Approximate and Widespread Pareto Solutions in the Structure-Control Design of Mechatronic Systems

The structure-control design approach of mechatronic systems requires a different design formulation where the mechanical structure and control system are simultaneously designed. Optimization problems are commonly stated to confront the structure-control design formulation. Nevertheless, these problems are often very complex with a highly nonlinear dependence between the design variables and performance functions. This fact has made the use of evolutionary algorithms, a feasible alternative to solve the highly nonlinear optimization problem; the method to find the best solution is an open issue in the structure-control design approach. Hence, this paper presents a mechanism to exhaustively exploit the solutions in the differential evolution (DE) algorithm in order to find more non-dominated solutions with uniformly distributed Pareto front and better trade-offs in the structure-control design framework. The proposed approach adopts an external population to retain the non-dominated solutions found during the evolutionary process and includes a mechanism to mutate the individuals in their corresponding external population region. As a study case, the structure-control design of a serial-parallel manipulator with its control system is stated as a dynamic optimization problem and is solved by using the proposed approach. A comparative analysis shows that the multi-objective exhaustive exploitation differential evolution obtained a superior performance in the structure-control design framework than a DE algorithm which did not consider the proposal. Hence, the resulting designs provide better trade-offs between the structure-control performance functions.     

Convex hull-based multi-objective evolutionary computation for maximizing receiver operating characteristics performance

The receiver operating characteristics (ROC) analysis has gained increasing popularity for analyzing the performance of classifiers. In particular, maximizing the convex hull of a set of classifiers in the ROC space, namely ROCCH maximization, is becoming an increasingly important problem. In this work, a new convex hull-based evolutionary multi-objective algorithm named ETriCM is proposed for evolving neural networks with respect to ROCCH maximization. Specially, convex hull-based sorting with convex hull of individual minima (CH-CHIM-sorting) and extreme area extraction selection (EAE-selection) are proposed as a novel selection operator. Empirical studies on 7 high-dimensional and imbalanced datasets show that ETriCM outperforms various state-of-the-art algorithms including convex hull-based evolutionary multi-objective algorithm (CH-EMOA) and non-dominated sorting genetic algorithm II (NSGA-II).     

A preference-based multi-objective evolutionary algorithm R-NSGA-II with stochastic local search

Incorporation of a decision maker’s preferences into multi-objective evolutionary algorithms has become a relevant trend during the last decade, and several preference-based evolutionary algorithms have been proposed in the literature. Our research is focused on improvement of a well-known preference-based evolutionary algorithm R-NSGA-II by incorporating a local search strategy based on a single agent stochastic approach. The proposed memetic algorithm has been experimentally evaluated by solving a set of well-known multi-objective optimization benchmark problems. It has been experimentally shown that incorporation of the local search strategy has a positive impact to the quality of the algorithm in the sense of the precision and distribution evenness of approximation.     

Multi-strategy ensemble evolutionary algorithm for dynamic multi-objective optimization

Dynamic optimization and multi-objective optimization have separately gained increasing attention from the research community during the last decade. However, few studies have been reported on dynamic multi-objective optimization (dMO) and scarce effective dMO methods have been proposed. In this paper, we fulfill these gabs by developing new dMO test problems and new effective dMO algorithm. In the newly designed dMO problems, Pareto-optimal decision values (i.e., Pareto-optimal solutions: POS) or both POS and Pareto-optimal objective values (i.e., Pareto-optimal front: POF) change with time. A new multi-strategy ensemble multi-objective evolutionary algorithm (MS-MOEA) is proposed to tackle the challenges of dMO. In MS-MOEA, the convergence speed is accelerated by the new offspring creating mechanism powered by adaptive genetic and differential operators (GDM); a Gaussian mutation operator is employed to cope with premature convergence; a memory like strategy is proposed to achieve better starting population when a change takes place. In order to show the advantages of the proposed algorithm, we experimentally compare MS-MOEA with several algorithms equipped with traditional restart strategy. It is suggested that such a multi-strategy ensemble approach is promising for dealing with dMO problems.     

A new mechanism to maintain diversity in multi-objective metaheuristics

In this article, a new mechanism to spread the solutions generated by a multi-objective evolutionary algorithm is proposed. This approach is based on the use of stripes that are applied in objective function space and is independent of the search engine adopted. Additionally, it overcomes some of the drawbacks of other previous proposals such as the ?-dominance method. In order to validate the proposed approach, it is coupled to a multi-objective particle swarm optimizer and its performance is assessed with respect to that of state-of-the-art algorithms, using standard test problems and performance measures taken from the specialized literature. The results indicate that the proposed approach is a viable diversity maintenance mechanism that can be incorporated to any multi-objective metaheuristic used for multi-objective optimization.     

