Target shape design optimization by evolving B-splines with cooperative coevolution

For problems involving uncertainties in design variables and parameters, a bi-objective evolutionary algorithm (EA) based approach to design optimization using evidence theory is proposed and implemented in this paper. In addition to a functional objective, a plausibility measure of failure of constraint satisfaction is minimized. Despite some interests in classical optimization literature, this is the first attempt to use evidence theory with an EA. Due to EA's flexibility in modifying its operators, nonrequirement of any gradient, its ability to handle multiple conflicting objectives, and ease of parallelization, evidence-based design optimization using an EA is promising. Results on a test problem and two engineering design problems show that the modified evolutionary multi-objective optimization algorithm is capable of finding a widely distributed trade-off frontier showing different optimal solutions corresponding to different levels of plausibility failure limits. Furthermore, a single-objective evidence-based EA is found to produce better optimal solutions than a previously reported classical optimization algorithm. Furthermore, the use of a graphical processing unit (GPU) based parallel computing platform demonstrates EA's performance enhancement around 160–700 times in implementing plausibility computations. Handling uncertainties of different types are getting increasingly popular in applied optimization studies and this EA based study is promising to be applied in real-world design optimization problems.

In this paper, we propose a hierarchical Cooperative Coevolution framework (hCC) to deal with the Very Large-scale Traveling Salesman Problem (VLSTSP). Due to the existence of the curse of dimensionality, it is difficult to find an acceptable solution for VLSTSP with conventional Evolutionary Algorithms (EAs). Cooperative Coevolution (CC) framework, which divides the problems into multiple subcomponents and optimizes them independently, offers a potential opportunity to find suitable solutions. However, conventional CC with large-scale sub-size decomposition will still be affected by the curse of dimensionality, and small-scale sub-size decomposition ignores many interactions between subcomponents. Although the initial sub-size of the proposed hCC is small-scale, the ignored interactions will be reconsidered in the higher layer of optimization. Another issue is how to decompose the VLSTSP. In the numerical experiments, we design two strategies: (1). Random decomposition. (2). Decomposition based on the greedy solution. 10 symmetric instances of VLSTSP ranging from 38,478 to 238,025 are employed to evaluate our proposal, and the basic optimizer is greedy Local Search (gLS). Experimental results show that our proposal has great potential and scalability to deal with VLSTSP, which can be easily extended to deal with various types of TSP.

A number of multi-objective evolutionary algorithms have been proposed in recent years and many of them have been used to solve engineering design optimization problems. However, designs need to be robust for real-life implementation, i.e. performance should not degrade substantially under expected variations in the variable values or operating conditions. Solutions of constrained robust design optimization problems should not be too close to the constraint boundaries so that they remain feasible under expected variations. A robust design optimization problem is far more computationally expensive than a design optimization problem as neighbourhood assessments of every solution are required to compute the performance variance and to ensure neighbourhood feasibility. A framework for robust design optimization using a surrogate model for neighbourhood assessments is introduced in this article. The robust design optimization problem is modelled as a multi-objective optimization problem with the aim of simultaneously maximizing performance and minimizing performance variance. A modified constraint-handling scheme is implemented to deal with neighbourhood feasibility. A radial basis function (RBF) network is used as a surrogate model and the accuracy of this model is maintained via periodic retraining. In addition to using surrogates to reduce computational time, the algorithm has been implemented on multiple processors using a master–slave topology. The preliminary results of two constrained robust design optimization problems indicate that substantial savings in the actual number of function evaluations are possible while maintaining an acceptable level of solution quality.

In this paper, a novel cooperative coevolution (CC)-based model predictive control (MPC) is proposed to deal with formation control problem. While conventional evolutionary algorithm (EA)-based MPC approaches cannot guarantee the stability, the proposed CC-based MPC guarantees the asymptotic stability regardless of the optimality of the solution that the CC-based algorithm generates with a small number of individuals. To guarantee the stability, a terminal state constraint is found, and then a repair algorithm is applied to all candidate solutions to meet the constraint. The cooperatively coevolving particle swarm optimization (CCPSO), most recently developed algorithm among CC-based EAs, is adopted and modified to fit into the formation control problem. Experiments are performed on a group of nonholonomic mobile robots to demonstrate the effectiveness of the CC-based MPC.

