Multiobjective optimization of trusses using genetic algorithms

In this paper we propose the use of the genetic algorithm (GA) as a tool to solve multiobjective optimization problems in structures. Using the concept of min–max optimum, a new GA-based multiobjective optimization technique is proposed and two truss design problems are solved using it. The results produced by this new approach are compared to those produced by other mathematical programming techniques and GA-based approaches, proving that this technique generates better trade-offs and that the genetic algorithm can be used as a reliable numerical optimization tool.     

Topology design of large displacement compliant mechanisms with multiple materials and multiple output ports

Topology optimization of compliant mechanisms is presented in this paper wherein the layout design problem is addressed in its original binary or discrete (0-1) form. Design variables are modeled as discrete variables and allowed to assume values pertaining only to their void (0) or solid (1) states. Due to this discrete nature, a genetic algorithm is employed as an optimization routine. Using the barrier assignment approach, the search algorithm is extended to use with multiple materials. The layout design of compliant mechanisms is performed wherein displacements at multiple points (ports) in the design region are maximized along the respective prescribed directions. With multiple output ports and multiple materials, additional freedom in motion and force transduction can be achieved with compliant mechanisms. Geometrically large deformation analysis is employed to compute the displacement-based multiple objectives that are extremized using Nondominated Sorting in Genetic Algorithms (or NSGA). With genetic algorithms, buckling or snap through like issues with nonconvergent solutions in the population when computing nonlinear deformations can be implicitly circumvented.     

Performance evaluation of evolutionary multiobjective optimization algorithms for multiobjective fuzzy genetics-based machine learning

Recently, evolutionary multiobjective optimization (EMO) algorithms have been utilized for the design of accurate and interpretable fuzzy rule-based systems. This research area is often referred to as multiobjective genetic fuzzy systems (MoGFS), where EMO algorithms are used to search for non-dominated fuzzy rule-based systems with respect to their accuracy and interpretability. In this paper, we examine the ability of EMO algorithms to efficiently search for Pareto optimal or near Pareto optimal fuzzy rule-based systems for classification problems. We use NSGA-II (elitist non-dominated sorting genetic algorithm), its variants, and MOEA/D (multiobjective evolutionary algorithm based on decomposition) in our multiobjective fuzzy genetics-based machine learning (MoFGBML) algorithm. Classification performance of obtained fuzzy rule-based systems by each EMO algorithm is evaluated for training data and test data under various settings of the available computation load and the granularity of fuzzy partitions. Experimental results in this paper suggest that reported classification performance of MoGFS in the literature can be further improved using more computation load, more efficient EMO algorithms, and/or more antecedent fuzzy sets from finer fuzzy partitions.     

A Genetic Algorithm for Multiobjective Robust Design

The goal of robust design is to develop stable products that exhibit minimum sensitivity to uncontrollable variations. The main drawback of many quality engineering approaches, including Taguchi's ideology, is that they cannot efficiently handle presence of several often conflicting objectives and constraints that occur in various design environments.Classical vector optimization and multiobjective genetic algorithms offer numerous techniques for simultaneous optimization of multiple responses, but they have not addressed the central quality control activities of tolerance design and parameter optimization. Due to their ability to search populations of candidate designs in parallel without assumptions of continuity, unimodality or convexity of underlying objectives, genetic algorithms are an especially viable tool for off-line quality control.In this paper we introduce a new methodology which integrates key concepts from diverse fields of robust design, multiobjective optimization and genetic algorithms. The genetic algorithm developed in this work applies natural genetic operators of reproduction, crossover and mutation to evolve populations of hyper-rectangular design regions while simultaneously reducing the sensitivity of the generated designs to uncontrollable variations. The improvement in quality of successive generations of designs is achieved by conducting orthogonal array experiments as to increase the average signal-to-noise ratio of a pool of candidate designs from one generation to the next.     

Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling

This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Pareto front. On the other hand, the main negative effect is the increase in the computation time per generation. Thus, the number of generations is decreased when the available computation time is limited. As a result, the global search ability of EMO algorithms is not fully utilized. These positive and negative effects are examined by computational experiments on multiobjective permutation flowshop scheduling problems. Results of our computational experiments clearly show the importance of striking a balance between genetic search and local search. In this paper, we first modify our former multiobjective genetic local search (MOGLS) algorithm by choosing only good individuals as initial solutions for local search and assigning an appropriate local search direction to each initial solution. Next, we demonstrate the importance of striking a balance between genetic search and local search through computational experiments. Then we compare the modified MOGLS with recently developed EMO algorithms: the strength Pareto evolutionary algorithm and revised nondominated sorting genetic algorithm. Finally, we demonstrate that a local search can be easily combined with those EMO algorithms for designing multiobjective memetic algorithms.     

