Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> The optical performance of interference filters depends on systematic and statistical variations of the thicknesses and indices of refraction of the layers that occur during production and use. Assuming that their distributions are known, the expected performance can be optimized as a function of the nominal layer thicknesses with the help of strategies that mimic biological evolution. This results in filter designs that are easier to manufacture and more robust to use. The method is illustrated for color shifts that are rather sensitive to layer thickness variations. Its scope is entirely general, and it could be applied to other tolerancing problems that arise in optical design. <s> BIB001 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> A large fraction of studies on genetic algorithms (GAs) emphasize finding a globally optimal solution. Some other investigations have also been made for detecting multiple solutions. If a global optimal solution is very sensitive to noise or perturbations in the environment then there may be cases where it is not good to use this solution. In this paper, we propose a new scheme which extends the application of GAs to domains that require the discovery of robust solutions. Perturbations are given to the phenotypic features while evaluating the functional value of individuals, thereby reducing the chance of selecting sharp peaks (i.e., brittle solutions). A mathematical model for this scheme is also developed. Guidelines to determine the amount of perturbation to be added is given. We also suggest a scheme for detecting multiple robust solutions. The effectiveness of the scheme is demonstrated by solving different one- and two-dimensional functions having broad and sharp peaks. <s> BIB002 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> Traditional evolutionary computing techniques use an explicit fitness function – mathematical or simulated – to derive a solution to a problem from a population of individuals, over a number of generations. In this paper an approach which allows such techniques to be used on problems in which evaluations are costly, which cannot be expressed formally, or which are difficult to simulate, is examined. A neural network is trained using example individuals with the explicit fitness and the resulting model of the fitness function is then used by the evolutionary algorithm to find a solution. It is shown that the approach is effective over a small range of function types in comparison to the traditional approach when limited training data is available. An iterative step is then added whereby after a number of generations the current best individual in a population is evaluated directly on the explicit fitness function. The individual and its “real” fitness are then added to the training data and the neural network is re-trained to improve its approximation of the fitness function. It is shown that in this way the performance of the model-based architecture is greatly improved on more rugged/complex landscapes without a large increase in the amount of training data required. <s> BIB003 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> In the present paper, online optimiza­ tion of an engine controller by means of Genetic Algorithms (GA) is discussed. In optimization of real complex systems through experiments and computer simulation using randolll variables, op­ timization methods must cope with uncertainty of objective function and limitation of possible number of evaluation. Sano et a1. have pro­ posed a GA utilizing history of search (GA with Memory-based Fitness Evaluation: MFEGA)(l) so as to reduce number of fitness evaluation for such applications of GA. In the proposed method, value of fitness function at a novel search point is estimated not only by the sampled fitness value at that point but also by utilizing the fitness val­ ues of individuals stored in the history of search. In the present paper, this method is applied to online optimization of an engine controller for ve­ hicles. Computer experiments using an engine simulator show that the proposed method out­ performs conventional GAs both in convergence speed and accuracy of solution under fluctu ation of fitness evaluation. <s> BIB004 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> We study the combinatorial optimization task of choosing the smoothest map from a given family of maps, which is motivated from motor control unit calibration. The problem is of a particular interest because of its characteristics: it is NP-hard, it has a direct and important industrial application, it is easy-to-state and it shares some properties of the wellknown Ising spin glass model. Moreover, it is appropriate for the application of randomized algorithms: for local search heuristics because of its strong 2-dimensional local structure, and for Genetic Algorithms since there is a very natural and direct encoding which results in a variable alphabet. We present the problem from two points of view, an abstract view with a very simple definition of smoothness and the real-world application. We run local search, Genetic and Memetic Algorithms. We compare the direct encoding with unary and binary codings, and we try a 2-dimensional encoding. For a simple smoothness criterion, the Memetic Algorithm clearly performs best. However, if the smoothness citerion is more complex, the local search needs many function evaluations. Therefore we prefer the pure Genetic Algorithm