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ordinal optimization APPROACH TO RARE EVENT PROBABILITY PROBLEMS

DISCRETE EVENT DYNAMIC SYSTEMS-THEORY AND APPLICATIONS 1995年第2-3期5卷 281-301页

作者： HO, YC LARSON, ME Division of Applied Sciences Harvard University Cambridge

In this paper we introduce a new approach to rare event simulation. Because of the extensive simulation required for precise estimation of performance criterion dependent on rare event occurrences, obstacles such as computing budget/time constraints and pseudo-random number generator limitations can become prohibitive, particularly if comparative study of different system designs is involved. Existing methods for rare events simulation have focused on simulation budget reduction while attempting to generate accurate performance estimates. In this paper we propose a new approach for rare events system analysis in which we relax the simulation god to the isolation of a set of ''good enough'' designs with high probability Given this relaxation, referred to as ordinal optimization and advanced by Ho et al. (1992), this paper's approach calls instead for the consideration of an appropriate surrogate design problem. This surrogate problem is characterized by its approximate ordinal equivalence to the original problem and its performance criterion's dependence not on rare event occurrences, but on more frequent events. Evaluation of such a surrogate problem under the relaxed goals of ordinal optimization has experimentally resulted in orders of magnitude reduction in simulation burden.

关键词： DISCRETE EVENT DYNAMIC SYSTEM ordinal optimization RARE EVENT PROBABILITY PROBLEM SURROGATE PROBLEM

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ordinal optimization based approach to the optimal resource allocation of grid computing system

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MATHEMATICAL AND COMPUTER MODELLING 2011年第1-2期54卷 519-530页

作者： Horng, Shih-Cheng Chaoyang Univ Technol Dept Comp Sci & Informat Engn Taichung 41349 Taiwan

In this paper, we have formulated the resource allocation optimization problem for expanding service and increasing reliability of a grid computing system. The formulated problem is a combinational optimization as well as an NP-hard problem. We firstly decompose this problem into a minimizing budget problem and a maximizing reliability problem. An approximate model is proposed to estimate the service reliability of a resource allocation design within a tolerable computation time. Secondly, we employ an ordinal optimization (OO) based approach to solve the maximizing reliability problem and a bisection method to solve the minimizing budget problem. The proposed OO based approach consists of two stages. A binary particle swarm optimization (BPSO) algorithm is employed in the first stage using the approximate model for fitness evaluation and selects a subset of good enough solutions. Then we proceed with the goal softening searching procedure in the second stage using more refined approximate models to search for a good enough solution from the subset obtained in the first stage. We have demonstrated the test results by the simulation on a 16-node and 25-link large grid computing system including two resource-managing nodes. We used 8 bisection iterations that consumed 20 minutes to obtain a good enough resource allocation design and the corresponding minimum budget. To test the optimality of the solutions obtained by our approach, we also solved the maximizing reliability problem using two competing methods, the GA and classical BPSO algorithm. The good enough solution obtained by the proposed approach is promising in the aspects of solution quality and computational efficiency. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Binary particle swarm optimization ordinal optimization Bisection method Grid computing system Service reliability Resource allocation

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ordinal optimization with subset selection rule

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JOURNAL OF optimization THEORY AND APPLICATIONS 2002年第3期113卷 597-620页

作者： Yang, MS Lee, LH Akamai Technol Inc Cambridge MA 02139 USA Natl Univ Singapore Dept Ind & Syst Engn Singapore 117548 Singapore

ordinal optimization (OO) has enjoyed a great degree of success in addressing stochastic optimization problems characterized by an independent and identically distributed (i.i.d.) noise. The methodology offers a statistically quantifiable avenue to find good enough solutions by means of soft computation. In this paper, we extend the OO methodology to a more general class of stochastic problems by relaxing the i.i.d. assumption on the underlying noise. Theoretical results and their applications to simple examples are presented.

关键词： ordinal optimization goal softening

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ordinal optimization and Quantification of Heuristic Designs

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DISCRETE EVENT DYNAMIC SYSTEMS-THEORY AND APPLICATIONS 2009年第3期19卷 317-345页

作者： Shen, Zhen Ho, Yu-Chi Zhao, Qian-Chuan Tsinghua Univ TNLIST Dept Automat Ctr Intelligent & Networked Syst CFINS Beijing 100084 Peoples R China Boston Univ Dept Mfg Engn Brookline MA 02446 USA Boston Univ Ctr Informat & Syst Engn Brookline MA 02446 USA Harvard Univ Sch Engn & Appl Sci Cambridge MA 02138 USA

