Fuzzy Random Simulation Research Articles

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.

A Multiperiod Multiobjective Portfolio Selection Model With Fuzzy Random Returns for Large Scale Securities Data

It is agreed that portfolio selection models are of great importance for the financial market. In this article, a constrained multiperiod multiobjective portfolio model is established. This model introduces several constraints to reflect the trading restrictions and quantifies future security returns by fuzzy random variables to capture fuzzy and random uncertainties in the financial market. Meanwhile, it considers terminal wealth, conditional value at risk (CVaR), and skewness as tricriteria for decision making. Obviously, the proposed model is computationally challenging. This situation gets worse when investors are interested in a larger financial market since the data they need to analyze may constitute typical big data. Whereafter, a novel intelligent hybrid algorithm is devised to solve the presented model. In this algorithm, the uncertain objectives of the model are approximated by a simulated annealing resilient back propagation (SARPROP) neural network which is trained on the data provided by fuzzy random simulation. An improved imperialist competitive algorithm, named IFMOICA, is designed to search the solution space. The intelligent hybrid algorithm is compared with the one obtained by combining NSGA-II, SARPROP neural network, and fuzzy random simulation. The results demonstrate that the proposed algorithm significantly outperforms the compared one not only in the running time but also in the quality of obtained Pareto frontier. To improve the computational efficiency and handle the large scale securities data, the algorithm is parallelized using MPI. The conducted experiments illustrate that the parallel algorithm is scalable and can solve the model with the size of securities more than 400 in an acceptable time.

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).

A hybrid priority-based genetic algorithm for simultaneous pickup and delivery problems in reverse logistics with time windows and multiple decision-makers

This article puts forward a hybrid priority-based nested genetic algorithm with fuzzy logic controller and fuzzy random simulation (hpn-GA with FLC–FRS) for solving a variant of the vehicle routing problem. To meet all the complex restrictions contained in practical reverse logistics, a new mathematical model is developed for simultaneous pickup and delivery problems with time windows and multiple decision-makers (SPDTW–MDM). Then, a hpn-GA with FLC–FRS is proposed, where the priority-based initializing method makes the initializing more applicable, a nested procedure structure handles multiple decision-makers, a fuzzy logic controller helps adjust the mutation rate, and a fuzzy random simulation is used to deal with uncertainties. Finally, in the case study, GA parameters are tuned by Taguchi method and result analyses are presented to highlight the performance of the optimization method for the SPDTW–MDM, while algorithm comparisons by instance applications in different scales show its efficiency and effectiveness.

Multi-objective Inventory Model with Both Stock-Dependent Demand Rate and Holding Cost Rate Under Fuzzy Random Environment

In this paper, we investigated a multi-objective inventory model under both stock-dependent demand rate and holding cost rate with fuzzy random coefficients. Chance constrained fuzzy random multi-objective model and a traditional solution procedure based on an interactive fuzzy satisfying method are discussed. In addition, the technique of fuzzy random simulation is applied to deal with general fuzzy random objective functions and fuzzy random constraints which are usually difficult to converted into their crisp equivalents. The purposed of this study is to determine optimal order quantity and inventory level such that the total profit and wastage cost are maximized and minimize for the retailer respectively. Finally, illustrate example is given in order to show the application of the proposed model.

Random fuzzy power flow of distribution network with uncertain wind turbine, PV generation, and load based on random fuzzy theory

No study in the literature considers both randomness and fuzziness simultaneously, which actually coexist as the penetration of renewable energy in power system increases. In order to handle these two kinds of uncertain features simultaneously, a novel random fuzzy power flow (RFPF) calculation method for a distribution network based on random fuzzy theory is presented here. Firstly, the random fuzzy models of wind and photovoltaic (PV) generation, and loads are set up for the first time according to their features of randomness and fuzziness. Then, a two-fold random fuzzy simulation is conducted to obtain the results of the RFPF calculations; the random simulation stage is based on the 2m + 1 scheme of the point estimate method. Finally, the proposed method is applied to two test systems. The results show that the proposed method is feasible and effective in identifying important areas in the power system affected by distribution generation and loads with these two uncertainties.