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.     

A strain based topology optimization method for compliant mechanism design

The Energy based topology optimization method has been used in the design of compliant mechanisms for many years. Although many successful examples from the energy based topology optimization method have been presented, optimized configurations of these designs are often very similar to their rigid linkage counterparts; except using compliant joints in place of rigid links. These complaint joints will endure large strain under the applied forces in order to perform the specified motions which are very undesirable in a compliant mechanism design. In this paper, a strain based topology optimization method is proposed to avoid a localized high strain of the compliant mechanism design, which is one of the drawbacks using strain energy formulation. Therefore, instead of minimizing the strain energy for structural rigidity, a global effective strain function is minimized. This is done in order to distribute the strain within the entire mechanism while maximizing the structural rigidity. Furthermore, the physical programming method is adopted to accommodate both flexibility and rigidity design objectives. Design examples from both the strain energy based topology optimization and the strain based method are presented and discussed.     

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.     

Multiobjective cuckoo search for design optimization

Many design problems in engineering are typically multiobjective, under complex nonlinear constraints. The algorithms needed to solve multiobjective problems can be significantly different from the methods for single objective optimization. Computing effort and the number of function evaluations may often increase significantly for multiobjective problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we formulate a new cuckoo search for multiobjective optimization. We validate it against a set of multiobjective test functions, and then apply it to solve structural design problems such as beam design and disc brake design. In addition, we also analyze the main characteristics of the algorithm and their implications.     

基于自适应变异的多目标鸽群优化的无人机目标搜索

无人机在搜索任务中起着关键的作用,它能够在复杂环境中寻找到目标.无人机搜索问题是一个相对复杂的多约束条件下的多目标优化问题.大多数搜索算法不能满足搜索过程中高效率和低功耗的要求.本文所采用的目标搜索方法是一种基于Agent路由和光传感器的解耦滚动时域方法.为了优化目标搜索方法的参数,本文提出一种基于Agent路由和光传感器的自适应变异多目标鸽群优化(AMMOPIO)算法.利用自适应飞行机制可以获得较好的鸽群分布,种群具有多样性和收敛性.利用变异机制简化了鸽群优化算法中的模型,提高了搜索效率.实验仿真结果验证了所提出的AMMOPIO算法在目标搜索问题中的可行性和有效性.     

Evolutionary optimization of a geometrically refined truss

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly, traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This paper will present a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation—genetic algorithms and differential evolution—to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this paper, specifically, a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization tool set.     

Application of genetic algorithms to conceptual design of a micro-air vehicle

This paper investigates the feasibility of automating the conceptual design of a micro-air vehicle on a personal computer system. The proposed design methodology adopts the use of genetic algorithms as the search engine in the design process. The multidisciplinary optimization problem here is to maximize the lift-to-drag ratio subjected to static longitudinal stability, performance and physical constraints. The six design parameters chosen are angle of attack, main wing twist angle, winglet span, main wing chord length, main wing taper ratio and winglet taper ratio. A case study has been carried out to compare the performance of using genetic algorithms with well-established non-linear optimization method based on sequential quadratic programming.     

Target-matching test problem for multiobjective topology optimization using genetic algorithms

This paper describes the multiobjective topology optimization of continuum structures solved as a discrete optimization problem using a multiobjective genetic algorithm (GA) with proficient constraint handling. Crucial to the effectiveness of the methodology is the use of a morphological geometry representation that defines valid structural geometries that are inherently free from checkerboard patterns, disconnected segments, or poor connectivity. A graph- theoretic chromosome encoding, together with compatible reproduction operators, helps facilitate the transmission of topological/shape characteristics across generations in the evolutionary process. A multicriterion target-matching problem developed here is a novel test problem, where a predefined target geometry is the known optimum solution, and the good results obtained in solving this problem provide a convincing demonstration and a quantitative measure of how close to the true optimum the solutions achieved by GA methods can be. The methodology is then used to successfully design a path-generating compliant mechanism by solving a multicriterion structural topology optimization problem.     

Human-competitive lens system design with evolution strategies

Lens system design provides ideal problems for evolutionary algorithms: a complex non-linear optimization task, often with intricate physical constraints, for which there is no analytical solutions. This paper demonstrates, through the use of two evolution strategies, namely non-isotropic Self-Adaptive evolution strategy (SA-ES) and Covariance Matrix Adaptation evolution strategy (CMA-ES), as well as multiobjective Non-Dominated Sort Genetic Algorithm 2 (NSGA-II) optimization, the human competitiveness of an approach where an evolutionary algorithm is hybridized with a local search algorithm to solve both a classic benchmark problem, and a real-world problem.     