for the application. <s> BIB005 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> The use of statistical models to approximate ::: detailed analysis codes for evolutionary optimization has ::: attracted some attention [1-3]. However, those early ::: methodologies do suffer from some limitations, the most ::: serious of which being the extra tuning parameter ::: introduceds. Also the question of when to include more ::: data points to the approximation model during the search ::: remains unresolved. Those limitations might seriously ::: impede their successful application. We present here an ::: approach that makes use of the extra information ::: provided by a Gaussian processes (GP) approximation ::: model to guide the crucial model update step. We present ::: here the advantages of using GP over other neural-net ::: biologically inspired approaches. Results are presented ::: for a real world-engineering problem involving the ::: structural optimization of a satellite boom. <s> BIB006 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> Evolutionary Dynamic Weighted Aggregation (EDWA) has shown to be both effective and computationally efficient [1] for multi-objective optimization (MOO). Besides, it was also found empirically and surprisingly that EDWA was able to deal with multi-objective optimization problems with a concave Pareto front, which has proved to be beyond the capability of the Conventional Weighted Aggregation (CWA) methods [2]. In this paper, a theory on why CWA fails for multi-objective problems with a concave Pareto front is provided schematically. According to this theory, it can easily be explained why EDWA has worked well for both convex and concave multi-objective problems. Simulation examples are conducted on various test functions to support our theory. It is concluded that EDWA is an effective and efficient method for solving multi-objective optimization problems. <s> BIB007 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> Several combinatorial optimisation problems occur during the calibration of combustion engines. In this work, it is shown that three particular process steps benefit from genetic algorithms: First, the D-optimal experimental design is improved by the use of an appropriate crossover operator. Thereby the heuristics DETMAX or k-exchange perform a local search. The second problem concerns the optimal test bed scheduling for a more efficient and thus less expensive execution of measurements. This higher dimensional variant of the Travelling Salesman Problem (TSP) is solved by a hybrid genetic algorithm using adjacency coded individuals and a 2-opt heuristic as a local search. Finally, well-defined look-up tables, that lead to smooth maps, are composed from multiple valued look-up tables. Again a genetic algorithm finds better solutions than local search heuristics. <s> BIB008 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> This paper presents various Metamodel-Assisted Evolution Strategies which reduce the computational cost of optimisation problems involving time-consuming function evaluations. The metamodel is built using previously evaluated solutions in the search space and utilized to predict the fitness of new candidate solutions. In addition to previous works by the authors, the new metamodel takes also into account the error associated with each prediction, by correlating neighboring points in the search space. A mathematical problem and the problem of designing an optimal airfoil shape under viscous flow considerations have been worked out. Both demonstrate the noticeable gain in computational time one might expect from the use of metamodels in Evolution Strategies. <s> BIB009 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> Dynamic optimization using evolutionary algorithms is receiving increasing interests. However, typical test functions for comparing the performance of various dynamic optimization algorithms still lack. This paper suggests a method for constructing dynamic optimization test problems using multi-objective optimization (MOO) concepts. By aggregating different objectives of an MOO problem and changing the weights dynamically, we are able to construct dynamic single objective and multi-objective test problems systematically. The proposed method is computationally efficient, easily tunable and functionally powerful. This is mainly due to the fact that the proposed method associates dynamic optimization with multi-objective optimization and thus the rich MOO test problems can easily be adapted to dynamic optimization test functions. <s> BIB010 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> Many combinatorial optimization problems occur in the calibration of modern automotive combustion engines. In this contribution, simple hill-climbing algorithms (HCs) for three special problems are incorporated in Memetic Algorithms (MAs) using specific crossover and mutation operators. First, the k-exchange algorithm as a well known technique of D-optimal design of experiments (DOE) is improved. Second, a (near-)optimum test bed measurement scheduling (TBS) as a variant of the traveling salesman problem (TSP) is calculated, and third, the final design of look-up tables (LTD) for electronic control units is optimized. It is shown that in all cases MAs that work on locally optimal solutions calculated by the corresponding HCs significantly improve former results using Genetic Algorithms (GAs). The algorithms have been successfully applied at BMW Group