The scheme of wind-storage combined system capacity configuration based on random fuzzy chance constrained bi-level programming

A random fuzzy chance constrained bilevel programming scheme for distributed wind-storage combined system is proposed. The random fuzzy simulation is used to describe the uncertainty of distributed wind power output. The reliability of randomness and ambiguity is taken as the index to evaluate the capacity allocation scheme of the distributed wind-storage combined system. Considering system power balance, opportunity measurement constraint of static security index and active management (AM) measures, the random fuzzy expectation value of maximum annual profit is set as the upper optimization goal, and the minimum random fuzzy expectation value of the distributed wind power active reduction is set as the lower optimization target. The scheme is constructed by judging whether the static security index of the upper goal satisfies the confidence level of the random fuzzy chance constraint and the coordination of the upper and lower goals. Finally, the random fuzzy simulation, the forward pushback power flow calculation and the genetic algorithm (GA) are applied to solve the model. The simulation result of IEEE 14-bus example shows the effectiveness and superiority of the model and scheme.

A Dynamic Programming-Based Sustainable Inventory-Allocation Planning Problem with Carbon Emissions and Defective Item Disposal under a Fuzzy Random Environment

There is a growing concern that business enterprises focus primarily on their economic activities and ignore the impact of these activities on the environment and the society. This paper investigates a novel sustainable inventory-allocation planning model with carbon emissions and defective item disposal over multiple periods under a fuzzy random environment. In this paper, a carbon credit price and a carbon cap are proposed to demonstrate the effect of carbon emissions’ costs on the inventory-allocation network costs. The percentage of poor quality products from manufacturers that need to be rejected is assumed to be fuzzy random. Because of the complexity of the model, dynamic programming-based particle swarm optimization with multiple social learning structures, a DP-based GLNPSO, and a fuzzy random simulation are proposed to solve the model. A case is then given to demonstrate the efficiency and effectiveness of the proposed model and the DP-based GLNPSO algorithm. The results found that total costs across the inventory-allocation network varied with changes in the carbon cap and that carbon emissions’ reductions could be utilized to gain greater profits.

Optimization of Logistics Path of Dangerous Chemicals Based on Uncertainty Theory

Based on the uncertainty theory, the logistics path optimization of dangerous chemicals is studied in the research. In the course of the research, time-varying parameters, fuzzy variables and fuzzy random variables are introduced to provide quantitative tools for the risk of uncertainty, so that parameters setting and problem hypothesis can better reflect the actual situation of the transport network, so as to eliminate the idealized model. At the same time, the fuzzy simulation is substituted into the genetic algorithm, and the fuzzy stochastic simulation is substituted into the particle swarm optimization algorithm to solve the location-path- dispatching model of dangerous chemicals. On the basis of the traditional heuristic algorithm, the greedy method and the self-adaptive method are used in this paper to improve efficiency of the algorithm and enhance robustness of the results. Finally, as for the small-scale model, exact value is calculated by using Lingo software and changing modes, and the exhaustive method is used to obtain all the optimal solutions. Meanwhile, the improved heuristic algorithm is used in this paper to solve this problem, and then, the comparative analysis is carried out to verify its efficiency and superiority. Finally, the genetic algorithm based on fuzzy simulation and the self-adaptive hybrid particle swarm algorithm based on the greedy method & fuzzy random simulation are proved to be improved effectively.

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.

The Shortest Path Problem on a Time-Dependent Network With Mixed Uncertainty of Randomness and Fuzziness

The uncertainty of travel times on a time-dependent network is conventionally considered as randomness or fuzziness. However, sometimes, randomness or fuzziness cannot describe the uncertainty of the travel times on the time-dependent network. In this paper, we introduce a random fuzzy time-dependent network (RFTDN), in which travel times of a time-dependent network are represented as mixed uncertainty of randomness and fuzziness. With these conditions, the resulting RFTDN is far more complex when compared with the known networks. The complexity stems from estimating the length of a path, which is a basic and core issue when analyzing a network. To address this problem, we propose an optimized method that is suitable to cope with the shortest path problem of the RFTDN. The proposed method is realized by means of random fuzzy simulation and a new repair-based genetic optimization. Random fuzzy simulation is used to estimate the random fuzzy functions that describe the length of arcs, whereas the repair-based genetic algorithm is presented for finding the shortest path on the network. Furthermore, the proposed repair-based genetic operators are demonstrated their effectiveness by analyzing running time. A numerical example is also provided to show the robustness of the proposed approach.

