Dependent-chance Programming Research Articles

Enhancing irrigation water productivity and controlling salinity under uncertainty: A full fuzzy dependent linear fractional programming approach

An integrated simulation-optimization framework is developed under uncertainty to enhance irrigation water productivity and control salinity in an arid area. A full fuzzy dependent linear fractional programming approach is formulated by incorporating fuzzy dependent-chance programming, fuzzy credibility-constrained programming and linear fractional programming within a general framework of irrigation planning. Then, simulation module concerning water, salt balance process and crop water-salt production functions enables to quantify daily physical process of water and salt movement among the soil water, crop root zone and groundwater aquifers. Thus, this study can readily handle fuzzy uncertainty existing concurrently in the ratio objective (i.e., economic water productivity) through the concept of fuzzy dependent chance and double-sided constraints. It can also simultaneously provide the maximum credibility level that the objective is achievable and credibility levels implying that optimal solutions are believable. Besides, daily variations of simulated physical parameters are illustrated corresponding to management strategies. To demonstrate its applicability, it’s then applied to a case study of irrigation planning in the Jiefangzha Irrigation Subarea in Hetao Irrigation District, northwest China. Results can clearly analyze tradeoffs among satisfaction degree of fuzzy objective, fuzzy constraints and optimal solutions. Moreover, by examining different management targets and salt accumulation constraints, this study demonstrates the merits and importance of the work to promote irrigation water productivity and control salinity. Dynamic decision making of irrigation planning is possibly made by coupling daily simulation and optimization modules. Therefore, these findings can support decision makers to identify appropriate solutions for irrigation planning.

Optimal dispatching strategy for user-side integrated energy system considering multiservice of energy storage

The user-side integrated energy system is of great significance for promoting the energy revolution. However, the multiple coupling forms of energy, as well as uncertainties from generation sources and loads have brought tremendous challenges to its optimal dispatch. In this paper, a two-stage coordinated scheduling method is proposed for the user-side integrated energy system that considers energy storage multiple services to minimize long-term operation costs. Besides, the proposed scheduling model is based on a two-part time-of-use electricity price mechanism. The first stage of the model determines the daily initial state of charge of energy storage, the demand management coefficient, and the baseline of demand response. The second stage is intra-day rolling scheduling, and the power scheduling of each unit in the system is optimized under the premise that the closer the time period, the higher the prediction accuracy. Energy storage is investigated for four main service options: 1) demand management; 2) demand response; 3) energy arbitrage; 4) providing reserve capacity. At the same time, a linear energy storage degradation cost model is established. The combined goal programming and dependent chance programming in the fuzzy environment is implemented to obtain a scheduling plan for the UIES efficiently and to ensure the system’s economy and the most possibility of the events of power balance in an uncertain environment. A case study verifies the effectiveness and advantages of the proposed method.

Distributed AquaCrop simulation-nonlinear multi-objective dependent-chance programming for irrigation water resources management under uncertainty

In the agricultural water resources system, the regional yield is hard to be simulated accurately under the impacts of spatial heterogeneities of soil, weather, and crop types. The optimal water allocation schemes may be not in accordance with actual conditions due to neglecting the actual crop growth process. Meanwhile, the uncertainties in the simulation-optimization models are not easy to be addressed. To deal with the above problems, this paper develops a framework of the distributed AquaCrop simulation nonlinear multi-objective dependent-chance programming (distributed AquaCrop NMOFDCP) for irrigation water resources management under uncertainties. This developed model is applied to a case study of irrigation water resources management in the middle reaches of the Heihe River Basin in China. The 134 homogeneous decision-making units (DMUs) are divided to depict the spatial heterogeneities of the study area, and 472 decision variables (irrigation amount) for 134 DMUs are optimized. Moreover, the model deals with uncertainties expressed as fuzzy goals and tradeoffs relationships between objectives of the yield and water productivity, and measures the satisfactory degrees between objectives and their fuzzy goals. Two groups of Pareto solutions corresponding to the maximum satisfactory degree of the yield, and the maximum satisfactory degree of the water productivity are obtained by the parallel genetic algorithm (PGA) method respectively. In addition, water allocation, satisfactory degree of the yield, and satisfactory degree of water productivity are analyzed at the decision-making unit scale, crop scale, and irrigation-district scale separately. Besides the effects of three weather conditions and four soil types on the system’s outputs are conducted. The results show that weather conditions and soil types have obvious effects on the system’s outputs at three analysis scales, and different water allocation patterns at the growth period affect the yield and water productivity.

