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An uncertain structural optimization method based on nonlinear interval number programming and interval analysis method

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ENGINEERING STRUCTURES 2007年第11期29卷 3168-3177页

作者： Jiang, C. Han, X. Guan, F. J. Li, Y. H. Hunan Univ Coll Mech & Automot Engn State Key Lab Adv Design & Manufacture Vehicle Bo Changsha 410082 Peoples R China

An optimization method is proposed to solve uncertain structural problems based on a nonlinear interval number programming method and an interval analysis method. A nonlinear interval number programming method is suggested to transform the uncertain optimization problem to a deterministic multi-objective optimization problem based on an order relation of interval. For each specific design vector, an interval analysis method is applied to calculate the interval of the objective function caused by uncertainty, and whereby the optimization nesting problem can be solved. A non-constraint and single-objective optimization problem is then formulated through the linear combination method of multi-objective optimization and the penalty function method. An intergeneration projection genetic algorithm is employed to seek for Pareto optimum of the uncertain problem. The presented method is applied to a benchmark test of ten-bar truss and a practical automobile frame, and the optimization results demonstrate its efficiency. (c) 2007 Published by Elsevier Ltd.

关键词： uncertainty nonlinear interval number programming interval analysis method genetic algorithm structural optimization

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A multi-objective optimization method for uncertain structures based on nonlinear interval number programming method

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MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES 2017年第1期45卷 25-42页

作者： Liu, Xin Zhang, Zhiyong Yin, Lairong Changsha Univ Sci & Technol Educ Dept Hunan Prov Key Lab Lightweight & Reliabil Technol Engn Vehic Wang Jia Li South Rd 960 Changsha 410004 Hunan Peoples R China Xi An Jiao Tong Univ State Key Lab Strength & Vibrat Mech Struct Xian Shanxi Peoples R China

A multi-objective optimization method for uncertain structures is developed based on nonlinear interval number programming (NINP) method. The NINP method is employed to transform each uncertain objective function into a deterministic single-objective optimization problem. Using the constraint penalty function method, a deterministic multi-objective and non-constraint optimization problem is formulated in terms of penalty functions. Then the micro multi-objective genetic algorithm and the intergeneration projection genetic algorithm are adopted as outer layer and inner optimization operator to solve the nesting optimization problem, respectively. Finally, four numerical examples are provided to demonstrate the effectiveness of the present method.

关键词： Multi-objective optimization nonlinear interval number programming Pareto optimal set uncertainty structures

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An interval uncertain optimization method using back-propagation neural network differentiation

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2020年 366卷 113065-113065页

作者： Wang, Liqun Chen, Zengtao Yang, Guolai Sun, Qinqin Ge, Jianli Nanjing Univ Sci & Technol Sch Mech Engn Nanjing 210094 Peoples R China Univ Alberta Dept Mech Engn Edmonton AB T6G 1H9 Canada

An interval uncertain optimization method is proposed for engineering uncertain optimization problems. The first-order derivative information may be unavailable in practical engineering systems. To overcome this drawback, the method to calculate the first-order partial derivatives with a back-propagation neural network is investigated, and a numerical example is presented to demonstrate its fine precision. In the optimization process, the back-propagation neural network and its first-order derivatives are introduced into the interval perturbation method and combined with the subinterval method, the extrema of the uncertain objective function and uncertain constraints can be approximated without much computational cost. Thus the most challenging problem in current interval optimization, namely low optimization efficiency caused by nested optimization can be solved to a certain extent. A two-bar structure system is adopted to validate its fine precision and high computational efficiency in interval bounds estimation. Based on the interval order relation and interval possibility degree model, an interval uncertain optimization model can be transformed into a deterministic optimization model, and be solved by some auxiliary optimization algorithm. A numerical example and an engineering application have indicated that this method is efficient for uncertain optimization problems. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Uncertain optimization nonlinear interval number programming Back-propagation neural network interval analysis Engineering optimization

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A Conditional Value at Risk-Based Model for Planning Agricultural Water and Return Flow Allocation in River Systems

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WATER RESOURCES MANAGEMENT 2016年第1期30卷 427-443页

作者： Soltani, Maryam Kerachian, Reza Nikoo, Mohammad Reza Noory, Hamideh Univ Tehran Sch Civil Engn Coll Engn Tehran Iran Univ Tehran Sch Civil Engn Coll Engn Tehran Iran Univ Tehran Ctr Excellence Engn & Management Civil Infrastruc Coll Engn Tehran Iran Shiraz Univ Sch Civil & Environm Engn Shiraz Iran Univ Tehran Dept Irrigat & Reclamat Engn Karaj Iran