Planning and optimization of intermodal hub-and-spoke network under mixed uncertainty

This paper addresses the planning and optimization of intermodal hub-and-spoke (IH&S) network considering mixed uncertainties in both transportation cost and travel time. Different from previous studies, this paper develops a novel modeling framework for the IH&S network design problem to jointly minimize the expected value of total transportation costs and the maximum travel time requirement in term of critical value. A new hybrid methodology by combining fuzzy random simulation (FRS) technique and multi-start simulated annealing (MSA) algorithm is designed to solve the proposed model. Numerical experiments are implemented to verify the effectiveness of the proposed model and solution approach.

Fuzzy random cost–profit tradeoff location model for a vehicle inspection station with regional constraints

Transportation facility and automotive service enterprise location is an interesting and important issue. In practice, such factors as customer demand, allocations, even locations of customers and facilities are usually changing, thus making facility location problematic with uncertainty. To account for it, some researchers have addressed stochastic/fuzzy models for locating an automotive service enterprise. However, probabilistic/fuzzy models are not suitable to describe all kinds of uncertainty, but only randomness or fuzziness. In fact, the uncertain environment of locating an automotive service enterprise is a mixed one with both randomness and fuzziness. To handle this issue in a practical manner, this work proposes fuzzy random tradeoff issues for it. Moreover, some regional constraints can greatly influence its location. By taking the vehicle inspection station as a typical example, this work presents new fuzzy random cost–profit tradeoff models of its location problem with regional constraints. A hybrid algorithm integrating fuzzy random simulation and genetic algorithms is adopted to solve the proposed models. Additionally, some risk factors have a great impact on decision making when faced with a location problem. This work thus conducts a risk performance analysis for locating an automotive service enterprise. Some numerical examples are given to illustrate the proposed models. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Random fuzzy mean-absolute deviation models for portfolio optimization problem with hybrid uncertainty

Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. The existing mean-absolute deviation models are devoted to either stochastic portfolio optimization or fuzzy one. However, practical investment decision problems often involve the mixture of randomness and fuzziness such as stochastic returns with fuzzy information. Thus it is necessary to model portfolio selection problem in such a hybrid uncertain environment. In this paper, we employ random fuzzy variable to describe the stochastic return on individual security with ambiguous information. We first define the absolute deviation of random fuzzy variable and then employ it as risk measure to formulate mean-absolute deviation portfolio optimization models. To find the optimal portfolio, we design random fuzzy simulation and simulation-based genetic algorithm to solve the proposed models. Finally, a numerical example for synthetic data is presented to illustrate the validity of the method.

Bilevel Construction Site Layout Optimization Based on Hazardous-Material Transportation

AbstractConstruction site layout optimization (CSLO) involves many important issues vital for the success of construction projects. One of the most important is the hazardous-material transportation (HT) problem. This paper concurrently considers CSLO and HT, namely the CSLO-HT problem, and proposes a bilevel multiobjective decision-making model (BMDMM). In this model, the upper-level decision-maker is the project manager, who aims to minimize site layout costs and economic losses from potential HT accidents. The lower-level decision-maker is the carrier, to whom the HT work is subcontracted, and whose goal is to reduce transportation costs. To solve the proposed bi-level multiobjective model, a fuzzy random simulation–based bilevel multiobjective genetic algorithm (frs-BLMOGA) is proposed. The approach is then applied to a hydropower construction project to illustrate the performance of the proposed methodology. The results and further analyses of the methodology prove that both the project manager and t...

