Sequential approximate robust design optimization using radial basis function network

This paper proposes a sequential approximate robust design optimization (SARDO) with the radial basis function (RBF) network. In RDO, the mean and the standard deviation of objective should be minimized simultaneously. Therefore, the RDO is generally formulated as bi-objective design optimization. Our goal is to find a robust optimal solution with a small number of function evaluations, not identifying a set of Pareto-optimal solution using Multi-Objective Evolutionary Algorithms. The weighted sum is often used to find a robust optimal solution. In contrast, the weighted lp norm method is used in this paper. Through illustrative examples, some validations of the weighted lp norm method to the RDO are clarified. Next, SARDO with the RBF network is discussed. In general, the standard deviation of functions is obtained by using the finite difference method. Thus, in order to obtain the standard deviation of functions, the finite difference method is directly applied to the response surface. High accuracy of the finite difference method will leads to highly accurate robust optimal solution. In order to avoid the inaccurate numerical calculation, the standard deviation is expressed by only the Gaussian kernel. As the result, it is expected that a highly accurate robust optimal solution can be found with a small number of function evaluations. Through numerical examples, the validity of the proposed approach is examined. Finally, the variable blank holder force trajectory for reducing springback is examined.     

Reliability-based robust multi-objective optimization applied to engineering system design

ABSTRACT

Probabilistic and non-probabilistic methods have been proposed to deal with design problems under uncertainties. Reliability-based design and robust design are probabilistic strategies traditionally used for this purpose. In the present contribution, reliability-based robust design optimization (RBRDO) is formulated as a multi-objective problem considering the interaction of both approaches. The proposed methodology is based on the differential evolution algorithm associated with two strategies to deal with reliability and robustness, respectively, namely inverse reliability analysis and the effective mean concept. This multi-objective optimization problem considers the maximization of reliability and robustness coefficients as additional objective functions. The effectiveness of the methodology is illustrated by two classical test cases and a rotor-dynamics application. The results demonstrate that the proposed methodology is an alternative method to solve RBRDO problems.     

基于多目标优化策略的扭杆可靠性稳健优化设计

为提高机械零部件的安全性和稳健性,应用可靠性稳健优化设计理论和多目标决策方法,建立了适合结构可靠性稳健优化设计的多目标优化模型.为能迅速准确地对具有约束条件的多目标优化模型进行求解,提出一种利用模糊理论对约束条件进行处理的方法,然后应用灰色粒子群算法对多目标优化模型进行求解.通过对正态分布参数和任意分布参数的扭杆可靠性稳健优化设计,表明该方法行之有效.     

VIS: An artificial immune network for multi-objective optimization

The aim of this work is to propose and validate a novel multi-objective optimization algorithm based on the emulation of the behaviour of the immune system. The rationale of this work is that the artificial immune system has, in its elementary structure, the main features required by other multi-objective evolutionary algorithms described in the literature, such as diversity preservation, memory, adaptivity, and elitism. The proposed approach is compared with three multi-objective evolutionary algorithms that are representative of the state of the art in multi-objective optimization. Algorithms are tested on six standard problems (both unconstrained and constrained) and comparisons are carried out using three different metrics. Results show that the proposed approach has very good performances and can become a valid alternative to standard algorithms for solving multi-objective optimization problems.     

Parameter identification of autonomous vehicles using multi-objective optimization

In order to properly operate an autonomous vehicle navigation system, it is important that the vehicle and sensor models of the vehicle are defined by an accurate parameter set. This paper presents a technique for identifying parameters of an autonomous vehicle using multi-objective optimization, which enables the identification process without introducing additional parameters. A multi-objective optimization method has been further proposed to solve the optimization problem defined for the identification efficiently and promisingly. Results of numerical examples first show that the proposed optimization method can work well for various multi-objective optimization problems. Then, the proposed identification technique has been applied to the actual parameter identification of the autonomous vehicle developed by the authors, and an appropriate parameter set has been obtained.     