In this study, a new methodology is presented for simultaneous agricultural water and return flow (waste load) allocation in rivers. In this methodology, an objective function based on Conditional Value at Risk (CVaR) and a nonlinear interval number programming (NINP) technique are utilized. The CVaR can handle uncertainties in the form of probability distributions, while NINP incorporates uncertain inputs which are only available as intervals. This CVaR-NINP framework is used for agricultural water and return flow allocation planning under uncertainty. In this paper, to reduce the amount of saline return flow discharged into the river, a part of return flow of each agricultural network is diverted to an evaporation pond. Some meta-models based on Artificial Neural Network (ANN) are trained and validated using the results of Soil, Water, Atmosphere and Plant (SWAP) simulation model to reliably approximate the quantity and Total Dissolved Solids (TDS) load of agricultural return flows in a critical 7-day period. The effectiveness of the proposed methodology is examined through applying it to a part of Karkheh River catchment in the southwestern part of Iran. The results confirm the applicability of the model in incorporating the main uncertainties and generating water and waste load allocation policies in the form of interval numbers.

关键词： Water and waste load allocation Uncertainty Conditional value at risk nonlinear interval number programming The Karkheh river SWAP

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A game theoretical low impact development optimization model for urban storm water management

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JOURNAL OF CLEANER PRODUCTION 2019年 241卷 118323-000页

作者： Latifi, Morvarid Rakhshandehroo, Gholamreza Nikoo, Mohammad Reza Sadegh, Mojtaba Shiraz Univ Dept Civil & Environm Engn Shiraz Iran Boise State Univ Dept Civil Engn Boise ID 83725 USA

This study presents a novel framework to optimize Low Impact Development (LID) practices for urban storm water management. First, the Storm Water Management Model (SWMM) model was executed for different possible scenarios of input parameters and various LIDs to simulate runoff volume, Biochemical Oxygen Demand (BOD) and Total Suspended Solids (TSS) loads. Next, a neural network (MLP-ANN) was trained and validated, as a surrogate model, against the set of inputs and output variables from the SWMM model simulations. The inherent uncertainties in the rainfall-runoff modeling were accounted for using a nonlinear interval number programming (NINP) model, and stakeholders' interactions are considered using a leader-follower game model. Velenjak urban watershed in Tehran, Iran, with four key stakeholders was considered as the study area. Tehran Municipality is the financial service provider that makes the first decision the leader-follower structure, and is considered as the leader with the priority of minimizing LIDs' construction and maintenance costs. Tehran Department of Environmental Protection, Tehran Regional Water company, and Tehran Province Water and Wastewater company are the main followers in the decision making structure in the study area. This game theoretical framework yields several Pareto optimal solutions given the conflicting utilities of various players, and a Multi Criteria Decision Making procedure - i.e. PROMETHEE model - selects the most preferred compromised option. Fourteen weighting scenarios were considered in the PROMETHEE model to determine the compromise solution among the 52 solutions on the trade-off curve. The novelty of this study lies in using a nonlinear interval conflict resolution multi-objective optimization model for urban storm water management based on a leader-follower game. The proposed methodology warrants BOD and TSS loads, as well as storm water volume, are all reduced, with the highest reductions of 93, 86 and 90 percent, re

关键词： Urban storm water management Leader-follower game nonlinear interval number programming Low impact development Multi-objective optimization model

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Handling uncertainty in optimal design of reservoir water quality monitoring systems

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ENVIRONMENTAL POLLUTION 2020年第Part2期266卷 115211-115211页

作者： Pourshahabi, Shokoufeh Rakhshandehroo, Gholamreza Talebbeydokhti, Nasser Nikoo, Mohammad Reza Masoumi, Fariborz Shiraz Univ Dept Civil & Environm Engn Shiraz Iran Shiraz Univ Environm Res & Sustainable Dev Ctr Shiraz Iran Univ Mohaghegh Ardabili Dept Civil Engn Ardebil Iran