This paper presents a heuristic design optimization method specifically developed for practicing structural engineers. Practical design optimization problems are often governed by buildability constraints. The majority of optimization methods that have recently been proposed for design optimization under buildability constraints are based on evolutionary computing. While these methods are generally easy to implement, they require a large number of function evaluations (finite element analyses), and they involve algorithmic parameters that require careful tuning. As a consequence, both the computation time and the engineering time are high. The discrete design optimization algorithm presented in this paper is based on the optimality criteria method for continuous optimization. It is faster than an evolutionary algorithm and it is free of tuning parameters. The algorithm is successfully applied to two classical benchmark problems (the design of a ten-bar truss and an eight-story frame) and to a practical truss design optimization problem.

A number of game strategies have been developed in past decades and used in the fields of economics, engineering, computer science, and biology due to their efficiency in solving design optimization problems. In addition, research in multiobjective and multidisciplinary design optimization has focused on developing a robust and efficient optimization method so it can produce a set of high quality solutions with less computational time. In this paper, two optimization techniques are considered; the first optimization method uses multifidelity hierarchical Pareto-optimality. The second optimization method uses the combination of game strategies Nash-equilibrium and Pareto-optimality. This paper shows how game strategies can be coupled to multiobjective evolutionary algorithms and robust design techniques to produce a set of high quality solutions. Numerical results obtained from both optimization methods are compared in terms of computational expense and model quality. The benefits of using Hybrid and non-Hybrid-Game strategies are demonstrated.

Large-scale global optimization (LSGO) problems are emergent in many domains of applied sciences. LSGO is a hard challenge for the majority of state-of-the-art optimization methods. Evolution algorithms (EAs) combined with Cooperative Coevolution (CC) are able to perform well when solving many real-world LSGO problems. The grouping of variables at the problem decomposition stage has a significant impact on the performance of the CC approach. This study proposes an improvement of the previously developed random adaptive grouping (RAG) approach for CC. The new method is titled as RAG2, and the whole optimization algorithm, based on RAG2, is called CC-SHADE-RAG2. The influence of the choice of the population size and the number of subcomponents on the algorithm performance have been investigated using the IEEE LSGO CEC’2013 benchmark. The set of test problems in the benchmark contains fifteen functions with dimensionality equal to one thousand. We have also compared the performance of the novel algorithm with some EAs, which are applied for solving LSGO problems.

The paper presents an approach to design optimization using parallel evolutionary algorithms. The only use of a simple evolutionary algorithm in order to generate the optimal solution for complex problems can be ineffective due to long calculation time. Thus a tournament evolutionary algorithm (EA) and a parallel computation method are proposed and used. The proposed EA does not require an analysis of the optimization model for each potential solution from evolutionary populations. The second element of the method consists in parallel running of evolutionary algorithms using multi-threads approach. The experiments were carried out for many different single design optimization problems and two of them are presented in the paper. The first problem considers a task of robot gripper mechanism optimization and the second one deals with the optimization of a shaft based on Finite Element Method analysis. From the generated results it is clear that proposed approach is a very effective tool for solving fairly complicated tasks considering both the accuracy and the time of calculation.

Cooperation coevolution with fast interdependency identification for large scale optimization

An efficient combination of multi-objective evolutionary optimization and reliability analysis for reliability-based design optimization of truss structures