Munich. <s> BIB011 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> The tuning of parameter values in parametric modelling can be viewed as an optimization problem where the outcome of the optimal model is to be as similar as possible to the experimental data. We give a general formulation of the problem with different fitness function definitions, both in terms of single-objective and multi-objective evolutionary optimization. As a test case we show results on a parametric model of combustion in a combustion chamber of a diesel engine. Such an optimal model will therefore be used for a controller design. The outputs (pressure inside combustion chamber versus rotation angle) of the resulting optimal models are compared to experimental data. Results of different optimization runs with Differential Evolution (DE) and Evolution Strategy (ES) as search algorithms and with different fitness definitions are compared. <s> BIB012 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> This paper proposes a multi-objective structure for the optimization of an engine control unit mapping. In this way, first an integrated engine-vehicle model is developed. The objective functions for the optimization problem can be defined from this model. After describing the structure of the optimization problem, two different multi-objective genetic algorithms, namely distance-based Pareto genetic algorithm and non-dominated sorting genetic algorithm (together with entropy-based multi-objective genetic algorithm), are proposed and implemented. The results demonstrate the superiority of this computerized structure to the manual mapping methods and also more generality of the multi-objective methods compared to single-objective ones. <s> BIB013 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> Evolutionary algorithms usually require a large number of objective function evaluations before converging to a good solution. However, many real-world applications allow for only very few objective function evaluations. To solve this predicament, one promising possibility seems to not evaluate every individual, but to just estimate the quality of some of the individuals. In this paper, we estimate an individual’s fitness on the basis of previously observed objective function values of neighboring individuals. Two estimation methods, interpolation and regression, are tested and compared. The experiments show that by using fitness estimation, it is possible to either reach a better fitness level in the given time, or to reach a desired fitness level much faster (roughly half the number of evaluations) than if all individuals are evaluated. <s> BIB014 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> In this paper, we present our work on self-learning engine control using "derivative" adaptive critics. In the derivative version of adaptive critic designs, the derivative of the cost function of dynamic programming with respect to the state of the process is estimated. As the goal of dynamic programming is to maximize the overall cost function, direct estimation of the cost function derivatives will naturally lead to better algorithm performance. In our previous studies of the regular version of adaptive critic techniques, a model of the process for controller training was not necessary. However, for the implementation of the "derivative" version of adaptive critic designs, a process model in the form of neural network is required. In this way, the derivative information can be propagated back to the controller in order to update the controller parameters. The objectives of the present learning control design for automotive engines are to improve performance, reduce emissions and maintain optimum performance under various operating conditions. Using data from the test vehicle equipped with a 5.3 L V8 engine, we built a neural network model of the engine. The model is then used in the development of self-learning neural network controllers based on the idea of approximate dynamic programming to achieve optimal control for both engine torque and exhaust air-fuel ratio control. The goals of the engine torque and air-fuel ratio control are to track the commanded torque and to regulate the air-fuel ratio at specified set-points, respectively. For both control problems, reasonably good neural network controller transient performance under a wide range of operating conditions have been achieved and reported. <s> BIB015 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> Since multi-objective optimizations are becoming more important in engine calibration, the paper investigates multi-objective genetic algorithms in the application of engine optimization. Although several multi-objective genetic algorithms have been developed and some have been applied successfully in the automotive industry, it is difficult to determine which multi-objective genetic algorithm outperforms others in finding the set of optimal solutions or Pareto-optimal front in a practical multi-objective optimization problem. Based on some widely used multi-objective genetic algorithms, the paper proposes a combined scheme to deal with the difficulties in finding the optimal solution set during the engine calibration process. In the proposed approach the real-coded representation is employed in the genetic algorithm and the elitist strategy is applied for each multi-objective genetic algorithm used. To assess the proposed approach, two computational examples are given to minimize the brake specific fuel ... <s> BIB016 