FEMOEA: a fast and efficient multi-objective evolutionary algorithm

A multi-objective evolutionary algorithm which can be applied to many nonlinear multi-objective optimization problems is proposed. Its aim is to quickly obtain a fixed size Pareto-front approximation. It adapts ideas from different multi-objective evolutionary algorithms, but also incorporates new devices. In particular, the search in the feasible region is carried out on promising areas (hyperspheres) determined by a radius value, which decreases as the optimization procedure evolves. This mechanism helps to maintain a balance between exploration and exploitation of the search space. Additionally, a new local search method which accelerates the convergence of the population towards the Pareto-front, has been incorporated. It is an extension of the local optimizer SASS and improves a given solution along a search direction (no gradient information is used). Finally, a termination criterion has also been proposed, which stops the algorithm if the distances between the Pareto-front approximations provided by the algorithm in three consecutive iterations are smaller than a given tolerance. To know how far two of those sets are from each other, a modification of the well-known Hausdorff distance is proposed. In order to analyze the algorithm performance, it has been compared to the reference algorithms NSGA-II and SPEA2 and the state-of-the-art algorithms MOEA/D and SMS-EMOA. Several quality indicators have been considered, namely, hypervolume, average distance, additive epsilon indicator, spread and spacing. According to the computational tests performed, the new algorithm, named FEMOEA, outperforms the other algorithms.     

An efficient multi-objective evolutionary fuzzy system for regression problems

During the last years, multi-objective evolutionary algorithms (MOEAs) have been extensively employed as optimization tools for generating fuzzy rule-based systems (FRBSs) with different trade-offs between accuracy and interpretability from data. Since the size of the search space and the computational cost of the fitness evaluation depend on the number of input variables and instances, respectively, managing high-dimensional and large datasets is a critical issue.In this paper, we focus on MOEAs applied to learn concurrently the rule base and the data base of Mamdani FRBSs and propose to tackle the issue by exploiting the synergy between two different techniques. The first technique is based on a novel method which reduces the search space by learning rules not from scratch, but rather from a heuristically generated rule base. The second technique performs an instance selection by exploiting a co-evolutionary approach where cyclically a genetic algorithm evolves a reduced training set which is used in the evolution of the MOEA.The effectiveness of the synergy has been tested on twelve datasets. Using non-parametric statistical tests we show that, although achieving statistically equivalent solutions, the adoption of this synergy allows saving up to 97.38% of the execution time with respect to a state-of-the-art multi-objective evolutionary approach which learns rules from scratch.     

ParEGO extensions for multi-objective optimization of expensive evaluation functions

This paper deals with multi-objective optimization in the case of expensive objective functions. Such a problem arises frequently in engineering applications where the main purpose is to find a set of optimal solutions in a limited global processing time. Several algorithms use linearly combined criteria to use directly mono-objective algorithms. Nevertheless, other algorithms, such as multi-objective evolutionary algorithm (MOEA) and model-based algorithms, propose a strategy based on Pareto dominance to optimize efficiently all criteria. A widely used model-based algorithm for multi-objective optimization is Pareto efficient global optimization (ParEGO). It combines linearly the objective functions with several random weights and maximizes the expected improvement (EI) criterion. However, this algorithm tends to favor parameter values suitable for the reduction of the surrogate model error, rather than finding non-dominated solutions. The contribution of this article is to propose an extension of the ParEGO algorithm for finding the Pareto Front by introducing a double Kriging strategy. Such an innovation allows to calculate a modified EI criterion that jointly accounts for the objective function approximation error and the probability to find Pareto Set solutions. The main feature of the resulting algorithm is to enhance the convergence speed and thus to reduce the total number of function evaluations. This new algorithm is compared against ParEGO and several MOEA algorithms on a standard benchmark problems. Finally, an automotive engineering problem allowing to illustrate the applicability of the proposed approach is given as an example of a real application: the parameter setting of an indirect tire pressure monitoring system.     

Expected runtimes of a simple evolutionary algorithm for the multi-objective minimum spanning tree problem

Evolutionary algorithms are applied to problems that are not well understood as well as to problems in combinatorial optimization. The analysis of these search heuristics has been started for some well-known polynomial solvable problems. Such analyses are starting points for the analysis of evolutionary algorithms on difficult problems. We present the first runtime analysis of a multi-objective evolutionary algorithm on a NP-hard problem. The subject of our analysis is the multi-objective minimum spanning tree problem for which we give upper bounds on the expected time until a simple evolutionary algorithm has produced a population including for each extremal point of the Pareto front a corresponding spanning tree. These points are of particular interest as they give a 2-approximation of the Pareto front. We show that in expected pseudopolynomial time a population is produced that includes for each extremal point a corresponding spanning tree.     