:A robust multi-objective wing design optimization procedure using CFD is presented in this work. Instead of directly applying CFD to wing design optimization, a Kriging aerodynamic model that approximates CFD result is proposed to save computational cost. By introducing 6σ robust approach as a sub-objective function, multi-objective wing design problems can be solved with aerodynamic robustness. Non-Uniform Rational B-Spline curves (NURBS) are introduced to depict the wing geometry in design optimization process. The most important parameters of the wing geometry can then be screened by design of experiment and treated as design variables due to the local variation property of NURBS. Under this formulation, a multi-objective genetic algorithm based on non-dominated sorting is employed to handle multiple flight conditions in wing design. The optimum wing geometry is selected according to trade-off among design objects on the non-dominated front. To validate the proposed approach, two robust design optimization cases are studied for ONERA-M6-Wing. It turns out that the drag coefficient is insensitive to Mach number between Ma0.8–Ma0.9 after robust optimization. The result also verifies the effectiveness of our method in boosting performance and robustness of multiple flight conditions: the lift curve slope (Ma0.3) of optimum wing and the 6σ objective function of transonic drag (Ma0.8–Ma0.9) increase by 11.9% and 25.4%, respectively. Observations in the optimization cases are concluded as follows: 1) For wing aerodynamic design problems, the multi-objective robust optimization can both improve the performance at different flight conditions and provide robustness. 2) The Kriging aerodynamic model derived from CFD result can satisfy the precision requirement of wing design. 3) Even though the optimization result is subject to the weights of the 6σ function in sub-object, the influence is not comparable to the trade-off among design objects. 4) The optimum solution obtained by proposed approach is superior to gradient based optimization method, while the computational cost is acceptable.

Evolutionary algorithms (EA), such as the genetic algorithm (GA), have found wide popularity because of their capability of global optimum search. As an answer to the quest for faster converging evolutionary algorithms, particle swarm optimization (PSO) was introduced to the electromagnetics domain (Robinson, J. and Rahmat-Samii, Y., IEEE Trans. Antennas Propag., vol.AP-52, no.2, p.397-407, 2004). PSO is a relatively new stochastic evolutionary computation technique, based on the movement and intelligence of swarms. PSO is found to hold a superior position with respect to other evolutionary methods, such as GA. Since PSO is a very recent method, many of its capabilities are still unexplored. It benefits from the inherent simplicity of GA while it converges much faster than conventional evolutionary algorithms. The paper presents a simple and universal design procedure for planar microwave filters. To accelerate the computation phase, an equivalent circuit topology is derived from FDTD formulation. The method is fast and robust and is well suited to the fast paced engineering design environment. As a case study, a microwave band-pass filter is designed.

Checkers is a very simple game and easy to learn. Unlike chess, it is simple to move and needs a few rules. With respect to checkers, the evolutionary algorithm can discover a neural network that can be used to play at a near-expert level without injecting expert knowledge about how to play the game. Evolutionary approach does not need any prior knowledge to develop machine player but can develop high-level player. However, conventional evolutionary algorithms have a property of genetic drift that only one solution often dominates at the last generation. Because of genetic drift, it is difficult to discover diverse checkers players that have different properties in search space with simple evolutionary algorithm. Combining diverse solutions can make better performance than single dominating solution by complementing each other.

In this paper, an algorithm is proposed to solve the problem of optimal selected harmonic elimination (SHE) pulse-width modulation (PWM) under a fuzzy constraint that consecutive switching angles are well separated from each other. The problem is first formulated to a fuzzy constrained optimization problem and then a Quantum-inspired Evolutionary Algorithm, which is more efficient than conventional evolutionary algorithms, is applied to approximate the fuzzy solution. The proposed method can effectively reduce switching losses and the probability of switch damages in inverter bridges, and thus can improve the performance of PWM strategy and extend the life of the inverter. This work is the first report on successful application of a Quantum-inspired Evolutionary Algorithm to solve the fuzzy constrained optimization problem.

Complex engineering design (CED) optimization problems in science and engineering commonly have large design spaces. In such design spaces, typically thousands of exact fitness evaluations are required to locate a near optimal design. Often in photonics, electromagnetic, aerospace, biomedical and microwave circuits detailed design processes, variable-fidelity analysis codes are employed to strike a balance between design cost, time and estimation accuracy. Nevertheless, in analysis and design optimization processes where high-fidelity analysis codes are used, each exact fitness evaluation requiring the simulation of analysis codes may cost hours of supercomputer time. Therefore, the overwhelming part of the total run time in CED optimization is usually taken up by the simulation of analysis codes. This often poses a serious impediment to the practical application of high-fidelity analysis codes and evolutionary algorithms to CED optimization problems.