This paper focuses on the performance evaluation of complex man-made systems, such as assembly lines, electric power grid, traffic systems, and various paper processing bureaucracies, etc. For such problems, applying the traditional optimization tool of mathematical programming and gradient descent procedures of continuous variables optimization are often inappropriate or infeasible, as the design variables are usually discrete and the accurate evaluation of the system performance via a simulation model can take too much calculation. General search type and heuristic methods are the only two methods to tackle the problems. However, the "goodness" of heuristic methods is generally difficult to quantify while search methods often involve extensive evaluation of systems at many design choices in a large search space using a simulation model resulting in an infeasible computation burden. The purpose of this paper is to address these difficulties simultaneously by extending the recently developed methodology of ordinal optimization (OO). Uniform samples are taken out from the whole search space and evaluated with a crude but computationally easy model when applying OO. And, we argue, after ordering via the crude performance estimates, that the lined-up uniform samples can be seen as an approximate ruler. By comparing the heuristic design with such a ruler, we can quantify the heuristic design, just as we measure the length of an object with a ruler. In a previous paper we showed how to quantify a heuristic design for a special case but we did not have the OO ruler idea at that time. In this paper we propose the OO ruler idea and extend the quantifying method to the general case and the multiple independent results case. Experimental results of applying the ruler are also given to illustrate the utility of this approach.

关键词： ordinal optimization Order statistics Discrete event dynamic systems Hypothesis testing

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ordinal optimization based metaheuristic algorithm for optimal inventory policy of assemble-to-order systems

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APPLIED MATHEMATICAL MODELLING 2017年 42卷 43-57页

作者： Horng, Shih-Cheng Lin, Shieh-Shing Chaoyang Univ Technol Dept Comp Sci & Informat Engn 168 Jifong E Rd Taichung 41349 Taiwan

Assemble-to-order (ATO) systems refer to a manufacturing process in which a customer must first place an order before the ordered item is manufactured. An ATO system that operates under a continuous-review base-stock policy can be formulated as a stochastic simulation optimization problem (SSOP) with a huge search space, which is known as NP hard. This work develops an ordinal optimization (OO) based metaheuristic algorithm, abbreviated to OOMH, to determine a near-optimal design (target inventory level) in ATO systems. The proposed approach covers three main modules, which are meta-modeling, exploration, and exploitation. In the meta-modeling module, the extreme learning machine (ELM) is used as a meta-model to estimate the approximate objective value of a design. In the exploration module, the elite teaching-learning-based optimization (TLBO) approach is utilized to select N candidate designs from the entire search space, where the fitness of a design is evaluated using the ELM. In the exploitation module, the sequential ranking and -selection (R&S) scheme is used to optimally allocate the computing resource and budget for effective selecting the critical designs from the N candidate designs. Finally, the proposed algorithm is applied to two general ATO systems. The large ATO system comprises 12 items on eight products and the moderately sized ATO system is composed of eight items on five products. Test results that are obtained using the OOMH approach are compared with those obtained using three heuristic methods and a discrete optimization via -simulation (DOvS) algorithm. Analytical results reveal that the proposed method yields solutions of much higher quality with a much higher computational efficiency than the three heuristic methods and the DOvS algorithm. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Assemble-to-order system Continuous-review base-stock policy ordinal optimization Extreme learning machine Teaching-learning-based optimization Ranking and selection

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ordinal optimization-Based Performance Model Estimation Method for HDFS

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IEEE ACCESS 2020年 8卷 889-899页

作者： Ma, Tian Tian, Feng Dong, Bo Xi An Jiao Tong Univ Dept Automat Sci & Technol Xian 710049 Peoples R China Xi An Jiao Tong Univ Natl Engn Lab Big Data Analyt Xian 710049 Peoples R China Xi An Jiao Tong Univ Sch Continuing Educ Xian 710049 Peoples R China

Modeling and analyzing the performance of distributed file systems (DFSs) benefit the reliability and quality of data processing in data-intensive applications. Hadoop Distributed File System (HDFS) is a typical representative of DFSs. Its internal heterogeneity and complexity as well as external disturbance contribute to HDFS's built-in features of nonlinearity as well as randomness in system level, which raises a great challenge in modeling these features. Particularly, the randomness results in the uncertainty of HDFS performance model. Due to the complex mathematical structure and parameters hardly estimated of analytical models, it is highly complicated and computationally impossible to build an explicit and precise analytical model of the randomness. The measurement-based methodology is a promising way to model HDFS performance in terms of randomness since it requires no knowledge of system's internal behaviors. In this paper, the estimation of HDFS performance models on account of the randomness is transformed to an optimization problem of finding out the real best design of performance model structure with large design space. Core ideas of ordinal optimization (OO) are introduced to solve this problem with a limited computing budget. Piecewise linear (PL) model is applied to approximate the nonlinear characteristics and randomness of HDFS performance. The experimental results show that the proposed method is effective and practical to estimate the optimal design of the PL-based performance model structure for HDFS. It not only provides a globally consistent evaluation of the design space but also guarantees the goodness of the solution with high probability. Moreover, it improves the accuracy of system model-based HDFS performance models.

