MRCD: a genetic algorithm for multiobjective robust control design

A genetic algorithm (GA) for the class of multiobjective optimization problems that appears in the design of robust controllers is presented in this paper. The design of a robust controller is a trade-off problem among competitive objectives such as disturbance rejection, reference tracking, stability against unmodeled dynamics, moderate control effort and so on. However, general methodologies for solving this class of design problems are not easily encountered in the literature because of the complexity of the resultant multiobjective problems. In this paper, a recently developed class of GAs, multiobjective GAs, are used to solve robust control design problems. Here, a new algorithm, called multiobjective robust control design, has been proposed. The structure and operators of this algorithm have been specifically developed for control design problems. The performace of the algorithm is evaluated by solving several test cases and is also compared to the standard algorithms used for the multiobjective design of robust controllers.     

Crashworthiness design of vehicle by using multiobjective robust optimization

Although deterministic optimization has to a considerable extent been successfully applied in various crashworthiness designs to improve passenger safety and reduce vehicle cost, the design could become less meaningful or even unacceptable when considering the perturbations of design variables and noises of system parameters. To overcome this drawback, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on multiple crashworthiness criteria, where several different sigma criteria are adopted to measure the variations. As an example, a full front impact of vehicle is considered with increase in energy absorption and reduction of structural weight as the design objectives, and peak deceleration as the constraint. A multiobjective particle swarm optimization is applied to generate robust Pareto solution, which no longer requires formulating a single cost function by using weighting factors or other means. From the example, a clear compromise between the Pareto deterministic and robust designs can be observed. The results demonstrate the advantages of using multiobjective robust optimization, with not only the increase in the energy absorption and decrease in structural weight from a baseline design, but also a significant improvement in the robustness of optimum.     

Multiobjective optimization–based fault‐tolerant flight control system design

The loss of measurements used for controller scheduling or envelope protection in modern flight control systems due to sensor failures leads to a challenging fault‐tolerant control law design problem. In this article, an approach to design such a robust fault‐tolerant control system, including full envelope protections using multiobjective optimization techniques, is proposed. The generic controller design and controller verification problems are derived and solved using novel multiobjective hybrid genetic optimization algorithms. These algorithms combine the multiobjective genetic search strategy with local, single‐objective optimization to improve convergence speed. The proposed strategies are applied to the design of a fault‐tolerant flight control system for a modern civil aircraft. The results of an industrial controller verification and validation campaign using an industrial benchmark simulator are reported.     

Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator

Most controllers optimization and design problems are multiobjective in nature, since they normally have several (possibly conflicting) objectives that must be satisfied at the same time. Instead of aiming at finding a single solution, the multiobjective optimization methods try to produce a set of good trade-off solutions from which the decision maker may select one. Several methods have been devised for solving multiobjective optimization problems in control systems field. Traditionally, classical optimization algorithms based on nonlinear programming or optimal control theories are applied to obtain the solution of such problems. The presence of multiple objectives in a problem usually gives rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Recently, Multiobjective Evolutionary Algorithms (MOEAs) have been applied to control systems problems. Compared with mathematical programming, MOEAs are very suitable to solve multiobjective optimization problems, because they deal simultaneously with a set of solutions and find a number of Pareto optimal solutions in a single run of algorithm. Starting from a set of initial solutions, MOEAs use iteratively improving optimization techniques to find the optimal solutions. In every iterative progress, MOEAs favor population-based Pareto dominance as a measure of fitness. In the MOEAs context, the Non-dominated Sorting Genetic Algorithm (NSGA-II) has been successfully applied to solving many multiobjective problems. This paper presents the design and the tuning of two PID (Proportional–Integral–Derivative) controllers through the NSGA-II approach. Simulation numerical results of multivariable PID control and convergence of the NSGA-II is presented and discussed with application in a robotic manipulator of two-degree-of-freedom. The proposed optimization method based on NSGA-II offers an effective way to implement simple but robust solutions providing a good reference tracking performance in closed loop.     