Integrated multi-objective robust optimization and sensitivity analysis with irreducible and reducible interval uncertainty

Uncertainty considered in robust optimization is usually treated as irreducible since it is not reduced during an optimization procedure. In contrast, uncertainty considered in sensitivity analysis is treated as partially or fully reducible in order to quantify the effect of input uncertainty on the outputs of the system. Considering this, and the usual existence of both reducible and irreducible uncertainty, an approach that can perform robust optimization and sensitivity analysis simultaneously is of much interest. This article presents such an integrated optimization model that can be used for both robust optimization and sensitivity analysis for problems that have irreducible and reducible interval uncertainty, multiple objective functions and mixed continuous-discrete design variables. The proposed model is demonstrated by two engineering examples with differing complexity to demonstrate its applicability.     

Studying unbalanced workload and buffer allocation of production systems using multi-objective optimisation

Numerous studies have investigated the effects of unbalanced service times and inter-station buffer sizes on the efficiency of discrete part, unpaced production lines. There are two main disadvantages of many of these studies: (1) only some predetermined degree of imbalance and patterns of imbalance have been evaluated against the perfectly balanced configuration, making it hard to form a general conclusion on these factors; (2) only a single objective has been set as the target, which neglects the fact that different patterns of imbalance may outperform with respect to different performance measures. Therefore, the aim of this study is to introduce a new approach to investigate the performance of unpaced production lines by using multiple-objective optimisation. It has been found by equipping multi-objective optimisation with an efficient, equality constraints handling technique, both the optimal pattern and degree of imbalance, as well as the optimal relationship among these factors and the performance measures of a production system can be sought and analysed with some single optimisation runs. The results have illustrated that some very interesting relationships among the key performance measures studied, including system throughput, work-in-process and average buffer level, could only be observed within a truly multi-objective optimisation context. While these results may not be generalised to apply to any production lines, the genericity of the proposed simulation-based approach is believed to be applicable to study any real-world, complex production lines.     

Modeling and multi-objective optimization of an M-cycle cross-flow indirect evaporative cooler using the GMDH type neural network

A model was presented to determine product air properties of dew-point indirect evaporative coolers with cross flow heat exchanger, M-cycle CrFIEC. In this regard, the most powerful statistical method known as the group method of data handling-type neural network (GMDH) was employed. Then the developed GMDH model was implemented for multi-objective optimization of a prototype CrFIEC and the average annual values of coefficient of performance (COP) and cooling capacity (CC) were maximized, simultaneously, while working to air ratio (WAR) and inlet air velocity were decision variables of optimization. Accordingly, features of the proposed system were optimized at twelve diverse climates of the world based on Koppen–Geiger's classification. Results implied that the optimized inlet air velocity for all climates varied between 1.796 and 1.957 m.s⁻¹, while the optimum WAR was 0.318 for “A” class cities. Moreover, the mean values of the COP and CC were improved 8.1% and 6.9%, respectively.     

Constrained multi-objective optimization using constrained non-dominated sorting combined with an improved hybrid multi-objective evolutionary algorithm

Constrained multi-objective optimization problems (cMOPs) are complex because the optimizer should balance not only between exploration and exploitation, but also between feasibility and optimality. This article suggests a parameter-free constraint handling approach called constrained non-dominated sorting (CNS). In CNS, each solution in a population is assigned a constrained non-dominated rank based on its constraint violation degree and Pareto rank. An improved hybrid multi-objective optimization algorithm called cMOEA/H for solving cMOPs is proposed. Additionally, a dynamic resource allocation mechanism is adopted by cMOEA/H to spare more computational efforts for those relatively hard sub-problems. cMOEA/H is first compared with the baseline algorithm using an existing constraint handling mechanism, verifying the advantages of the proposed constraint handling mechanism. Then cMOEA/H is compared with some classic constrained multi-objective optimizers, experimental results indicating that cMOEA/H could be a competitive alternative for solving cMOPs. Finally, the characteristics of cMOEA/H are studied.     