Optimal irrigation water allocation in Hetao Irrigation District considering decision makers’ preference under uncertainties

In this study, a fuzzy multi-objective mλ-measure dependent-chance programming model was proposed to optimize limited irrigation water among three crops and five subareas in Hetao Irrigation District (HID) under uncertainties, with the objectives of ensuring food security and maximizing economic benefits. Three levels of droughts (100%, 85%, and 70% of annual average water diversion) that may happen in HID were set as future possible droughts scenarios. The optimization model considered the detailed physical process of soil water balance, which is necessary for irrigation districts where groundwater recharge plays a major role when available water limited. Moreover, sensitivities of crop yield to water deficit during crop growth periods were involved in model formulation to reflect the difference of crop water demand in different subareas. In optimization model, mλ-measure was introduced into the first objective to quantify optimistic and pessimistic decision attitudes of decision makers, and a series of alternatives were obtained. The obtained results indicate that: (1) the irrigation water of wheat, maize, and sunflower at rapid growth stage and middle growth stage should be preferentially guaranteed due to their high water-deficit sensitivities. The water demand at initial growth stage and late growth stage can be satisfied by soil water and groundwater recharge. (2) maize has the priority of irrigation in almost all subareas while sunflower has to face water deficit when drought occurs. (3) allocating more irrigation water to Yongji and Jiefangzha subareas can help increase food production. (4) the irrigation water allocated to grain crops increases along with the decrease of λ, representing decision makers’ more conservative preference. The optimization model and results in this study provide decision makers abundant water-allocation schemes under drought conditions.

Power System Day-Ahead Unit Commitment Based on Chance-Constrained Dependent Chance Goal Programming

In the context of large-scale renewable energy integrated into an electrical power system, the effects of power forecast errors on the power balance equation of the power system unit commitment model is considered. In this paper, the problem of solving the power balance equation with uncertain variables was studied. The unit commitment model with random variables in the power balance equation was solved by establishing a power system day-ahead optimisation unit commitment model based on chance-constrained dependent chance goal programming. First, to achieve the solution of the power balance equation with random variables, the equality constraint is loosened into an inequality constraint, and the power balance equation constraint is transformed into a dependent chance programming model aimed at maximising the probability of occurrence of random events in an uncertain environment. Then, the dependent chance programming model is proposed to ensure the economy and security of the scheme, and the goal programming model is introduced to facilitate an efficient solution. By combining dependent chance programming and goal programming, a power system day-ahead unit commitment model based on chance-constrained dependent chance goal programming is established. Finally, an example is discussed to demonstrate the effectiveness of the proposed model.

New approaches for optimizing standby redundant systems with fuzzy lifetimes

Abstract Standby redundancy is one of the most popular ways to optimize systems reliability with several applications in modern engineering. Under real-world conditions, the system lifetime can be modeled as a fuzzy interval due to parameter uncertainty and data inaccuracy. In this paper, several fuzzy standby redundancy optimization models are proposed utilizing three distinct types of decision criteria, namely as the expected value model, the chance-constrained and the dependent-chance programming. Thereafter, two solution processes are proposed. The first one utilizes a novel algorithm with lower computational complexity for a specific fuzzy objective which is embedded into intelligent optimization algorithms to derive a hybrid algorithm. While the other approach relies upon the transformation of the fuzzy model into its deterministic counterpart employing a family of fuzzy operational laws, then the solution derives in a straightforward manner using classical optimization algorithms or some well-developed software packages. Finally, several diverse numerical examples are considered for demonstrating the superiority of our treatment. It is shown that the herein developed solution approaches for the fuzzy standby redundancy optimization problems exhibit higher efficiency and satisfactory accuracy as compared with standard solution methods.