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> A hybrid evolutionary algorithm, consisting of a genetic algorithm (GA) and particle swarm optimization (PSO), is proposed. Generally, GAs maintain diverse solutions of good quality in multi-objective problems, while PSO shows fast convergence to the optimum solution. By coupling these algorithms, GA will compensate for the low diversity of PSO, while PSO will compensate for the high computational costs of GA. The hybrid algorithm was validated using standard test functions. The results showed that the hybrid algorithm has better performance than either a pure GA or pure PSO. The method was applied to an engineering design problem—the geometry of diesel engine combustion chamber reducing exhaust emissions such as NOx, soot and CO was optimized. The results demonstrated the usefulness of the present method to this engineering design problem. To identify the relation between exhaust emissions and combustion chamber geometry, data mining was performed with a self-organising map (SOM). The results indicate th... <s> BIB017 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> This paper presents the design and experimental test of a fixed-structure LPV controller for the charge control of a spark-ignition engine. A nonlinear model of the plant is transformed into an affine LPV model in the form of an LFT representation. Using a hybrid evolutionary-algebraic synthesis approach that combines LMI techniques based on K-S iteration with evolutionary search, a scheduled PID controller is designed. To reduce conservatism, the technique of quadratic separators is used in the analysis step. To improve tracking behavior, the gain scheduled feedback controller is supported by an LTI feedforward controller. The controller has been implemented on a standard electronic control unit, and experimental results on a test car illustrate that it meets the performance requirements in a wide range of operation. <s> BIB018 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> Genetic Algorithms (GAs) generally maintain diverse solutions of good quality in multi-objective problems, while Particle Swarm Optimization (PSO) shows rapid convergence to the optimum solution. Previous studies indicated that search abilities can be improved by simply coupling these two algorithms; GA compensates for the low diversity of PSO, while PSO compensates for the high computational costs of GA. In this study, the configurations of the two methods when used in a fully coupled hybrid algorithm were investigated to achieve an improvement in diversity and convergence simultaneously for application to real-world engineering design problems. The new hybrid algorithm was validated using standard test function problems, and it was demonstrated that the new hybrid algorithm showed better performance than the simply coupled hybrid algorithm, as well as both pure GA and pure PSO. Especially, the new hybrid algorithm shows robust search ability regardless of initial population selection. This feature is very important in real-world engineering design problems, which do not allow multiple optimization runs to be implemented due to heavy computational costs. The new method was applied to optimization of a diesel engine combustion chamber to reduce exhaust emissions, such as NOx and soot. The results demonstrated the applicability of the present method to real-world design problems. In addition, important geometry design variables controlling the emission performance were investigated to obtain useful knowledge about low emission diesel engine design. <s> BIB019 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> In previous study [1] the Non-dominated Sorting Genetic Algorithm II (NSGA II) [2] performed better than other popular Multi-Objective Genetic Algorithms (MOGA) in engine optimization that sought optimal combinations of the piston bowl geometry, spray targeting, and swirl ratio. NSGA II is further studied in this paper using different niching strategies that are applied to the objective-space and design-space, which diversify the optimal objectives and design parameters accordingly. Convergence and diversity metrics are defined to assess the performance of NSGA II using different niching strategies. It was found that use of the design niching achieved more diversified results with respect to design parameters, as expected. Regression was then conducted on the design datasets that were obtained from the optimizations with two niching strategies. Four regression methods, including K-nearest neighbors (KN), Kriging (KR), Neural Networks (NN), and Radial Basis Functions (RBF), were compared. The results showed that the dataset obtained from optimization with objective niching provided a more fitted learning space for the regression methods. The KN, KR, outperformed the other two methods with respect to the prediction accuracy. Furthermore, a log transformation to the objective-space improved the prediction accuracy for the KN, KR, and NN methods but not the RBF method. The results indicate that it is appropriate to use a regression tool to partly replace the actual CFD evaluation tool in engine optimization designs using the genetic algorithm. This hybrid mode saves computational resources (processors) without losing optimal accuracy. A Design of Experiment (DoE) method (the Optimal Latin Hypercube method) was also used to generate a dataset for the regression processes. However, the predicted results were much less reliable than results