Blast furnace charging optimization using multi-objective evolutionary and genetic algorithms

Charging programs giving rise to desired burden and gas distributions in the ironmaking blast furnace were detected through an evolutionary multi-objective optimization strategy. The Pareto optimality condition traditionally used in such studies was substituted by a recently developed k-optimality criterion that allowed for simultaneous optimization of a large number of objectives, leading to a significant improvement over the results of earlier studies. A large number of optimum charging strategies were identified through this procedure and thoroughly analyzed, in view of an efficient blast furnace operation.     

Identification of Constitutive Parameters using Hybrid ANN multi-objective optimization procedure

This paper deals with the identification of material parameters for an elastoplastic behaviour model with isotropic hardening using several experimental tests at the same time. But, these tests are generally inhomogeneous and finite element simulations are necessary for their analysis. Therefore an inverse analysis is carried out and the identification problem is converted into a multi-objective optimization where prohibitive computing time is required. We propose in this work a hybrid approach where Artificial Neural Networks (ANN) are trained by finite element results. Then, the multi objective procedure calls the ANN function in place of the finite element code. The proposed approach is exemplified on the identification of non-associative Hill’48 criterion and Voce parameters model of the Stainless Steel AISI 304.     

Gender approaches to evolutionary multi-objective optimization using pre-selection of criteria

A novel idea to perform evolutionary computations (ECs) for solving highly dimensional multi-objective optimization (MOO) problems is proposed. Following the general idea of evolution, it is proposed that information about gender is used to distinguish between various groups of objectives and identify the (aggregate) nature of optimality of individuals (solutions). This identification is drawn out of the fitness of individuals and applied during parental crossover in the processes of evolutionary multi-objective optimization (EMOO). The article introduces the principles of the genetic-gender approach (GGA) and virtual gender approach (VGA), which are not just evolutionary techniques, but constitute a completely new rule (philosophy) for use in solving MOO tasks. The proposed approaches are validated against principal representatives of the EMOO algorithms of the state of the art in solving benchmark problems in the light of recognized EC performance criteria. The research shows the superiority of the gender approach in terms of effectiveness, reliability, transparency, intelligibility and MOO problem simplification, resulting in the great usefulness and practicability of GGA and VGA. Moreover, an important feature of GGA and VGA is that they alleviate the ‘curse’ of dimensionality typical of many engineering designs.     

Critical chain project buffer sizing based on resource constraints

Project scheduling is a complex process involving many types of resources and activities that require optimisation. The resource-constrained project scheduling problem is one of the well-known problematic issues when project activities have to be scheduled to minimise the project duration. Consequently, several methods have been proposed for adjusting the buffer size but none of these traditional methods consider buffer sizing accuracy based on resource constraints. The purpose of this paper is to develop a buffer sizing method based on a fuzzy resource-constrained project scheduling problem in order to obtain an appropriate proportionality between the activity duration and the buffer size. Specifically, a comprehensive resource-constrained method that considers both the general average resource constraints (GARC) and the highest peak of resource constraints (HPRC) is proposed in order to obtain a new buffer sizing method. This paper contributes to the research by considering several different aspects. First, this paper adopts a fuzzy method to calculate and obtain the threshold amount. Second, this paper discusses the resource levelling problem and proposes the HPRC method. Third, the proposed method uses a fuzzy quantitative model to calculate the resource requirement. The findings indicate that the project achieved higher efficiency, providing effective protection and an appropriate buffer size.     

Mooring system design optimization using a surrogate assisted multi-objective genetic algorithm

This article presents a novel framework for the multi-objective optimization of offshore renewable energy mooring systems using a random forest based surrogate model coupled to a genetic algorithm. This framework is demonstrated for the optimization of the mooring system for a floating offshore wind turbine highlighting how this approach can aid in the strategic design decision making for real-world problems faced by the offshore renewable energy sector. This framework utilizes validated numerical models of the mooring system to train a surrogate model, which leads to a computationally efficient optimization routine, allowing the search space to be more thoroughly searched. Minimizing both the cost and cumulative fatigue damage of the mooring system, this framework presents a range of optimal solutions characterizing how design changes impact the trade-off between these two competing objectives.     