Ant colony approaches for multiobjective structural optimization problems with a cardinality constraint

Two Ant Colony Optimization algorithms are proposed to tackle multiobjective structural optimization problems with an additional constraint. A cardinality constraint is introduced in order to limit the number of distinct values of the design variables appearing in any candidate solution. Such constraint is directly enforced when an ant builds a candidate solution, while the other mechanical constraints are handled by means of an adaptive penalty method (APM). The test-problems are composed by structural optimization problems with discrete design variables, and the objectives are to minimize both the structure’s weight and its maximum nodal displacement. The Pareto sets generated in the computational experiments are evaluated by means of performance metrics, and the obtained designs are also compared with solutions available from single-objective studies in the literature.     

Robust control design using eigenstructure assignment and multi-objective optimization

This paper develops a new approach to multiple objective optimization design for robust multivariable control systems, based on eigenstructure assignment and genetic algorithms. It considers various performance indices (or cost functions) in the objectives, which are individual eigenvalue sensitivity functions, and the sensitivity and the complementary sensitivity functions in the frequency domain, instead of a single performance index for a control system. Based on these performance indices, the robustness criteria are expressed by a set of inequalities. The paper will make full use of the freedom provided by eigenstructure assignment to find a controller to satisfy the robustness criteria. A numerical algorithm for multi-objective optimization using genetic algorithm approaches is developed and applied to the simulation of a distillation column control system design     

A Novel Intelligent Multiobjective Simulated Annealing Algorithm for Designing Robust PID Controllers

This paper proposes an intelligent multiobjective simulated annealing algorithm (IMOSA) and its application to an optimal proportional integral derivative (PID) controller design problem. A well-designed PID-type controller should satisfy the following objectives: 1) disturbance attenuation; 2) robust stability; and 3) accurate setpoint tracking. The optimal PID controller design problem is a large-scale multiobjective optimization problem characterized by the following: 1) nonlinear multimodal search space; 2) large-scale search space; 3) three tight constraints; 4) multiple objectives; and 5) expensive objective function evaluations. In contrast to existing multiobjective algorithms of simulated annealing, the high performance in IMOSA arises mainly from a novel multiobjective generation mechanism using a Pareto-based scoring function without using heuristics. The multiobjective generation mechanism operates on a high-score nondominated solution using a systematic reasoning method based on an orthogonal experimental design, which exploits its neighborhood to economically generate a set of well-distributed nondominated solutions by considering individual and overall objectives. IMOSA is evaluated by using a practical design example of a super-maneuverable fighter aircraft system. An efficient existing multiobjective algorithm, the improved strength Pareto evolutionary algorithm, is also applied to the same example for comparison. Simulation results demonstrate high performance of the IMOSA-based method in designing robust PID controllers.     

Reliability-based robust assessment for multiobjective optimization design of improving occupant restraint system performance

Optimal performance of vehicle occupant restraint system (ORS) requires an accurate assessment of occupant injury values including head, neck and chest responses, etc. To provide a feasible framework for incorporating occupant injury characteristics into the ORS design schemes, this paper presents a reliability-based robust approach for the development of the ORS. The uncertainties of design variables are addressed and the general formulations of reliable and robust design are given in the optimization process. The ORS optimization is a highly nonlinear and large scale problem. In order to save the computational cost, an optimal sampling strategy is applied to generate sample points at the stage of design of experiment (DOE). Further, to efficiently obtain a robust approximation, the support vector regression (SVR) is suggested to construct the surrogate model in the vehicle ORS design process. The multiobjective particle swarm optimization (MPSO) algorithm is used for obtaining the Pareto optimal set with emphasis on resolving conflicting requirements from some of the objectives and the Monte Carlo simulation (MCS) method is applied to perform the reliability and robustness analysis. The differences of three different Pareto fronts of the deterministic, reliable and robust multiobjective optimization designs are compared and analyzed in this study. Finally, the reliability-based robust optimization result is verified by using sled system test. The result shows that the proposed reliability-based robust optimization design is efficient in solving ORS design optimization problems.     