经费分配中基于多目标优化的遗传规划模型

在传统遗传规划中引入多目标优化原理,探索新的经费分配方法和管理模式,建立了一种多目标优化的非线性遗传规划模型,提出了一种先进的基于正交试验的新型混合遗传算法来求解该问题.对求解过程中的选择算子、交叉算子和变异算子等进行正交试验,得到的种群个体明显优于基本遗传算法的个体.这种基于多目标优化的遗传规划模型能产生精度更高的最优解,通过对经费分配问题的实验验证,得到了较好的结果.     

Multiobjective fuzzy mathematical model for a financially constrained closed-loop supply chain with labor employment

This paper addresses the multiobjective, multiproducts and multiperiod closed-loop supply chain network design with uncertain parameters, whose aim is to incorporate the financial flow as the cash flow and debts' constraints and labor employment under fuzzy uncertainty. The objectives of the proposed mathematical model are to maximize the increase in cash flow, maximize the total created jobs in the supply chain, and maximize the reliability of consumed raw materials. To encounter the fuzzy uncertainty in this model, a possibilistic programming approach is used. To solve large-sized problems, the multiobjective simulated annealing algorithm, multiobjective gray wolf optimization, and multiobjective invasive weed optimization are proposed and developed. The numerical results demonstrate that these algorithms solve the problems within about 1% of the required solving time for the augmented ε-constraint and have similar performance and even better in some cases. The multiobjective simulated annealing algorithm with a weak performance takes less time than the other two algorithms. The multiobjective gray wolf optimization and multiobjective invasive weed optimization algorithms are superior based on the multiobjective performance indices.     

An advanced multiobjective genetic algorithm design for the time and space assembly line balancing problem

Time and space assembly line balancing considers realistic multiobjective versions of the classical assembly line balancing industrial problems involving the joint optimization of conflicting criteria such as the cycle time, the number of stations, and/or the area of these stations. In addition to their multi-criteria nature, the different problems included in this field inherit the precedence constraints and the cycle time limitations from assembly line balancing problems, which altogether make them very hard to solve. Therefore, time and space assembly line balancing problems have been mainly tackled using multiobjective constructive metaheuristics. Global search algorithms in general - and multiobjective genetic algorithms in particular - have shown to be ineffective to solve them up to now because the existing approaches lack of a proper design taking into account the specific characteristics of this family of problems. The aim of this contribution is to demonstrate the latter assumption by proposing an advanced multiobjective genetic algorithm design for the 1/3 variant of the time and space assembly line balancing problem which involves the joint minimization of the number and the area of the stations given a fixed cycle time limit. This novel design takes the well known NSGA-II algorithm as a base and considers the use of a new coding scheme and sophisticated problem specific operators to properly deal with the said problematic questions. A detailed experimental study considering 10 different problem instances (including a real-world instance from the Nissan plant in Barcelona, Spain) will show the good yield of the new proposal in comparison with the state-of-the-art methods.     

Genetic algorithms optimization for normalized normal constraint method under Pareto construction

This paper presents the resolution of multiobjective optimization problems as a tool in engineering design. In the literature, the solutions of this problems are based on the Pareto frontier construction. Therefore, substantial efforts have been made in recent years to develop methods for the construction of Pareto frontiers that guarantee uniform distribution and exclude the non-Pareto and local Pareto points. The normalized normal constraint is a recent contribution that generates a well-distributed Pareto frontier. Nevertheless, these methods are susceptible of improvement or modifications to obtain the same level of results more efficiently. This paper proposes a modification of the original normalized normal constraint method using a genetic algorithms in the optimization task. The results presented in this paper show a suitable behavior for the genetic algorithms method compared to classical Gauss–Newton optimization methods which are used by the original normalized normal constraint method.     

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.     

Grammar-based generation of stochastic local search heuristics through automatic algorithm configuration tools

Several grammar-based genetic programming algorithms have been proposed in the literature to automatically generate heuristics for hard optimization problems. These approaches specify the algorithmic building blocks and the way in which they can be combined in a grammar; the best heuristic for the problem being tackled is found by an evolutionary algorithm that searches in the algorithm design space defined by the grammar.In this work, we propose a novel representation of the grammar by a sequence of categorical, integer, and real-valued parameters. We then use a tool for automatic algorithm configuration to search for the best algorithm for the problem at hand. Our experimental evaluation on the one-dimensional bin packing problem and the permutation flowshop problem with weighted tardiness objective shows that the proposed approach produces better algorithms than grammatical evolution, a well-established variant of grammar-based genetic programming. The reasons behind such improvement lie both in the representation proposed and in the method used to search the algorithm design space.