基于种群自适应调整的多目标差分进化算法

为提高已有多目标进化算法在求解复杂多目标优化问题上的收敛性和解集分布性,提出一种基于种群自适应调整的多目标差分进化算法。该算法设计一个种群扩增策略,它在决策空间生成一些新个体帮助搜索更优的非支配解;设计了一个种群收缩策略,它依据对非支配解集的贡献程度淘汰较差的个体以减少计算负荷,并预留一些空间给新的带有种群多样性的扰动个体;引入精英学习策略,防止算法陷入局部收敛。通过典型的多目标优化函数对算法进行测试验证,结果表明所提算法相对于其他算法具有明显的优势,其性能优越,能够在保证良好收敛性的同时,使获得的Pareto最优解集具有更均匀的分布性和更广的覆盖范围,尤其适合于高维复杂多目标优化问题的求解。     

Balancing exploration and exploitation with adaptive variation for evolutionary multi-objective optimization

Although recent studies have shown that evolutionary algorithms are effective tools for solving multi-objective optimization problems, their performances are often bottlenecked by the suitability of the evolutionary operators with respect to the optimization problem at hand and their corresponding parametric settings. To adapt the search dynamic of evolutionary operation in multi-objective optimization, this paper proposes an adaptive variation operator that exploits the chromosomal structure of binary representation and synergizes the function of crossover and mutation. The overall search ability is deterministically tuned online to maintain a balance between extensive exploration and local fine-tuning at different stages of the evolutionary search. Also, the coordination between the two variation operators is achieved by means of an adaptive control that ensures an efficient exchange of information between the different chromosomal sub-structures throughout the evolutionary search. Extensive comparative studies with several representative variation operators are performed on different benchmark problems and significant algorithmic performance improvements in terms of proximity, uniformity and diversity are obtained with the incorporation of the proposed adaptive variation operator into the evolutionary multi-objective optimization process.     

Particle swarm with equilibrium strategy of selection for multi-objective optimization

A new ranking scheme based on equilibrium strategy of selection is proposed for multi-objective particle swarm optimization (MOPSO), and the preference ordering is used to identify the “best compromise” in the ranking stage. This scheme increases the selective pressure, especially when the number of objectives is very large. The proposed algorithm has been compared with other multi-objective evolutionary algorithms (MOEAs). The experimental results indicate that our algorithm produces better convergence performance.     

A new orthogonal evolutionary algorithm based on decomposition for multi-objective optimization

The diversity of solutions is very important for multi-objective evolutionary algorithms to deal with multi-objective optimization problems (MOPs). In order to achieve the goal, a new orthogonal evolutionary algorithm based on objective space decomposition (OEA/D) is proposed in this paper. To be specific, the objective space of an MOP is firstly decomposed into a set of sub-regions via a set of direction vectors, and OEA/D maintains the diversity of solutions by making each sub-region have a solution to the maximum extent. Also, the quantization orthogonal crossover (QOX) is used to enhance the search ability of OEA/D. Experimental studies have been conducted to compare this proposed algorithm with classic MOEA/D, NSGAII, NICA and D2MOPSO. Simulation results on six multi-objective benchmark functions show that the proposed algorithm is able to obtain better diversity and more evenly distributed Pareto fronts than other four algorithms.     

A new multi-objective genetic algorithm applied to hot-rolling process

A new genetic algorithms based multi-objective optimization algorithm (NMGA) has been developed during study. It works on a neighborhood concept in the functional space, utilizes the ideas on weak dominance and ranking and uses its own procedures for population sizing. The algorithm was successfully tested with some standard test functions, and when applied to a real-life data of the hot-rolling campaign of an integrated steel plant, it outperformed another recently developed multi-objective evolutionary algorithm.     

Optimizing of bullwhip effect and net stock amplification in three-echelon supply chains using evolutionary multi-objective metaheuristics

In this article, we intend to model and optimize the bullwhip effect (BWE) and net stock amplification (NSA) in a three-stage supply chain consisting of a retailer, a wholesaler, and a manufacturer under both centralized and decentralized scenarios. In this regard, firstly, the causes of BWE and NSA are mathematically formulated using response surface methodology (RSM) as a multi-objective optimization model that aims to minimize the BWE and NSA on both chains. The simultaneous analysis of the BWE and NSA is considered as the main novelty of this paper. To tackle the addressed problem, we propose a novel multi-objective hybrid evolutionary approach called MOHES; MOHES is a hybrid of two known multi-objective algorithms i.e. multi-objective electro magnetism mechanism algorithm (MOEMA) and population-based multi-objective simulated annealing (PBMOSA). We applied a co-evolutionary strategy for this purpose with eligibility of both algorithms. Proposed MOHES is compared with three common and popular algorithms (i.e. NRGA, NSGAII, and MOPSO). Since the utilized algorithms are very sensitive to parameter values, RSM with the multi-objective decision making (MODM) approach is employed to tune the parameters. Finally, the hybrid algorithm and the singular approaches are compared together in terms of some performance measures. The results indicate that the hybrid approach achieves better solutions when compared with the others, and also the results show that in a decentralized chain, the order batching factor and the demand signal processing in wholesaler are the most important factors on BWE. Conversely, in a centralized chain, factors such as rationing, shortage gaming, and lead time are the most effective at reducing the BWE.     