Multiobjective optimization using variable complexity modelling for control system design

A multi-stage design approach that uses a multiobjective genetic algorithm as the framework for optimization and multiobjective preference articulation, and an H_infty loop-shaping technique are used to design controllers for a gas turbine engine. A non-linear model is used to assess performance of the controller. Because the computational load of applying multiobjective genetic algorithm to this control strategy is very high, a neural network and response surface models are used in order to speed up the design process within the framework of a multiobjective genetic algorithm. The final designs are checked using the original non-linear model.     

A Comparative study on multiobjective reliable and robust optimization for crashworthiness design of vehicle structure

Design optimization without considering uncertainties of system variables and parameters can be problematic in real life. In order to take into account the effect of uncertainties, reliable and robust design schemes have proven effective, but limited studies have been reported to compare their difference in a multiobjective framework. This paper takes a typical vehicle structure subject to offset frontal crashing scenario as an example to compare reliable and robust designs with their deterministic counterpart. The thicknesses of some key components of vehicle frontal structures were selected as design variables, the vehicle weight and energy absorption as the objectives, deceleration and firewall intrusion as the constraints. The deterministic multiobjective optimization problem was first solved by adopting Design of Experimental (DOE), metamodels and Non-dominated Sorting Genetic Algorithm II (NSGA-II). Take into account the uncertainties, a Monte Carlo Simulation (MCS) is adopted to generate random distributions of the objective and constraint functions for each design. For the reliability-based optimization the desired reliabilities of 90 %, 95 % and 99 % are considered, respectively. For the robustness-based optimization, two different formulation strategies are adopted. The optimization showed that the reliable and robust Pareto fronts are shifted away from their deterministic counterpart due to uncertainties. The different Pareto fronts yielded from the deterministic, reliable and robust designs are compared to provide some quantitative insights into how to apply these different design schemes for resolving uncertainty problems. It is shown that, compared with the baseline design, the optimizations enhance the crashworthiness of vehicle, though more conservative solutions could have been generated from the reliable and robust optimizations.     

Ergonomic Chair Design by Fusing Qualitative and Quantitative Criteria Using Interactive Genetic Algorithms

This paper emphasizes the necessity of formally bringing qualitative and quantitative criteria of ergonomic design together, and provides a novel complementary design framework with this aim. Within this framework, different design criteria are viewed as optimization objectives, and design solutions are iteratively improved through the cooperative efforts of computer and user. The framework is rooted in multiobjective optimization, genetic algorithms, and interactive user evaluation. Three different algorithms based on the framework are developed, and tested with an ergonomic chair design problem. The parallel and multiobjective approaches show promising results in fitness convergence, design diversity, and user satisfaction metrics.     

Evolutionary Multiobjective Design in Automotive Development

This paper describes the use of evolutionary algorithms to solve multiobjective optimization problems arising at different stages in the automotive design process. The problems considered are black box optimization scenarios: definitions of the decision space and the design objectives are given, together with a procedure to evaluate any decision alternative with regard to the design objectives, e.g., a simulation model. However, no further information about the objective function is available. In order to provide a practical introduction to the use of multiobjective evolutionary algorithms, this article explores the three following case studies: design space exploration of road trains, parameter optimization of adaptive cruise controllers, and multiobjective system identification. In addition, selected research topics in evolutionary multiobjective optimization will be illustrated along with each case study, highlighting the practical relevance of the theoretical results through real-world application examples. The algorithms used in these studies were implemented based on the PISA (Platform and Programming Language Independent Interface for Search Algorithm) framework. Besides helping to structure the presentation of different algorithms in a coherent way, PISA also reduces the implementation effort considerably.     