that were learned using the dynamically increasing datasets from the NSGA II generations. Applying the dynamical learning strategy during the optimization processes allows computationally expensive CFD evaluations to be partly replaced by evaluations using the regression techniques. The present study demonstrates the feasibility of applying the hybrid mode to engine optimization problems, and the conclusions can also extend to other optimization studies (numerical or experimental) that feature time-consuming evaluations and have highly non-linear objective-spaces.Copyright © 2009 by ASME <s> BIB020 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> The basic parameters of internal combustion engines reflect the working performance and quality of the internal combustion engine. Therefore it is of great significance to design the operating parameters of vehicle engine by design optimization method. In this paper, hybrid genetic algorithm is adopted to optimize operating parameters of vehicle engine, so that optimization process was simplified and the global optimal solution is ensured reliably. Being satisfied with the heating loading, mechanical loading and the conditions of gas mixture of engine and boundary constraints, the optimization mathematical model is created which is to minimize the heating surface area of engine. Considering the problem of low efficiency and local optimum caused by traditional optimal methods, the hybrid Genetic Algorithm are adopted to solve the optimization model. So that the optimization process is simplified and global optimum is acquired reliably. <s> BIB021 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> A novel process has been developed for reducing complexity in real-world, high-dimensional, multi-objective optimisation problems. This approach relies on being able to identify and exploit local harmony between objectives to reduce dimensionality. To achieve this, a systematic and modular process has been designed to cluster the Pareto-optimal front and apply a rule-based Principal Component Analysis including preference articulation for potential objective reduction. This many-objective optimisation decision-making process is demonstrated on a real-world, automotive diesel engine calibration optimisation problem comprising six objectives. The complexity reduction process resulted in three- and four-objective sub-problems. In the former, a significant improvement was achieved in one of the retained objectives at very little cost to the others. <s> BIB022 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> The characteristic vector of cylinder vibration signal is extracted by wavelet packet decomposition. The factor of selection is proposed to take adaptive integration on basis of improved super parent one dependence estimator Bayesian method and back propagation genetic algorithm neural network method. Experimental results on WD615 diesel engine showed that the method has high accuracy rate of detection. <s> BIB023 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> according to the stability of the membership degree and low identification rate in fuzzy inference system, this dissertation proposes the application of adaptive neural network-based fuzzy inference system to engine error diagnosis. To reduce the impact of excessive parameters on classification accuracy and cost, it also raises an asynchronous parallel particle swarm optimization method applied to the selection of feature subset. The method use uniform mutation operator, balancing effectively the particles' ability to search globally and to develop. The asynchronous parallel particle swarm optimization algorithm(AP-PSO) that is used to select the feature subset is a potential feature subset that carries the characteristic of firstly initializing every particle as the selection question. Then, the method adopts improved asynchronous parallel particle swarm algorithm to conduct optimal searching based on the particle swarm that include several feature subsets and evaluate the classification ability (adaptive value) of the feature subset selected by way of Support Vector Machine. Finally, the optimal feature subset is got. Through verification of the build diagnosis model with data of engine tests, it has been found that the recognition accuracy attain to 98.72%, training error falling to 0.004423.The experiment indicates that the recognition rate of ANFIS system is significantly better than independent neural network reasoning system, fuzzy inference system. <s> BIB024 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> The computer simulation technology of the work process of internal-combustion engine is the important measure to study the internal-combustion engine, but generally, because of the uncertainty of input parameters, the precision of the simulation model of the engine work process, which largely limits the application of the simulation model, so the parameters of the simulation model needs to be calibrated. Taking the work process of the certain one type turbocharging diesel engine as the example, and combining the genetic algorithm with the ant colony algorithm, the parameter combination which can satisfy the requirements of precision, is selected in this article to effectively reduce the simulation experiment times of parameter calibration, and realize the automatic calibration of the simulation model parameters. By comparing and analyzing the practical result of the experiment and the result of the simulation