Function-transformation methods for multi-objective optimization

It is useful with multi-objective optimization (MOO) to transform the objective functions such that they all have similar units and orders of magnitude. This article evaluates various transformation methods using simple example problems. Viewing these methods as different means to restrict function values sheds light on how the methods perform. The weighted sum approach for MOO is used to study how well different methods aid in depicting the Pareto optimal set. Whereas using unrestricted weights is well suited for providing a single solution that reflects preferences, it is found that using a convex combination of functions is desirable when generating the Pareto set. In addition, it is shown that some transformation methods are detrimental to the process of generating a diverse spread of points, and criteria are proposed for determining when the methods fail to generate an accurate representation of the Pareto set. Advantages of using a simple normalization–modification are demonstrated.     

Gearbox design for uncertain load requirements using active robust optimization

Design and optimization of gear transmissions have been intensively studied, but surprisingly the robustness of the resulting optimal design to uncertain loads has never been considered. Active Robust (AR) optimization is a methodology to design products that attain robustness to uncertain or changing environmental conditions through adaptation. In this study the AR methodology is utilized to optimize the number of transmissions, as well as their gearing ratios, for an uncertain load demand. The problem is formulated as a bi-objective optimization problem where the objectives are to satisfy the load demand in the most energy efficient manner and to minimize production cost. The results show that this approach can find a set of robust designs, revealing a trade-off between energy efficiency and production cost. This can serve as a useful decision-making tool for the gearbox design process, as well as for other applications.     

Fatigue design of a cellular phone folder using regression model-based multi-objective optimization

In a folding cellular phone, the folding device is repeatedly opened and closed by the user, which eventually results in fatigue damage, particularly to the front of the folder. Hence, it is important to improve the safety and endurance of the folder while also reducing its weight. This article presents an optimal design for the folder front that maximizes its fatigue endurance while minimizing its thickness. Design data for analysis and optimization were obtained experimentally using a test jig. Multi-objective optimization was carried out using a nonlinear regression model. Three regression methods were employed: back-propagation neural networks, logistic regression and support vector machines. The AdaBoost ensemble technique was also used to improve the approximation. Two-objective Pareto-optimal solutions were identified using the non-dominated sorting genetic algorithm (NSGA-II). Finally, a numerically optimized solution was validated against experimental product data, in terms of both fatigue endurance and thickness index.     

Effective multi-objective optimization with the coral reefs optimization algorithm

In this article a new algorithm for multi-objective optimization is presented, the Multi-Objective Coral Reefs Optimization (MO-CRO) algorithm. The algorithm is based on the simulation of processes in coral reefs, such as corals' reproduction and fight for space in the reef. The adaptation to multi-objective problems is a process based on domination or non-domination during the process of fight for space in the reef. The final MO-CRO is an easily-implemented and fast algorithm, simple and robust, since it is able to keep diversity in the population of corals (solutions) in a natural way. The experimental evaluation of this new approach for multi-objective optimization problems is carried out on different multi-objective benchmark problems, where the MO-CRO has shown excellent performance in cases with limited computational resources, and in a real-world problem of wind speed prediction, where the MO-CRO algorithm is used to find the best set of features to predict the wind speed, taking into account two objective functions related to the performance of the prediction and the computation time of the regressor.     

Local Pareto approximation for multi-objective optimization

The design process of complex systems often resorts to solving an optimization problem, which involves different disciplines and where all design criteria have to be optimized simultaneously. Mathematically, this problem can be reduced to a vector optimization problem. The solution of this problem is not unique and is represented by a Pareto surface in the objective function space. Once a Pareto solution is obtained, it may be very useful for the decision-maker to be able to perform a quick local approximation in the vicinity of this Pareto solution for sensitivity analysis. In this article, new linear and quadratic local approximations of the Pareto surface are derived and compared to existing formulas. The case of non-differentiable Pareto points (solutions) in the objective space is also analysed. The concept of a local quick Pareto analyser based on local sensitivity analysis is proposed. This Pareto analysis provides a quantitative insight into the relation between variations of the different objective functions under constraints. A few examples are considered to illustrate the concept and its advantages.