems are introduced based on considering the failure probability of hubs, in which the parameters are random fuzzy variables, but the decision variables are real variables. Then, the proposed hub location problems under uncertainty are solved by new methods using random fuzzy chance-constrained programming based on the idea of possibility theory. These methods can satisfy optimistic and pessimistic decision makers under uncertain framework. Finally, some benchmark problems are solved as numerical examples to clarify the described methods and show their efficiency.

Short-Term Line Maintenance Scheduling of Distribution Network With PV Penetration Considering Uncertainties

In this paper, the methodology for short-term line maintenance scheduling in distribution network with PV penetration is proposed, in which the mixed randomness and fuzziness of solar power generation concerning the available cloud amount forecasting, along with other random or fuzzy factors, such as electricity demand and component historical failure rate, are considered. First, based on the obtained historical data from NASA, the empirical mapping from cloud amount to solar irradiance can be established where the uncertainty is represented by combining randomness and fuzziness. Second, the short-term line maintenance scheduling of distribution network with uncertainties is modeled by using random fuzzy chance-constrained programming aiming at minimizing the pessimistic value in terms of economics and reliability subject to the chance constraints. Finally, a hybrid intelligent algorithm with two-layer optimization is implemented to solve the model. Simulation experiments are carried out on the IEEE 33-Bus and IEEE RBTS 2-Bus systems, and the results demonstrate the effectiveness of the proposed short-term line maintenance scheduling solution for distribution network with the mixed uncertainties of randomness and fuzziness.

Resource management of opportunistic digital array radar antenna aperture for pattern synthesis

Due to the complex time-varying environments and the unknown target information, the uncertainty of target information is introduced into the echo signal. Owing to the uncertainty of target information, the number and operating modes of antenna array elements allocated for pattern synthesis are uncertain. Hence to reduce the influence of uncertainty of target information and save the antenna array elements, in the light of the uncertainty of the number and the distribution of the array elements in working state, a novel fuzzy random chance-constrained programming model of opportunistic digital array radar antenna aperture resource management is proposed. Moreover, this model can determine the information of radar target from the echo signal by reasonable resource management and allocation under the condition that the specified confidence levels are satisfied. Meanwhile, for solving the multi-object model, the fuzzy random simulation is integrated into fast and elitist non-dominated sorting genetic algorithm (NSGA_II) to compose a hybrid intelligent optimisation algorithm. Finally, two simulations are carried out to verify the validity of this model.

Mathematical Programming for Modelling Green Supply Chains Under Randomness and Fuzziness

Nowadays by growing concerns about environmental problems, businesses and industries are under pressure to decrease their negative impact on environment, consequently firms and industries have to reconsider about their activities and make their business compatible with environment. So industries should green their supply chains to optimize economic and environmental concerns, but because of uncertainty in the real world like inconsistency of world economy, the process of greening supply chains can be more complex. To optimize total costs and the unfavourable sides of supply chains simultaneously in an uncertain situation, this paper presents a multi-objective mixed integer programming with fuzzy random variables (FRVs) and by using fuzzy theory and fuzzy random chance-constrained programming (FRCCP), the proposed model is converted to deterministic model. This paper can be also suitable for decision making with optimistic, pessimistic and realistic notion. Finally, a numerical example is presented to illustrate the model.

New methods for solving a vertex p-center problem with uncertain demand-weighted distance: A real case study

Article history: Received July 11 2014 Received in Revised Format October 23 2014 Accepted October 26 2014 Available online October 26 2014 Vertex and p-center problems are two well-known types of the center problem. In this paper, a pcenter problem with uncertain demand-weighted distance will be introduced in which the demands are considered as fuzzy random variables (FRVs) and the objective of the problem is to minimize the maximum distance between a node and its nearest facility. Then, by introducing new methods, the proposed problem is converted to deterministic integer programming (IP) problems where these methods will be obtained through the implementation of the possibility theory and fuzzy random chance-constrained programming (FRCCP). Finally, the proposed methods are applied for locating bicycle stations in the city of Tabriz in Iran as a real case study. The computational results of our study show that these methods can be implemented for the center problem with uncertain frameworks. © 2015 Growing Science Ltd. All rights reserved

A random fuzzy multi-objective linear programming approach through possibility theory

This paper presents new methods for a multi-objective linear programming (MOLP) problem with random fuzzy variables (RFVs). First, a robust MOLP problem is introduced in which the coefficients of objective functions and constraints are RFVs. Then, the proposed problem is transformed into deterministic linear programming problems by new methods based on the idea of possibility theory and the random fuzzy chance-constrained programming. These methods can satisfy optimistic and pessimistic decision makers separately and simultaneously. Finally, an example is also solved to clarify the discussed methods. [Received 13 June 2013; Revised 24 November 2013; Revised 5 April 2014; Accepted 20 April 2014]

Random fuzzy chance-constrained programming based on adaptive chaos quantum honey bee algorithm and robustness analysis

This paper proposes an adaptive chaos quantum honey bee algorithm (CQHBA) for solving chance-constrained programming in random fuzzy environment based on random fuzzy simulations. Random fuzzy simulation is designed to estimate the chance of a random fuzzy event and the optimistic value to a random fuzzy variable. In CQHBA, each bee carries a group of quantum bits representing a solution. Chaos optimization searches space around the selected best-so-far food source. In the marriage process, random interferential discrete quantum crossover is done between selected drones and the queen. Gaussian quantum mutation is used to keep the diversity of whole population. New methods of computing quantum rotation angles are designed based on grads. A proof of convergence for CQHBA is developed and a theoretical analysis of the computational overhead for the algorithm is presented. Numerical examples are presented to demonstrate its superiority in robustness and stability, efficiency of computational complexity, success rate, and accuracy of solution quality. CQHBA is manifested to be highly robust under various conditions and capable of handling most random fuzzy programmings with any parameter settings, variable initializations, system tolerance and confidence level, perturbations, and noises.

Fuzzy random chance-constrained programming

By fuzzy random programming, we mean the optimization theory dealing with fuzzy random decision problems. This paper presents a new concept of chance of fuzzy random events, and constructs a general framework of fuzzy random chance-constrained programming. We also design a spectrum of fuzzy random simulations for computing uncertain functions arising in the area of fuzzy random programming. To speed up the process of handling uncertain functions, we train a neural network to approximate uncertain functions based on the training data generated by fuzzy random simulation. Finally, we integrate the fuzzy random simulation, neural network, and genetic algorithm to produce a more powerful and effective hybrid intelligent algorithm for solving fuzzy random programming models and illustrate its effectiveness by some numerical examples.