An Interval Quadratic Fuzzy Dependent-Chance Programming Model for Optimal Irrigation Water Allocation under Uncertainty

In this study, an interval quadratic fuzzy dependent-chance programming (IQFDCP) model is proposed for irrigation water management under uncertainty. This model can deal with the interval and fuzzy uncertainties encountered in optimal irrigation water resources allocation problems. It takes optimal credibility level of system revenue as the objective function for addressing the conflict between maximum system revenue and the credibility level of the system revenue. By providing three scenarios of precipitation, the optimal solutions are obtained. The developed model is applied to a case study for irrigation water allocation in Minqin Oasis, Wuwei city, northwest China. This study can help determine how much irrigation water should be allocated to different crops under the maximum credibility level of the system revenue. The optimal solutions can provide a certain credibility level of system revenue corresponding to different scenarios and mitigate the system-failure risk level of water shortages in arid areas. Moreover, because the IQFDCP can objectively reflect the interrelationship among crop irrigation water amount, system revenue, and system-failure risk level, the results are able to provide advices to decision makers for efficiently managing water resources in different scenarios.

Dependent-Chance Programming on Sugeno Measure Space

In order to solve the optimization problem of selecting the decision with maximal chance to meet the Sugeno event in Sugeno environment, dependent-chance programming on Sugeno measure space is proposed, which can be considered as a generalized extension of the stochastic dependent-chance programming. Firstly, the theoretical framework of dependent-chance programming on Sugeno measure space is established. Secondly, a Sugeno simulation-based hybrid approach, which consists of back propagation neural network and genetic algorithm, is presented to construct an approximate solution of the complex dependent-chance programming models on Sugeno measure space. Finally, some numerical examples are given to illustrate the effectiveness of the approach.

Supplier selection and order allocation using a stochastic multi-objective programming model and genetic algorithm

In this paper, we develop a supplier selection and order allocation multi-objective model in stochastic environment in which purchasing cost, percentage of delivered items with delay and percentage of rejected items provided by each supplier are supposed to be stochastic parameters following any arbitrary probability density function. To do so, we use dependent chance programming (DCP) that maximises probability of the event that total purchasing cost, total delivered items with delay and total rejected items are less than or equal to pre-determined values given by decision maker. After transforming the abovementioned stochastic multi-objective programming problem into a stochastic single objective problem using minimum deviation method, we apply a genetic algorithm to solve the later single objective problem. The employed genetic algorithm performs a simulation process in order to calculate the stochastic objective function as its fitness function. A stochastic analysis reveals that incorporation of stochasticity into the supplier selection and order allocation problem will be advantageous for a purchasing firm with respect to purchasing cost, percentage of delivered items with delay and percentage of rejected items. Furthermore, we explore the impact of stochastic parameters on the given solution via a sensitivity analysis exploiting coefficient of variation. The results show that as stochastic parameters have greater coefficients of variation, the value of objective function in the stochastic single objective programming problem is worsened.

Two-Stage Multi-Objective Collaborative Scheduling for Wind Farm and Battery Switch Station