computation, the effectiveness of the algorithm has been validated in the article. <s> BIB025 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> In the automotive industry the calibration of the engine control unit is getting more and more complex because of many various boundary conditions, like the demand on CO 2 and fuel reduction. One important calibration problem is the parameter estimation for the model of the intake system of the combustion engine. This system is modeled by a physically motivated system, which can be parameterized by black-box models, like neural nets and characteristic diagrams, whose parameters must be set by an intelligent optimizer. Further, two contradictory aims must be considered and the engineer expects at the end of the optimization a pareto-front, where he can choose the best settings for the application from the pareto-optimal parameter estimations. To solve this multi-criteria optimization task an evolutionary algorithm is used, which is a combination of a genetic algorithm and an evolutionary strategy. This evolutionary algorithm is like all other stochastic searching methods leaned on the naturally biological evolution. It combines the well-known covariance matrix adaption for the mutation of the individuals with the S-metric selection for the multi-criteria fitness assignment of the individuals. It also improves these combination by the use of many subpopulations, which work parallel on various clusters, and by the use of an intelligent DoE-strategy for the initialization of the start individuals. With these improvements the developed evolutionary algorithm can easily fit the model of the intake system to test bed measurements and can provide the user a pareto-optimal set of parameters, on which he can choose on his own that ones, which he find most plausible. <s> BIB026 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> Abstract This paper addresses artiﬁcial neural network (ANN) modeling followed by multi-objective optimization process to determine optimum biodiesel blends and speed ranges of a diesel engine fueled with castor oil biodiesel (COB) blends. First, an ANN model was developed based on standard back-propagation algorithm to model and predict brake power, brake speciﬁc fuel consumption (BSFC) and the emissions of engine. In this way, multi-layer perception (MLP) network was used for non-linear mapping between the input and output parameters. Second, modiﬁed NSGA-II by incorporating diversity preserving mechanism called the e-elimination algorithm was used for multi-objective optimization process. Six objectives, maximization of brake power and minimization of BSFC, PM, NO x , CO and CO 2 were simultaneously considered in this step. Optimization procedure resulted in creating of non-dominated optimal points which gave an insight on the best operating conditions of the engine. Third, an approach based on TOPSIS method was used for ﬁnding the best compromise solution from the obtained set of Pareto solutions. <s> BIB027 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> Most research in evolutionary dynamic optimization is based on the assumption that the primary goal in solving Dynamic Optimization Problems (DOPs) is Tracking Moving Optimum (TMO). Yet, TMO is impractical in cases where keeping changing solutions in use is impossible. To solve DOPs more practically, a new formulation of DOPs was proposed recently, which is referred to as Robust Optimization Over Time (ROOT). In ROOT, the aim is to find solutions whose fitnesses are robust to future environmental changes. In this paper, we point out the inappropriateness of existing robustness definitions used in ROOT, and therefore propose two improved versions, namely survival time and average fitness. Two corresponding metrics are also developed, based on which survival time and average fitness are optimized respectively using population-based algorithms. Experimental results on benchmark problems demonstrate the advantages of our metrics over existing ones on robustness definitions survival time and average fitness. <s> BIB028 </s> Meta-Heuristic Algorithms in Car Engine Design: A Literature Survey <s> VII. CONCLUSION <s> To deal with complex optimization problems plagued with computationally expensive fitness functions, the use of surrogates to replace the original functions within the evolutionary framework is becoming a common practice. However, the appropriate datacentric approximation methodology to use for the construction of surrogate model would depend largely on the nature of the problem of interest, which varies from fitness landscape and state of the evolutionary search, to the characteristics of search algorithm used. This has given rise to the plethora of surrogate-assisted evolutionary frameworks proposed in the literature with ad hoc approximation/surrogate modeling methodologies considered. Since prior knowledge on the suitability of the data centric approximation methodology to use in surrogate-assisted evolutionary optimization is typically unavailable beforehand, this paper presents a novel evolutionary framework with the evolvability learning of surrogates (EvoLS) operating on multiple diverse approximation methodologies in the search. Further, in contrast to the common use of fitness prediction error as a criterion for the selection of surrogates, the concept of evolvability to indicate the productivity or suitability of an approximation methodology that brings about fitness improvement in the evolutionary search