The aim of this paper is to construct a portfolio of eight different stocks from New York Stock Exchange market (AIR, ABM, TSCO, HLX, KO, DIS, AMZN, and VZ) using stochastic programming. The next stage (period) prices...
详细信息
Most existing distribution networks are difficult to withstand the impact of meteorological disasters. With the development of active distribution networks(ADNs), more and more upgrading and updating resources are app...
详细信息
Most existing distribution networks are difficult to withstand the impact of meteorological disasters. With the development of active distribution networks(ADNs), more and more upgrading and updating resources are applied to enhance the resilience of ADNs. A two-stage stochastic mixed-integer programming(SMIP) model is proposed in this paper to minimize the upgrading and operation cost of ADNs by considering random scenarios referring to different operation scenarios of ADNs caused by disastrous weather events. In the first stage, the planning decision is formulated according to the measures of hardening existing distribution lines, upgrading automatic switches, and deploying energy storage resources. The second stage is to evaluate the operation cost of ADNs by considering the cost of load shedding due to disastrous weather and optimal deployment of energy storage systems(ESSs) under normal weather condition. A novel modeling method is proposed to address the uncertainty of the operation state of distribution lines according to the canonical representation of logical constraints. The progressive hedging algorithm(PHA) is adopted to solve the SMIP model. The IEEE 33-node test system is employed to verify the feasibility and effectiveness of the proposed method. The results show that the proposed model can enhance the resilience of the ADN while ensuring economy.
Two-stage stochastic mixed-integer programs (SMIPs) with general integer variables in the second-stage are generally difficult to solve. This paper develops the theory of integer set reduction for characterizing a sub...
详细信息
Two-stage stochastic mixed-integer programs (SMIPs) with general integer variables in the second-stage are generally difficult to solve. This paper develops the theory of integer set reduction for characterizing a subset of the convex hull of feasible integer points of the second-stage subproblem which can be used for solving the SMIP with pure integer recourse. The basic idea is to use the smallest possible subset of the subproblem feasible integer set to generate a valid inequality like Fenchel decomposition cuts with a goal of reducing computation time. An algorithm for obtaining such a subset based on the solution of the subproblem linear programming relaxation is devised and incorporated into a decomposition method for SMIP. To demonstrate the performance of the new integer set reduction methodology, a computational study based on randomly generated knapsack test instances was performed. The results of the study show that integer set reduction aids in speeding up cut generation, leading to better bounds in solving SMIPs with pure integer recourse than using a direct solver.
This paper presents the determination of capacity and operational schedule for a grid-tied microgrid system based on a stochastic optimization method. A photovoltaic power system is used as a renewable energy source, ...
详细信息
ISBN:
(纸本)9781509013357
This paper presents the determination of capacity and operational schedule for a grid-tied microgrid system based on a stochastic optimization method. A photovoltaic power system is used as a renewable energy source, while battery system is utilized as energy storage systems. The microgrid system can be operated using the usual priority scheme or the proposed scheduling scheme. The mathematical model for the microgrid system is developed. The objective function is formulated from a capital and operational costs. The constraints for the optimization are formulated based on system model, physical limitations, and performance requirements. Performances required for microgrid system are high renewable energy penetration with low curtailed renewable energy. Two-stage stochastic linear programming method is used to solve the optimization problem. Proposed scheduling scheme is able to increase renewable energy penetration ratio by 4% and reduce curtailed renewable energy production ratio by 7%. The combination of scheduling scheme and stochastic optimization to improve performances of microgrid system are the key outcomes of this research.
In this work a recently developed mathematical programming formulation called adaptation is compared with the widely used stochastic programming method in the context of electric infrastructure expansion planning. Alt...
详细信息
ISBN:
(纸本)9781509032709
In this work a recently developed mathematical programming formulation called adaptation is compared with the widely used stochastic programming method in the context of electric infrastructure expansion planning. Although the structure of the adaptation method closely resembles that of a generic stochastic program it diverges from the temporal conventions of traditional electric infrastructure formulations. While traditional stochastic programming formulations restrict first and later stage capacity investments to separate time periods, the first and later stage capacity investments in adaptation overlap in time. Additionally, recourse decisions for all scenarios are defined relative to the central core trajectory in the same time period rather than the node at the previous time period in the stochastic programming scenario tree. After an in-depth discussion of stochastic programming and adaptations' formulations, a six bus simulation is provided to facilitate a more concrete comparison of the two methods. Uncertainties considered in the simulation include, wind and solar build costs, carbon taxes, demand and peak demand growth, natural gas fuel prices, and transmission costs.