关键词： Distributed file system HDFS performance modeling randomness ordinal optimization

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ordinal optimization Based Security Dispatching in Deregulated Power Systems

Ordinal Optimization Based Security Dispatching in Deregulat...

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Joint 48th IEEE Conference on Decision and Control (CDC) / 28th Chinese Control Conference (CCC)

作者： Jia, Qing-Shan Xie, Min Wu, Felix F. Tsinghua Univ Dept Automat Ctr Intelligent & Networked Syst CFINS Beijing 100084 Peoples R China South China Univ Technol Elect Power Coll Guangzhou Guangdong 510641 Peoples R China Univ Hong Kong Elect & Elect Engn Dept Hong Kong Hong Kong Peoples R China

ISBN: (纸本)9781424438723

Due to the uncertainty in the forecasting of load patterns, security dispatching finds the generation pattern, which is the most economic and passes all N - 1 contingency tests with respect to (w.r.t.) all possible load patterns. The Monte Carlo simulation based method is computationally infeasible for practical scale power systems. In practice, usually only the most possible load pattern is considered in the security dispatching. In this study, we first show that this leads to the highly optimized tolerant property of power systems, and sometimes cascading failure. Then we develop an ordinal optimization based method to address this issue. This new method finds an economic generation pattern with quantifiable secure probability w.r.t. all possible load patterns. This method is demonstrated on a modified IEEE 30-bus standard power system. We hope this study sheds some insight on the understanding of power system collapse, especially the cascading failure.

关键词： Security dispatching highly optimized tolerant ordinal optimization

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ordinal optimization-Based Multi-energy System Scheduling for Building Energy Saving

Ordinal Optimization-Based Multi-energy System Scheduling fo...

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7th International Conference on Intelligent Computing (ICIC)

作者： Su, Zhong-Hua Jia, Qing-Shan Song, Chen Tsinghua Univ Ctr Intelligent & Networked Syst Dept Automat Beijing 100084 Peoples R China

ISBN: (纸本)9783642259432

Buildings contribute a significant part in the energy consumption and CO2 emission in many countries. Building energy saving has thus become a hot research topic recently. The technology advances in power co-generation, on-site generation, and storage devices bring us the opportunity to reduce the cost and CO2 emission while meeting the demand in buildings. A fundamental difficulty to schedule this multi-energy system. besides other difficulties, is the discrete and large search space. In this paper, the multi-energy scheduling problem is modeled as a nonlinear programming problem with integer variables. A method is developed to solve this problem in two steps, which uses ordinal optimization to address the discrete and large search space and uses linear programming to solve the remaining sub-problems. The performance of this method is theoretically quantified, and compared with enumeration and a priority-and-rule-based scheduling policy. Numerical results show that our method provides a good tradeoff between the solution quality and the computational time comparing with the other two methods. We hope this work brings more insight on multi-energy scheduling problem in general.

关键词： Multi-energy system ordinal optimization linear programming building energy saving renewable energy

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ordinal optimization for Optimal Capacitor Placement and Network Reconfiguration in Radial Distribution Networks

Ordinal Optimization for Optimal Capacitor Placement and Net...

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IEEE International Conference on Systems, Man, and Cybernetics (SMC)

作者： El Ramli, R. Awad, M. Jabr, R. A. Amer Univ Beirut Dept Elect & Comp Engn Beirut Lebanon

ISBN: (纸本)9781467317146

Capacitor Placement (CP) is a complex non linear mixed integer optimization problem that includes both integer variables that correspond to the locations at which capacitors should be placed and discrete variables that represent the number of capacitor banks that should be installed. Motivated to efficiently reduce power losses in distribution networks by CP and network reconfiguration (NR) using some of the intelligent soft computing approaches, we propose to use in this study ordinal optimization (OO) which relies on order comparison and goal softening to make the computation more efficient. We tested OO on 33 and 69 bus systems and compared experimental results with other recently published methods. The reduction in losses obtained using OO for CP and NR motivates further studies.

关键词： ordinal optimization capacitor placement distribution networks soft computing

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ordinal optimization for power systems

Ordinal optimization for power systems

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IEEE/PES Power Systems Conference and Exposition

作者： Zhong, J. Xie, M. Wu, F. F. Univ Hong Kong Dept Elect & Elect Engn Pokfulam Rd Hong Kong Hong Kong Peoples R China South China Univ Technol Sch Ele Power Guangzhou Guangdong Peoples R China

ISBN: (纸本)9781424401772

The inherent complexity of large scale power system makes the optimization problems very complicated for power system planning and operation. ordinal optimization theory is developed to efficiently find good enough solutions with high probability for simulation-based optimization problems. Vector ordinal optimization theory is particularly useful in finding a good enough solution subset for multi-objective optimization problems. In this paper, we illustrate the principles of the ordinal optimization theory and the Vector ordinal optimization theory, and also discuss the potential applications of the theories in power system optimization problems.

关键词： power system optimization ordinal optimization vector ordinal optimization complex system

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