is introduced as the basis for adaptation. The backbone of the proposed EvoLS is a statistical learning scheme to determine the evolvability of each approximation methodology while the search progresses online. For each individual solution, the most productive approximation methodology is inferred, that is, the method with highest evolvability measure. Fitness improving surrogates are subsequently constructed for use within a trust-region enabled local search strategy, leading to the self-configuration of a surrogate-assisted memetic algorithm for solving computationally expensive problems. A numerical study of EvoLS on commonly used benchmark problems and a real-world computationally expensive aerodynamic car rear design problem highlights the efficacy of the proposed EvoLS in attaining reliable, high quality, and efficient performance under a limited computational budget. <s> BIB029
Car engine design is an extremely complex task that involves many different but interlinked challenges, including those in optimization, modeling, control, etc. This paper focuses on challenges related to optimization only. In particular, we have limited ourselves to meta-heuristic optimization in car engine design, because of its effectiveness in solving hard and complex optimization problems. In order to gain an overview of what have been done in applying metaheuristic optimization to car engine design, a comprehensive review has been carried out to understand where and how meta-heuristic algorithms were used in car engine design. We have categorized the research into five overlapping categories: 1) engine calibration; 2) optimization in control systems; 3) engine fault diagnosis; 4) meta-heuristic algorithms in modeling; and 5) mechanical part optimization. In spite of the huge range of applications of meta-heuristic algorithms in car engine design, some interesting observations can be made. First, there is a very close link between optimization and modeling. Almost all meta-heuristic optimization algorithms rely on an engine model for obtaining objective values, i.e., fitness values. This implies that the success of an optimizer, whether meta-heuristic or not, is not just an issue of a better and more powerful optimization algorithm. Instead, the success depends on both the optimization algorithm and modeling. Accurate models are essential in ensuring the success of optimization. At the same time, good optimization algorithms can help to learn/build more reliable and accurate models. While there has been much work on optimization and modeling separately, much fewer work has been on the interaction between optimization and modeling and their appropriate combinations. Second, most of the work in car engine design involve multiple objectives. MOEAs were very widely used in car engine design, although a detailed analysis of when to use which MOEA is still lacking. There are still a lot of trial-and-error in selecting an MOEA for a particular problem. Third, all the work in meta-heuristic optimization for car engine design implicitly assumes a static and deterministic optimization problem, while the real-world is dynamic and full of uncertainties. Fourth, many works try to benefit from the nature of meta-heuristic algorithms and improve the performance of the algorithms when solving engine management problems. These could be categorized into three different groups. The first group use a hybrid of a meta-heuristic algorithm with a local search or another type of meta-heuristic algorithms. For example, in BIB005 - BIB011 , BIB018 , BIB023 , BIB024 ,  , and BIB021 , a meta-heuristic algorithm is hybridized with a local search algorithm. Thus, the global search advantages of the meta-heuristic algorithm and the hill climbing and speed of local search are combined to achieve a better algorithm. Other examples of hybrid algorithms are BIB016 ,  , BIB023 , BIB017 , BIB019 , BIB019 , BIB025 , and BIB012 , where two types of meta-heuristic algorithms are combined so the advantages of one algorithm covers the weakness of the other one. The second group are the works that improve the performance of the algorithm with operators. Improving crossover BIB008 , BIB011 and mutation BIB026 operators, using history of search BIB004 and entropy in the individuals BIB013 to guide the individuals, preserving diversity among the individuals BIB027 and using niching strategies BIB020 are some examples of these works. The third group of works target the objective function. Some example of these are reducing the number of objectives to improve the speed BIB022 , using neural networks to estimate the derivative of fitness function BIB015 and replacing the fitness function with high speed equations that makes the optimization real-time. Note that here, neural network or machine-learning techniques could be employed to model the real fitness function, or they may be used to improve the performance of the algorithm. Despite the wide range applications of meta-heuristic algorithms, we believe there are still some ideas in the field of evolutionary computation which have not been adopted in car engine optimization. In this section, we try to suggest some research topics for future works. Four main types of uncertainties were identified in fitness evaluation within the evolutionary computation community BIB006 . None was considered in car engine design. The first uncertainty is noise, which may come from different sources including sensory measurement errors or randomized simulations. To date, many