A fast steady-state <Emphasis Type="Italic">ε</Emphasis>-dominance multi-objective evolutionary algorithm

Multi-objective evolutionary algorithms (MOEAs) have become an increasingly popular tool for design and optimization tasks in real-world applications. Most of the popular baseline algorithms are pivoted on the use of Pareto-ranking (that is empirically inefficient) to improve the convergence to the Pareto front of a multi-objective optimization problem. This paper proposes a new ε-dominance MOEA (EDMOEA) which adopts pair-comparison selection and steady-state replacement instead of the Pareto-ranking. The proposed algorithm is an elitist algorithm with a new preservation technique of population diversity based on the ε-dominance relation. It is demonstrated that superior results could be obtained by the EDMOEA compared with other algorithms: NSGA-II, SPEA2, IBEA, ε-MOEA, PESA and PESA-II on test problems. The EDMOEA is able to converge to the Pareto optimal set much faster especially on the ZDT test functions with a large number of decision variables.     

Evolutionary optimization of transition probability matrices for credit decision-making

Statistical transition probability matrices (TPMs), which indicate the likelihood of obligor credit state migration over a certain time horizon, have been used in various credit decision-making applications. A standard approach of calculating TPMs is to form a one-year empirical TPM and then project it into the future based on Markovian and time-homogeneity assumptions. However, the one-year empirical TPM calculated from historical data generally does not satisfy desired properties. We propose an alternative methodology by formulating the problem as a constrained optimization problem requiring satisfaction of all the desired properties and minimization of the discrepancy between predicted multi-year TPMs and empirical evidence. The problem is high-dimensional, non-convex, and non-separable, and is not effectively solved by nonlinear programming methods. To address the difficulty, we investigated evolutionary algorithms (EAs) and problem representation schemas. A self-adaptive differential evolution algorithm JADE, together with a new representation schema that automates constraint satisfaction, is shown to be the most effective technique.     

Local models—an approach to distributed multi-objective optimization

When solving real-world optimization problems, evolutionary algorithms often require a large number of fitness evaluations in order to converge to the global optima. Attempts have been made to find techniques to reduce the number of fitness function evaluations. We propose a novel framework in the context of multi-objective optimization where fitness evaluations are distributed by creating a limited number of adaptive spheres spanning the search space. These spheres move towards the global Pareto front as components of a swarm optimization system. We call this process localization. The contribution of the paper is a general framework for distributed evolutionary multi-objective optimization, in which the individuals in each sphere can be controlled by any existing evolutionary multi-objective optimization algorithm in the literature.     

Multi-objective open shop scheduling by considering human error and preventive maintenance

This study presents an open shop scheduling model by considering human error and preventive maintenance. The proposed mathematical model takes into account conflicting objective functions including makespan, human error and machine availability. In order to find the optimum scheduling, human error, maintenance and production factors are considered, simultaneously. Human error is measured by Human Error Assessment and Reduction Technique (HEART). Three metaheuristic methods including non-dominated sorting genetic algorithm-II (NSGA-II), multi-objective particle swarm optimization (MOPSO) and strength Pareto evolutionary algorithm II (SPEA-II) are developed to find near-optimal solution. The Taguchi method is applied by adjusting parameters of metaheuristic algorithms. Several illustrative examples and a real case study (auto spare parts manufacturer) are applied to show the applicability of the multi-objective mixed integer nonlinear programming model. The proposed approach of this study may be used for similar open shop problems with minor modifications.     

A dynamic multi-objective optimization model with interactivity and uncertainty for real-time reservoir flood control operation

Despite the successes of both multi-objective optimization and uncertainty handling techniques in reservoir flood control operation, no work has been done yet on developing and investigating dynamic multi-objective optimization models for this problem. In this work, a dynamic multi-objective optimization model with interactivity and uncertainty was developed for the real-time reservoir flood control operation. Accordingly, a dynamic multi-objective optimization algorithmic framework with two newly designed change reaction strategies was proposed for solving the proposed dynamic model. Following the proposed algorithmic framework, any evolutionary multi-objective optimization algorithm can be converted into a dynamic optimizer. After investigating the difficulty variation of the proposed dynamic model, the effectiveness and robustness of the proposed algorithmic framework have been validated based on experiential studies on two typical floods of Ankang reservoir.