In order to deal with the uncertainties of wind power, wind farm and electric vehicle (EV) battery switch station (BSS) were proposed to work together as an integrated system. In this paper, the collaborative scheduling problems of such a system were studied. Considering the features of the integrated system, three indices, which include battery swapping demand curtailment of BSS, wind curtailment of wind farm, and generation schedule tracking of the integrated system are proposed. In addition, a two-stage multi-objective collaborative scheduling model was designed. In the first stage, a day-ahead model was built based on the theory of dependent chance programming. With the aim of maximizing the realization probabilities of these three operating indices, random fluctuations of wind power and battery switch demand were taken into account simultaneously. In order to explore the capability of BSS as reserve, the readjustment process of the BSS within each hour was considered in this stage. In addition, the stored energy rather than the charging/discharging power of BSS during each period was optimized, which will provide basis for hour-ahead further correction of BSS. In the second stage, an hour-ahead model was established. In order to cope with the randomness of wind power and battery swapping demand, the proposed hour-ahead model utilized ultra-short term prediction of the wind power and the battery switch demand to schedule the charging/discharging power of BSS in a rolling manner. Finally, the effectiveness of the proposed models was validated by case studies. The simulation results indicated that the proposed model could realize complement between wind farm and BSS, reduce the dependence on power grid, and facilitate the accommodation of wind power.

Dependent-Chance Goal Programming for Water Resources Management under Uncertainty

Without sufficient data, consulting experts is a good way to quantify unknown parameters in water resources management which will result in human uncertainty. The aim of this paper is to introduce a new tool-uncertainty theory to deal with such uncertainty which is treated as uncertain variable with uncertainty distribution. And a dependent-chance goal programming (DCGP) model is provided for water resources management under such circumstance. In the model uncertain measure is used to measure possibility that an event will occur which is maximized by minimizing the deviation (positive or negative deviation) from target of objective event under a given priority structure. In the end, the developed model is applied to a numerical example to illustrate the effectiveness of the model. The result obtained contributes to the desired water-allocation schemes for decision-markers.

A multi-objective DCP model for bi-level resource-constrained project scheduling problems in grounding grid system project under hybrid uncertainty

Since more elements are involved in the construction projects, the decision making process of Resource-constrained Project Scheduling Problems (RCPSP) cannot be determined by a manager, but multiple level decision makers. This study focuses on the RCPSP in a practical grounding grid system project in Jin' An Qiao hydropower station, which consider the hierarchical organization structure and hybrid uncertainty environment simultaneously. In this practical RCPSP, the construction contractor is the Upper Level Decision Maker (ULDM), while the outsourcing partner is the Lower Level Decision Maker (LLDM). Considering the operations difficulties and practical decision making process in the RCPSP, a bi-level multi-objective RCPSP model with bi-random coefficients is developed. To deal with the bi-random variables in the model, the Dependent-Chance Programming (DCP) method is introduced and the equivalent crisp model is derived. Subsequently, motivated by the particular nature of model, Bi-level Global-local-neighbor Particle Swarm Optimization Algorithm (BGLN-PSO) is designed to obtain the optimal schedule for grounding grid system project. A practical application is presented to verify the efficiency of proposed bi-level multi-objective RCPSP model and algorithm.

Uncertain random time-cost trade-off problem

Since for most projects, ‘new’ parts (with little or no historical data) and ‘old’ parts (with sufficient historical data) always coexist in the same project, uncertainty and randomness should be considered simultaneously in time-cost trade-off problem. In this paper, combined with uncertainty theory and dependent-chance programming, an uncertain random time-cost trade-off model is built. A crisp equivalent model is also given for some special case. Besides, uncertain random simulation and genetic algorithm are integrated for solving the proposed model.

Optimization of variable demand fuzzy economic order quantity inventory models without and with backordering

A variable demand inventory model was developed for minimizing inventory cost, treating the holding and ordering costs and demand as independent fuzzy variables. Thereafter, backordering cost was also considered as an independent fuzzy variable. Fuzzy expected value model and fuzzy dependent chance programming model were constructed to find the optimal economic order quantity, which would minimize the fuzzy expected value of the total cost, so that the credibility of the total cost not exceeding a certain budget level was maximized. Optimization was carried out using genetic algorithms and particle swarm optimization algorithm, and their performances were compared. The developed model was found to be efficient not only in one artificial case study but also in two data sets collected from the industries. Therefore, this model could solve real-world problems, too.