In the present paper, a scenario-based many-objective optimization model is developed for the spatio-temporal optimal design of reservoir water quality monitoring systems considering uncertainties. The proposed methodology is based on the concept of nonlinear interval number programming and information theory, while handling uncertainties of temperature, reservoir inflow, and inflow constituent concentration. A reference-point-based non-dominated sorting genetic algorithm (NSGA-III) is used to deal with the many-objective optimization problem. The proposed model is developed for the Karkheh reservoir system in Iran as a real-world problem. The results show excellent performance of the optimized water quality sampling locations instead of all potential ones in providing adequate information about the reservoir water quality status. The presented uncertainty-based model leads to a 55.73% reduction in the radius of the uncertain interval caused by different scenarios. Handling uncertainties in a spatio-temporal many-objective optimization problem is the main contribution of this study, yielding a reliable and robust design of a reservoir monitoring system that is less sensitive to various scenarios. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Reservoir monitoring system Uncertainty Many-objective optimization model Information theory nonlinear interval number programming

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An efficient nonlinear interval uncertain optimization method using Legendre polynomial chaos expansion

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APPLIED SOFT COMPUTING 2021年 108卷 107454-107454页

作者： Wang, Liqun Yang, Guolai Li, Zixuan Xu, Fengjie Nanjing Univ Sci & Technol Sch Mech Engn Nanjing 210094 Peoples R China Shandong Univ Technol Sch Mech Engn Zibo 255000 Peoples R China

Many specialized numerical techniques have been developed on interval uncertainty optimization. However, the conventional nested optimization strategy is time-consuming. The improved Taylor-based interval optimization avoids the laborious inner optimization, nonetheless, it is intrusive and presents significant computational challenges in the large-level uncertain optimization problems. To end these, this paper proposes a Legendre polynomial expansion method combined with the subinterval technique to evaluate the range enclosure of an interval function, where the expansion coefficients are computed through the collocation method. The detailed comparisons demonstrate that such Legendre-based polynomial expansion provides much more confidence in interval bounds evaluation than the Taylor expansion, and is capable of maintaining very sharp solution enclosures even when the uncertainty level is increased. More exciting, it is highly efficient. Subsequent application of the Legendre polynomial expansion in the interval bound estimation of the uncertain objective function and constraints, and combining an appropriate outer optimizer, result in a novel nonlinear interval uncertain optimization method for complicated engineering systems, whereby the time-consuming optimization nesting is avoided. A beam design example and an electromagnetic buffer optimization example illustrate that the proposed interval optimization method has fine computational precision and high computational efficiency, especially is capable of attacking the increase of uncertainty level. Moreover, the new method does not require the derivative information of the uncertain objective and constraints, such that applies to any engineering uncertain optimization problems, including the complex engineering problems which are usually referred to as "black-box''. (C) 2021 Elsevier B.V. All rights reserved.

关键词： nonlinear interval number programming Uncertainty propagation Polynomial chaos expansion Meta model Electromagnetic buffer

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Optimization of double-layer perforated breakwater based on risk assessment of uncertainties

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OCEAN ENGINEERING 2022年 265卷

作者： Vahidi, Mehdi Pirooz, Moharram Dolatshahi Nikoo, Mohammad Reza Varjavand, Iman Amanat, Shahab Etri, Talal Gandomi, Mostafa Univ Tehran Coll Engn Sch Civil Engn Tehran Iran Sultan Qaboos Univ Coll Engn Dept Civil & Architectural Engn Muscat Oman Sultan Qaboos Univ Dept Civil & Architectural Engn Muscat Oman

In this work, the optimal dimensions of a double-layer perforated breakwater were determined by considering the risk of uncertainties in marine conditions, including wave height and wavelength. To do so, the CVaR-NINP technique combines Conditional Value-at-Risk (CVaR) and nonlinear interval number programming (NINP), which are useful in dealing with discrete interval uncertainties and probabilistic. Based on experimental data, two Extreme Learning Machine (ELM) models were developed to simulate the hydraulic behavior of the breakwater. To increase accuracy and performance, the parameters of these two models were optimized using single and multi-objective optimization algorithms. The obtained results indicate that the non-dominated sorting genetic algorithm (NSGA-II) exhibited better performance in optimizing ELM. Subsequently, optimized ELM, which better modeled the hydraulic performance of perforated breakwater, was selected to link to the NSGA-III algorithm to determine the trade-off between the defined objective functions based on the CVaR-NINP technique, namely, minimize CVaR of (Ct), minimize the radius of the interval number of (Ct), minimize CVaR of (Cr), minimize the radius of the interval number of (Cr). Pareto optimal solutions, obtained from NSGA-III, using the multi-attribute decision-making (MADM) method, also called the R-method, were ranked and applied to select the best solutions.

关键词： Perforated breakwater Extreme learning machine NSGA-III Multi -objective optimization Conditional value at risk nonlinear interval number programming

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