Coupling dynamic simulation and interactive multiobjective optimization for complex problems: An APROS-NIMBUS case study

Dynamic process simulators for plant-wide process simulation and multiobjective optimization tools can be used by industries as a means to cut costs and enhance profitability. Specifically, dynamic process simulators are useful in the process plant design phase, as they provide several benefits such as savings in time and costs. On the other hand, multiobjective optimization tools are useful in obtaining the best possible process designs when multiple conflicting objectives are to be optimized simultaneously. Here we concentrate on interactive multiobjective optimization. When multiobjective optimization methods are used in process design, they need an access to dynamic process simulators, hence it is desirable for them to coexist on the same software platform. However, such a co-existence is not common. Hence, users need to couple multiobjective optimization software and simulators, which may not be trivial. In this paper, we consider APROS, a dynamic process simulator and couple it with IND-NIMBUS, an interactive multiobjective optimization software. Specifically, we: (a) study the coupling of interactive multiobjective optimization with a dynamic process simulator; (b) bring out the importance of utilizing interactive multiobjective optimization; (c) propose an augmented interactive multiobjective optimization algorithm; and (d) apply an APROS-NIMBUS coupling for solving a dynamic optimization problem in a two-stage separation process.     

Multi-objective robust optimization using a sensitivity region concept

In multi-objective design optimization, it is quite desirable to obtain solutions that are multi-objectively optimum and insensitive to uncontrollable (noisy) parameter variations. We call such solutions robust Pareto solutions. In this paper we present a method to measure the multi-objective sensitivity of a design alternative, and an approach to use such a measure to obtain multi-objectively robust Pareto optimum solutions. Our sensitivity measure does not require a presumed probability distribution of uncontrollable parameters and does not utilize gradient information; therefore, it is applicable to multi-objective optimization problems that have non-differentiable and/or discontinuous objective functions, and also to problems with large parameter variations. As a demonstration, we apply our robust optimization method to an engineering example, the design of a vibrating platform. We show that the solutions obtained for this example are indeed robust.     

A new multiobjective clustering technique based on the concepts of stability and symmetry

Most clustering algorithms operate by optimizing (either implicitly or explicitly) a single measure of cluster solution quality. Such methods may perform well on some data sets but lack robustness with respect to variations in cluster shape, proximity, evenness and so forth. In this paper, we have proposed a multiobjective clustering technique which optimizes simultaneously two objectives, one reflecting the total cluster symmetry and the other reflecting the stability of the obtained partitions over different bootstrap samples of the data set. The proposed algorithm uses a recently developed simulated annealing-based multiobjective optimization technique, named AMOSA, as the underlying optimization strategy. Here, points are assigned to different clusters based on a newly defined point symmetry-based distance rather than the Euclidean distance. Results on several artificial and real-life data sets in comparison with another multiobjective clustering technique, MOCK, three single objective genetic algorithm-based automatic clustering techniques, VGAPS clustering, GCUK clustering and HNGA clustering, and several hybrid methods of determining the appropriate number of clusters from data sets show that the proposed technique is well suited to detect automatically the appropriate number of clusters as well as the appropriate partitioning from data sets having point symmetric clusters. The performance of AMOSA as the underlying optimization technique in the proposed clustering algorithm is also compared with PESA-II, another evolutionary multiobjective optimization technique.     