Hybrid multilevel programming with uncertain random parameters

Multilevel programming is developed for modeling decentralized decision-making processes. For different management requirements and risk tolerances of different-level decision-makers, the decision-making criteria applied in different levels cannot be always the same. In this paper, a hybrid multilevel programming model with uncertain random parameters based on expected value model (EVM) and dependent-chance programming (DCP), named as EVM---DCP hybrid multilevel programming, is proposed. The corresponding concepts of Nash equilibrium and Stackelberg---Nash equilibrium are given. For some special case, an equivalent crisp mathematical programming is proposed. An approach integrating uncertain random simulations, Nash equilibrium searching approach and genetic algorithm is designed. Finally, a numerical experiment of uncertain random supply chain pricing decision problem is given.

Optimal Control of Energy Storage Based on Fuzzy Dependent-Chance Programming

In order to maximize the match between the output of the Hybrid Wind/Photovoltaic/ Energy storage System and the scheduling curve,the article takes the measure that optimizes and controls the energy storage device one day ahead.Due to the fuzziness of the wind and photovoltaic output, the optimal control method of energy storage is proposed based on a fuzzy dependent-chance programming theory. This method considers the constraints of the energy storage device including the power output and energy constrain, and the matching degree of each time is represented by credibility value.So the final goal is maximizing the mean value of the total credibility within a day of 96 periods.The genetic algorithm based fuzzy simulation is used to solve the model,then we can get the different periods of energy storage charge and discharge power corresponding to the credibility of maximum mean value.

Based Stochastic Particle Swarm Optimization and Random Simulation for Solving Stochastic Dependent-Chance Programming

Aiming at being hard to solve stochastic Dependent-chance Programming in uncertainty programming,a new algorithm for stochastic dependent-chance programming combined particle swarm optimization with random simulation for approximation of the chance function is presented in the paper.It overcomes the defaults such as needing a long time,complex calculation,easy falling into local optimal in the hybrid intelligence algorithm based on GA,the result of experiment shows the correctness and effectiveness of the algorithm.After testing its performance and comparing with algorithm of based on GA,the results show that the algorithm is more preferable.

A new intelligent algorithm for dynamic facility layout problem in state of fuzzy constraints

In the present paper, the dynamic facilities layout problem is studied in presence of ambiguity of information flow. Product demand (and consequently material flow) is defined as fuzzy numbers with different membership functions. The problem is modeled in fuzzy programming. Three models of expected value, chance-constrained programming and dependent-chance programming and two hybrid intelligent algorithms are then presented. At the end, efficiency of algorithms for solving fuzzy models of dynamic facilities layout is shown through some numerical examples.

Diameter Constrained Fuzzy Minimum Spanning Tree Problem

Abstract In this paper, we have studied the constrained version of the fuzzy minimum spanning tree problem. Costs of all the edges are considered as fuzzy numbers. Using the m λ measure, a generalization of credibility measure, the problem is formulated as chance-constrained programming problem and dependent-chance programming problem according to different decision criteria. Then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers. Furthermore, a fuzzy simulation based hybrid genetic algorithm is designed to solve the proposed models using Prufer like code representation of labeled trees.

Route optimisation models and algorithms for hazardous materials transportation under different environments

This study focuses on how to determine the optimum transportation route for hazardous materials under the certain, fuzzy or stochastic environment. On the basis of analysing the transportation route selection problem of hazardous materials (TRSP-HM), three objectives are presented and the multi-objective routing programming model (MRPM) for hazardous materials transportation (HMT) is put forward under the certain environment, and an improved label algorithm is proposed to solve the MRPM. After defining the maximum-chance optimum route and the α-optimum routes, the multi-objective routing chance-constrained programming model (MRCPM) and multi-objective routing dependent-chance programming model (MRDPM) for HMT under the fuzzy or stochastic environment are established respectively. Then, the integration intelligent algorithm is developed to solve the proposed models, which integrates the fuzzy simulation, neural networks, stochastic simulation and genetic algorithm. Finally, the proposed models and algorithms are successfully tested with the help of two real cases.