Time-dependent fuzzy random location-scheduling programming for hazardous materials transportation

The tremendous use of hazardous materials has promoted the economic development, which also brings about a growing risk causing a widespread concern. In this work, we consider a location-scheduling problem on hazardous materials transportation under the assumption that transportation risks are time-dependent fuzzy random variables. First, we formulate a scheduling optimization model and design a fuzzy random simulation based genetic algorithm to optimize the departure time and dwell times for each depot–customer pair. Then we establish an expected value model and design a modified particle swarm optimization algorithm to minimize the en route risks and site risks. Finally, numerical examples are given to illustrate the effectiveness of the proposed models and algorithms.

Credibility Theory-Based Available Transfer Capability Assessment

Since the development of large scale power grid interconnections and power markets, research on available transfer capability (ATC) has attracted great attention. The challenges for accurate assessment of ATC originate from the numerous uncertainties in electricity generation, transmission, distribution and utilization sectors. Power system uncertainties can be mainly described as two types: randomness and fuzziness. However, the traditional transmission reliability margin (TRM) approach only considers randomness. Based on credibility theory, this paper firstly built models of generators, transmission lines and loads according to their features of both randomness and fuzziness. Then a random fuzzy simulation is applied, along with a novel method proposed for ATC assessment, in which both randomness and fuzziness are considered. The bootstrap method and multi-core parallel computing technique are introduced to enhance the processing speed. By implementing simulation for the IEEE-30-bus system and a real-life system located in Northwest China, the viability of the models and the proposed method is verified.

Random Fuzzy Decision Models for Pharmaceutical R&D Project Investment under Uncertainty

This paper considers an optimal stopping decision problem for pharmaceutical R&D project investment withoutrivalry in random fuzzy environments. Specifically, the R&D process can be regarded as a jump diffusion processof scientific knowledge full of complexity. Every jump represents a scientific breakthrough or a new knowledgediscovery. In classical R&D literature, the inter-arrival times between jumps are generally assumed as randomvariables which are exponentially distributed. Here, the inter-arrival times are treated as random fuzzy variablesobserve arbitrary distributions. Furthermore, the termination time of the project is incorporated into the R&Dmodels as a decision variable by allowing the decision-maker to sell the obtained technology at any point oftime. Three types of project return performance (expected net return, -optimistic net return and return reliability)are proposed and a spectrum of random fuzzy programming models are established to model the different R&Dinvestment decision problems according to the decision-maker’s attitude. Considering the complexity of thesemodels, the random fuzzy simulation is designed to estimate the values of project return performance and thesimultaneous perturbation stochastic approximation (SPSA) algorithm is employed to solve the proposed models.Finally, the effectiveness of the hybrid algorithm and the applicability of these models are illustrated by somenumerical examples.

Multidemand Multisource Order Quantity Allocation with Multiple Transportation Alternatives

This paper focuses on a multidemand multisource order quantity allocation problem with multiple transportation alternatives. To solve this problem, a bilevel multiobjective programming model under a mixed uncertain environment is proposed. Two levels of decision makers are considered in the model. On the upper level, the purchaser aims to allocate order quantity to multiple suppliers for each demand node with the consideration of three objectives: total purchase cost minimization, total delay risk minimization, and total defect risk minimization. On the lower level, each supplier attempts to optimize the transportation alternatives with total transportation and penalty costs minimization as the objective. In contrast to prior studies, considering the information asymmetry in the bilevel decision, random and fuzzy random variables are used to model uncertain parameters of the construction company and the suppliers. To solve the bilevel model, a solution method based on Kuhn-Tucker conditions, sectional genetic algorithm, and fuzzy random simulation is proposed. Finally, the applicability of the proposed model and algorithm is evaluated through a practical case from a large scale construction project. The results show that the proposed model and algorithm are efficient in dealing with practical order quantity allocation problems.

A Hybrid Intelligent Algorithm for Emergency Facility Location Problem

To build an emergency network, selecting location is the most important step. It is no longer a singleobjective problem. Both cost and e‐ciency should be taken into account. In this research, a multiobjective location model was established. Under the uncertain situation, a hybrid intelligent algorithm was developed to balance the two objects. This algorithm takes advantage of fuzzy random simulation, neural network and Elite Non-dominated Sorting Genetic Algorithms. Then it helped a power grid company select seven reasonable solutions to locate emergency facility. Therefore, a conclusion can be drawn that this model and algorithm is feasible and progressive for emergency facility location problem.