EAs have been developed to deal with noise in EAs  -  . It is interesting to investigate the application of such algorithms to car engine design in the future. The second source of uncertainty is robustness. Sometimes the design variables are subject to changes after the optimization. Therefore, the optimal solution has to be robust to minor changes in the fitness function. Some examples of research in this area can be found in BIB001 - BIB002 . Fitness approximation is the third source of uncertainty in optimization problems. Some examples of the research trying to manage this uncertainty are BIB003 - BIB009 . The final source of uncertainty is the time-varying fitness functions, which occur when the fitness function itself may change as time progresses and has been studied in a number of research  - BIB028 . All these four types of uncertainties exist in automobile engine design problems. Some examples are as follows. 1) Noise: When trying to optimize the emission, the sensors measuring the gasses and particles may induce noise to the fitness function. 2) Robustness: Engines are some mechanical machines subject to ageing; thus, the input parameters to a controller change over time. 3) Fitness Approximation: Many papers reviewed in this paper used the meta-model approach for their optimization, i.e., they used an engine simulation model to approximate the real fitness values. 4) Time-Varying Fitness Functions: Engines work in an ever-changing environment; therefore, the fitness function changes with time, depending on different aspects of an environment. Although these uncertainties occur in all the optimization problems in engine design, none of the research reviewed in this paper have developed algorithms to manage them. One of our future work is to tackle these uncertainties when optimizing automobile engines. The second future work is to investigate the relationship between uncertainties and multiobjectivity in engine design, as the uncertainties can be addressed from a multiobjective point of view  . Some research suggested that multiobjective optimization problems, which occur in engine design in great number, can be converted into dynamic single objective optimization problems BIB007 , BIB010 . Conversely, the concept of Pareto-optimality can be used to address fast changing dynamic optimization problems  . When converting a multiobjective problem to a dynamic single objective problem, different uncertainties may occur. First since the conversion is usually performed based on deterministic approaches, the noise uncertainty is less likely to occur due to the conversion. Second in terms of robustness, when the multiobjective optimization is converted to dynamic single objective optimization, there is usually some discrepancy between the two. One way of managing this uncertainty could be to make a model of the discrepancy using machine learning techniques. The model then can be used during the optimization to calibrate the fitness. The third class of uncertainty is fitness approximation that occurs during the conversion. Managing this type of uncertainty could be performed by measuring the uncertainty as proposed in BIB014 , incorporating the uncertainty in the fitness function and reevalute the individuals with uncertainty higher than a threshold. Finally, since multiobjective problems are not necessarily time varying, when a multiobjective problem is converted to a dynamic problem, the fourth uncertainty is introduced to the problem. To deal with this type of uncertainty different methods could be used, including restarting the search, generating and maintaining diversity, using memory-based approaches and multipopulation methods. The third future work is to further investigate memetic algorithms in automobile engine design, because they often provide a good framework for combining advantages of global search from a meta-heuristic algorithm and efficient local search. This scheme could specifically be useful when it is applied to engine calibration, when fitness evaluation is very expensive and usually a fitness approximation model of the engine is used. In this case, both the engine model and real engine could be used simultaneously. For example, since the local search performs exploitation and the evolutionary part acts for global exploration, the local search needs more accurate fitness estimation and the evolutionary part needs more general information of the landscape. Therefore, for the evolutionary part a faster and less accurate model could be used, and for the local search, a more accurate real engine can be employed. When choosing an existing EA for a specific problem in engine management, a researcher should take the nature of the problem and the algorithm into account. For example some problems, like engine calibration, have a few number of optimization parameters so the search space is not very large, but evaluating the fitness function is very time consuming. In this case, the EA should be able to find a good solution with the minimum number of fitness evaluations, so a more exploitive EA with faster convergence is more suitable or employing some optimization algorithms like surrogate-assisted evolutionary techniques BIB029 could be tried. In some other cases, the problems have a large number of optimization parameters while fitness evaluation is less expensive. Here, the EA can perform a larger number of fitness evaluations and should perform a more global search, so a more explorative algorithm would be more suitable.