A Study on Efficient Computing Budget Allocation for a Two-Stage Problem

2021 ◽  
pp. 2050044
Author(s):  
Tianxiang Wang ◽  
Jie Xu ◽  
Jian-Qiang Hu
Keyword(s):  
Optimization Problem ◽  
Simulation Optimization ◽  
Risk Measure ◽  
Budget Allocation ◽  
Optimal Decision ◽  
Two Stage ◽  
Second Stage ◽  
Allocation Procedure ◽  
Optimal Computing Budget Allocation ◽  
Sequential Allocation

We consider how to allocate simulation budget to estimate the risk measure of a system in a two-stage simulation optimization problem. In this problem, the first stage simulation generates scenarios that serve as inputs to the second stage simulation. For each sampled first stage scenario, the second stage procedure solves a simulation optimization problem by evaluating a number of decisions and selecting the optimal decision for the scenario. It also provides the estimated performance of the system over all sampled first stage scenarios to estimate the system’s reliability or risk measure, which is defined as the probability of the system’s performance exceeding a given threshold under various scenarios. Usually, such a two-stage procedure is very computationally expensive. To address this challenge, we propose a simulation budget allocation procedure to improve the computational efficiency for two-stage simulation optimization. After generating first stage scenarios, a sequential allocation procedure selects the scenario to simulate, followed by an optimal computing budget allocation scheme that determines the decision to simulate in the second stage simulation. Numerical experiments show that the proposed procedure significantly improves the efficiency of the two-stage simulation optimization for estimating system’s reliability.

scholarly journals An Efficient Two-Stage Sparse Representation Method

2015 ◽  
Vol 30 (01) ◽  
pp. 1651001 ◽  
Author(s):  
Chengyu Peng ◽  
Hong Cheng ◽  
Manchor Ko
Keyword(s):  
Sparse Representation ◽  
Large Scale ◽  
Optimization Problem ◽  
Two Stage ◽  
Linear Inverse Problems ◽  
Second Stage ◽  
Concrete Realization ◽  
Representation Method ◽  
Scale Optimization ◽  
Very High

There are a large number of methods for solving under-determined linear inverse problems. For large-scale optimization problem, many of them have very high time complexity. We propose a new method called two-stage sparse representation (TSSR) to tackle it. We decompose the representing space of signals into two parts”, the measurement dictionary and the sparsifying basis. The dictionary is designed to obey or nearly obey the sub-Gaussian distribution. The signals are then encoded on the dictionary to obtain the training and testing coefficients individually in the first stage. Then, we design the basis based on the training coefficients to approach an identity matrix, and we apply sparse coding to the testing coefficients over the basis in the second stage. We verify that the projection of testing coefficients onto the basis is a good approximation of the original signals onto the representing space. Since the projection is conducted on a much sparser space, the runtime is greatly reduced. For concrete realization, we provide an instance for the proposed TSSR. Experiments on four biometric databases show that TSSR is effective compared to several classical methods for solving linear inverse problem.

scholarly journals DA-OCBA: Distributed Asynchronous Optimal Computing Budget Allocation Algorithm of Simulation Optimization Using Cloud Computing

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1297 ◽  
Author(s):  
Yukai Wang ◽  
Wenjie Tang ◽  
Yiping Yao ◽  
Feng Zhu
Keyword(s):  
Cloud Computing ◽  
Systems Engineering ◽  
Simulation Optimization ◽  
Budget Allocation ◽  
Ranking And Selection ◽  
Allocation Rule ◽  
Computing Power ◽  
Computing Platform ◽  
Optimal Computing Budget Allocation ◽  
Selection Algorithms

The ranking and selection of simulation optimization is a very powerful tool in systems engineering and operations research. Due to the influence of randomness, the algorithms for ranking and selection need high and uncertain amounts of computing power. Recent advances in cloud computing provide an economical and flexible platform to execute these algorithms. Among all ranking and selection algorithms, the optimal computing budget allocation (OCBA) algorithm is one of the most efficient. However, because of the lack of sufficient samples that can be executed in parallel at each stage, some features of the cloud-computing platform, such as parallelism, scalability, flexibility, and symmetry, cannot be fully utilized. To solve these problems, this paper proposes a distributed asynchronous OCBA (DA-OCBA) algorithm. Under the framework of parallel asynchronous simulation, this algorithm takes advantage of every idle docker container to run better designs in advance that are selected by an asymptotic allocation rule. The experiment demonstrated that the efficiency of simulation optimization for DA-OCBA was clearly higher than that for the traditional OCBA on the cloud platform with symmetric architecture. As the number of containers grew, the speedup of DA-OCBA was linearly increasing for simulation optimization.