Multiobjective optimization and multiple constraint handling withevolutionary algorithms. I. A unified formulation

In optimization, multiple objectives and constraints cannot be handled independently of the underlying optimizer. Requirements such as continuity and differentiability of the cost surface add yet another conflicting element to the decision process. While “better” solutions should be rated higher than “worse” ones, the resulting cost landscape must also comply with such requirements. Evolutionary algorithms (EAs), which have found application in many areas not amenable to optimization by other methods, possess many characteristics desirable in a multiobjective optimizer, most notably the concerted handling of multiple candidate solutions. However, EAs are essentially unconstrained search techniques which require the assignment of a scalar measure of quality, or fitness, to such candidate solutions. After reviewing current revolutionary approaches to multiobjective and constrained optimization, the paper proposes that fitness assignment be interpreted as, or at least related to, a multicriterion decision process. A suitable decision making framework based on goals and priorities is subsequently formulated in terms of a relational operator, characterized, and shown to encompass a number of simpler decision strategies. Finally, the ranking of an arbitrary number of candidates is considered. The effect of preference changes on the cost surface seen by an EA is illustrated graphically for a simple problem. The paper concludes with the formulation of a multiobjective genetic algorithm based on the proposed decision strategy. Niche formation techniques are used to promote diversity among preferable candidates, and progressive articulation of preferences is shown to be possible as long as the genetic algorithm can recover from abrupt changes in the cost landscape     

多目标优化机制下DNA编码序列模型

针对现有DNA计算中存在的编码序列设计稳定性、可靠性不完善等问题,充分考虑基本编码问题,设计出一种基于多目标优化机制的DNA编码序列设计算法。在一定的约束条件下,该算法利用了多目标优化机制以及采取小种蚁群算法,将h-distance因子添加到单链DNA架构中,建立一种DNA序列公用方法。通过模拟实验表明,该算法与同类型算法相比,在计算效率、优化性方面具有一定优势。     

Multiobjective firefly algorithm for continuous optimization

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the methods for single objective optimization. To find the Pareto front and non-dominated set for a nonlinear multiobjective optimization problem may require significant computing effort, even for seemingly simple problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we extend the recently developed firefly algorithm to solve multiobjective optimization problems. We validate the proposed approach using a selected subset of test functions and then apply it to solve design optimization benchmarks. We will discuss our results and provide topics for further research.     

基于alpha支配的高维目标进化算法研究

基于Pareto支配的多目标进化算法能够很好地处理2～3维的多目标优化问题。但在处理高维多目标问题时,随着目标维数的增大,支配受阻解的数量急剧增加,导致现有的多目标算法存在选择压力不够、优化效果较差的问题。通过引入α支配提供严格的Pareto分层,在同层中挑选相对稀疏的解作为候选解,同时详细分析不同α对算法性能的影响,提出一种新的基于α偏序和拥塞距离抽样的高维目标进化算法。将该算法在DTLZ上进行性能测试,并采用世代距离(GD)、空间评价(SP)、超体积(HV)等多个指标评估算法的性能。实验结果表明,引入α支配能去除绝大部分支配受阻解(DRSs),提高算法的收敛性。与快速非支配排序算法(NSGA-II)、基于分解的多目标进化算法(MOEA/D)、基于距离更新的分解多目标进化算法(MOEA/D-DU)相比,该算法的整体解集的质量 有明显提高。     

Control-structure integrated multiobjective design for flexible spacecraft using MOEA/D

This paper proposes a multiobjective optimization method for the control-structure integrated design of flexible spacecraft to reduce the total mass and optimize the control performance. The equations of motion for flexible spacecraft are derived from the Lagrange’s principle and the assumed modes method. The design variables are the structural dimensions of the flexible structure and controller parameters. The objectives and constraints are derived from structure and control performance indexes. The objectives include total mass, control cost, and vibrational energy, and the constraints include the stability of the closed-loop system, settling time, overshoot, maximum control, and maximum vibrational displacement of the tip. A modified version of the multiobjective evolutionary algorithm based on decomposition (MOEA/D) with our proposed hybrid constraint handling method is proposed for optimization. As a case study, it has been applied to a spacecraft with symmetrically installed flexible appendages to find optimal tradeoffs in control-structure design. The simulation results show that the multiobjective optimization method for the control-structure integrated design of flexible spacecraft is feasible and effective, and could give an improvement of structural and control designs.