We introduce disciplined convex stochastic programming (DCSP), a modeling framework that can significantly lower the barrier for modelers to specify and solve convex stochastic optimization problems, by allowing model...
详细信息
ISBN:
(纸本)9780996643108
We introduce disciplined convex stochastic programming (DCSP), a modeling framework that can significantly lower the barrier for modelers to specify and solve convex stochastic optimization problems, by allowing modelers to naturally express a wide variety of convex stochastic programs in a manner that reflects their underlying mathematical representation. DCSP allows modelers to express expectations of arbitrary expressions, partial optimizations, and chance constraints across a wide variety of convex optimization problem families (e.g., linear, quadratic, second order cone, and semidefinite programs). We illustrate DCSP's expressivity through a number of sample implementations of problems drawn from the operations research, finance, and machine learning literatures.
This paper is concerned with the solution procedure of a multi-objective transportation problem with fuzzy stochastic simulation based genetic algorithm. Supplies and demands are considered as a fuzzy random variables...
详细信息
This paper is concerned with the solution procedure of a multi-objective transportation problem with fuzzy stochastic simulation based genetic algorithm. Supplies and demands are considered as a fuzzy random variables with fuzzy means and fuzzy variances in proposed multi-objective fuzzy stochastic transportation problem. The first step in fuzzy simulation based genetic algorithm is to deal with aspiration level of the constraints with the help of alpha-cut technique to obtain multi-objective stochastic transportation problem. In next step, fuzzy probabilistic constraints (fuzzy chance constraints) are handled within fuzzy stochastic simulation based genetic algorithm to obtain a feasible region. The feasibilities of the chance constraints are checked by the stochastic programming with the genetic process without deriving the deterministic equivalents. The feasibility condition for the transportation problem is maintained through out the problem. Finally, multiple objective functions are considered in order to generate a Pareto optimal solutions for the fuzzy stochastic transportation problem using the proposed algorithm. The proposed procedure is illustrated by two numerical examples.
In this work a scenario-based two-stage stochastic programming model is proposed to solve a microgrid's tertiary control optimization problem taking into account some renewable energy resource's uncertainty as...
详细信息
ISBN:
(纸本)9781467366922
In this work a scenario-based two-stage stochastic programming model is proposed to solve a microgrid's tertiary control optimization problem taking into account some renewable energy resource's uncertainty as well as uncertain energy deviation prices in the electricity market. Scenario generation methods for wind speed realizations are also studied. Results show that the introduction of stochastic programming represents a significant improvement over a deterministic model.
In this paper, a mathematical optimization approach for green energy portfolio is presented to strike a right balance between risk and profit associated with retailing in power market. This approach emphasizes on the ...
详细信息
ISBN:
(纸本)9781467373890
In this paper, a mathematical optimization approach for green energy portfolio is presented to strike a right balance between risk and profit associated with retailing in power market. This approach emphasizes on the increasing use of renewable resources to overcome conservation concerns to some degrees. Three different uncertainties are considered for electricity price and energy output of wind and solar distributed generation units. In order to model the uncertainties properly, scenario construction schemes, namely Monte Carlo and time series with ARIMA (Auto regressive integrated moving average) are implemented in this paper. Moreover, risk and elasticity analysis are considered simultaneously to enable consumers and retailers to manage their risk and incomes. Two-stage stochastic programming with fixed recourse is used to model the probabilistic space of decision making process in this paper. At the end, numerical results and simulations are presented which demonstrate the applicability of the proposed approach in a retail electricity market.
This paper addresses a multi-objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneous...
详细信息
This paper addresses a multi-objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneously minimized. We suppose that demands and travel durations are of a stochastic nature. In order to build a certainty equivalent program to the multi-objective stochastic vehicle routing problem, we propose a solution strategy based on a recourse approach, a chance-constrained approach and a goal-programming approach. The resulting certainty equivalent program is solved to optimality using CPLEX. Copyright (C) 2016 John Wiley & Sons, Ltd.
暂无评论