Real-Time Pricing for Smart Grid with Multiple Companies and Multiple Users Using Two-Stage Optimization

2018 ◽  
Vol 6 (5) ◽  
pp. 435-446 ◽  
Author(s):  
Li Tao ◽  
Yan Gao
Keyword(s):  
Smart Grid ◽  
Real Time ◽  
Optimization Problem ◽  
Statistical Approach ◽  
Electricity Price ◽  
Two Stage ◽  
Second Stage ◽  
Multiple Users ◽  
Utility Companies ◽  
Analytic Expression

AbstractIn this paper, we focus on the real-time interactions among multiple utility companies and multiple users and formulate real-time pricing (RTP) as a two-stage optimization problem. At the first stage, based on cost function, we propose a continuous supply function bidding mechanism to model the utility companies’ profit maximization problem, by which the analytic expression of electricity price is further derived. At the second stage, considering that individually optimal solution may not be socially optimal, we employ convex optimization with linear constraints to model the price anticipating users’ daily payoff maximum. Substitute the analytic expression of electricity price obtained at the first stage into the optimization problem at the second stage. Using customized proximal point algorithm (C-PPA), the optimization problem at the second stage is solved and electricity price is obtained accordingly. We also prove the existence and uniqueness of the Nash equilibrium in the mentioned two-stage optimization and the convergence of C-PPA. In addition, in order to make the algorithm more practical, a statistical approach is used to obtain the function of price only through online information exchange, instead of solving it directly. The proposed approach offers RTP, power production and load scheduling for multiple utility companies and multiple users in smart grid. Statistical approach helps to protect the company’s privacy and avoid the interference of random factors, and C-PPA has an advantage over Lagrangian algorithm because the former need not obtain the objection function of the dual optimization problem by solving an optimization problem with parameters. Simulation results show that the proposed framework can significantly reduce peak time loading and efficiently balance system energy distribution.

scholarly journals Two-Stage Supply-Chain Optimization Considering Consumer Low-Carbon Awareness under Cap-and-Trade Regulation

2019 ◽  
Vol 11 (20) ◽  
pp. 5727 ◽  
Author(s):  
Zhimiao Tao
Keyword(s):  
Supply Chain ◽  
Optimization Problem ◽  
Profit Sharing ◽  
Optimal Decision ◽  
Low Carbon ◽  
Cap And Trade ◽  
Supply Chain Optimization ◽  
Two Stage ◽  
Trade Regulation ◽  
Decision Policies

Cap-and-trade regulation is an effective mechanism to control carbon emissions. The optimization problem for a two-stage supply chain consisting of a manufacturer and a retailer under cap-and-trade regulation was investigated in this paper. Consumers’ low-carbon awareness level was considered in the decision models. Optimal decision policies, corresponding emissions, and profits were calculated for decentralized and centralized decision-making modes. Under a decentralized mode, the two-stage supply-chain optimization problem was formulated as a Stackelberg game model, where the manufacturer and retailer were the leader and follower, respectively. The manufacturer decides the emission-reduction levels per product unit and the retailer decides the retail price per unit product. The optimal decisions are derived using the reverse-solution method. By contrast, the two-stage supply-chain optimization problem under a decentralized mode was formulated as a single-level optimization model. The nonlinear model is handled by KKT optimality conditions. The influence of the regulation parameters (caps and carbon prices) and consumers’ low-carbon awareness on the optimal decision policies, the corresponding emissions, and profits is discussed in detail. A comparison between the two modes implies that the decentralized mode is dominated by the centralized mode in terms of profit and emissions. In order to provoke the decision makers under decentralized modes to make the decisions under the decentralized mode, a profit-sharing contract was designed. This study shows that higher consumer low-carbon awareness and carbon prices can improve the manufacturer-decision flexibility when there exists a profit-sharing contract. Finally, numerical experiments confirmed the analytical results.

Ordinal Optimization with Computing Budget Allocation for Selecting an Optimal Subset

2016 ◽  
Vol 33 (02) ◽  
pp. 1650009 ◽  
Author(s):  
Mohammad H. Almomani ◽  
Mahmoud H. Alrefaei
Keyword(s):  
High Probability ◽  
Budget Allocation ◽  
Ordinal Optimization ◽  
Second Stage ◽  
Optimal Subset ◽  
Alternative Systems ◽  
Optimal Computing Budget Allocation ◽  
Selected Subset ◽  
Two Stages ◽  
Simulation Time

In this paper, we consider the problem of selecting the top [Formula: see text] systems when the number of alternative systems is very large. We propose a sequential procedure that consists of two stages to solve this problem. The procedure is a combination of the ordinal optimization (OO) technique and optimal computing budget allocation (OCBA) method. In the first stage, the OO is used to select a subset that overlaps with the set of actual best [Formula: see text] systems with high probability. Then in the second stage the optimal computing budget is used to select the top [Formula: see text] systems from the selected subset. The proposed procedure is tested on two numerical examples. The numerical tests show that the proposed procedure is able to select a subset of best systems with high probability and short simulation time.

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