Optimization of the p-xylene oxidation process by a multi-objective differential evolution algorithm with adaptive parameters co-derived with the population-based incremental learning algorithm

Different operating conditions of p-xylene oxidation have different influences on the product, purified terephthalic acid. It is necessary to obtain the optimal combination of reaction conditions to ensure the quality of the products, cut down on consumption and increase revenues. A multi-objective differential evolution (MODE) algorithm co-evolved with the population-based incremental learning (PBIL) algorithm, called PBMODE, is proposed. The PBMODE algorithm was designed as a co-evolutionary system. Each individual has its own parameter individual, which is co-evolved by PBIL. PBIL uses statistical analysis to build a model based on the corresponding symbiotic individuals of the superior original individuals during the main evolutionary process. The results of simulations and statistical analysis indicate that the overall performance of the PBMODE algorithm is better than that of the compared algorithms and it can be used to optimize the operating conditions of the p-xylene oxidation process effectively and efficiently.     

A new multi-objective particle swarm optimizer using empirical movement and diversified search strategies

Most real-world optimization problems involve the optimization task of more than a single objective function and, therefore, require a great amount of computational effort as the solution procedure is designed to anchor multiple compromised optimal solutions. Abundant multi-objective evolutionary algorithms (MOEAs) for multi-objective optimization have appeared in the literature over the past two decades. In this article, a new proposal by means of particle swarm optimization is addressed for solving multi-objective optimization problems. The proposed algorithm is constructed based on the concept of Pareto dominance, taking both the diversified search and empirical movement strategies into account. The proposed particle swarm MOEA with these two strategies is thus dubbed the empirical-movement diversified-search multi-objective particle swarm optimizer (EMDS-MOPSO). Its performance is assessed in terms of a suite of standard benchmark functions taken from the literature and compared to other four state-of-the-art MOEAs. The computational results demonstrate that the proposed algorithm shows great promise in solving multi-objective optimization problems.     

Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems

Two techniques for the numerical treatment of multi-objective optimization problems—a continuation method and a particle swarm optimizer—are combined in order to unite their particular advantages. Continuation methods can be applied very efficiently to perform the search along the Pareto set, even for high-dimensional models, but are of local nature. In contrast, many multi-objective particle swarm optimizers tend to have slow convergence, but instead accomplish the ‘global task’ well. An algorithm which combines these two techniques is proposed, some convergence results for continuous models are provided, possible realizations are discussed, and finally some numerical results are presented indicating the strength of this novel approach.     

A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization

A concurrent-hybrid non-dominated sorting genetic algorithm (hybrid NSGA-II) has been developed and applied to the simultaneous optimization of the annual energy production, flapwise root-bending moment and mass of the NREL 5 MW wind-turbine blade. By hybridizing a multi-objective evolutionary algorithm (MOEA) with gradient-based local search, it is believed that the optimal set of blade designs could be achieved in lower computational cost than for a conventional MOEA. To measure the convergence between the hybrid and non-hybrid NSGA-II on a wind-turbine blade optimization problem, a computationally intensive case was performed using the non-hybrid NSGA-II. From this particular case, a three-dimensional surface representing the optimal trade-off between the annual energy production, flapwise root-bending moment and blade mass was achieved. The inclusion of local gradients in the blade optimization, however, shows no improvement in the convergence for this three-objective problem.     

一种基于“探测"与“开采"的多目标进化算法

针对实践中多目标优化问题(MOPs)的Pareto解集(PS)未知且比较复杂的特性,提出了一种基于"探测"(Exploration)与"开采"(Exploitation)的多目标进化算法(MOEA)——MOEA/2E。该算法在进化过程中采用"探测"与"开采"相结合的方法,用进化操作不断地探测新的搜索区域,用局部搜索充分开采优秀的解区域,并用隐最优个体保留机制保存每一代的最优个体。与目前最流行且有效的多目标进化算法NSGA-Ⅱ及SPEA-Ⅱ进行的比较实验结果表明,MOEA/2E获得的Pareto最优解集具有更好的收敛性与分布性。     

AMGA2: improving the performance of the archive-based micro-genetic algorithm for multi-objective optimization

In this article, an improved Archive-based Micro Genetic Algorithm (referred to as AMGA2) for constrained multi-objective optimization is proposed. AMGA2 is designed to obtain fast and reliable convergence on a wide variety of optimization problems. AMGA2 benefits from the existing literature in that it borrows and improves upon several concepts from existing multi-objective optimization algorithms. Improvements and modifications to the existing diversity assessment techniques and genetic variation operators are also proposed. AMGA2 employs a new kind of selection strategy that attempts to reduce the probability of exploring less desirable search regions. The proposed AMGA2 is a steady-state genetic algorithm that maintains an external archive of best and diverse solutions and a very small working population. AMGA2 has been designed to facilitate the decoupling of the working population, the external archive, and the number of solutions desired as the outcome of the optimization process. Comprehensive benchmarking and comparison of AMGA2 with the current state-of-the-art multi-objective optimization algorithms demonstrate its improved search capability.     

Evolutionary Algorithm Integrating Stress Heuristics for Truss Optimization

The optimal truss design using problem-oriented evolutionary algorithm is presented in the paper. The minimum weight structures subjected to stress and displacement constraints are searched. The discrete design variables are areas of members, selected from catalogues of available sections. The integration of the problem specific knowledge into the optimization procedure is proposed. The heuristic rules based on the concept of fully stressed design are introduced through special genetic operators, which use the information concerning the stress distribution of structural members. Moreover, approximated solutions obtained by deterministic, sequential discrete optimization methods are inserted into the initial population. The obtained hybrid evolutionary algorithm is specialized for truss design. Benchmark problems are calculated in numerical examples. The knowledge about the problem integrated into the evolutionary algorithm can enhance considerably the effectiveness of the approach and improve significantly the convergence rate and the quality of the results. The advantages and drawbacks of the proposed method are discussed.     

Hybrid evolutionary multi-objective optimization and analysis of machining operations

Evolutionary multi-objective optimization (EMO) has received significant attention in recent studies in engineering design and analysis due to its flexibility, wide-spread applicability and ability to find multiple trade-off solutions. Optimal machining parameter determination is an important matter for ensuring an efficient working of a machining process. In this article, the use of an EMO algorithm and a suitable local search procedure to optimize the machining parameters (cutting speed, feed and depth of cut) in turning operations is described. Thereafter, the efficiency of the proposed methodology is demonstrated through two case studies – one having two objectives and the other having three objectives. Then, EMO solutions are modified using a local search procedure to achieve a better convergence property. It has been demonstrated here that a proposed heuristics-based local search procedure in which the problem-specific heuristics are derived from an innovization study performed on the EMO solutions is a computationally faster approach than the original EMO procedure. The methodology adopted in this article can be used in other machining tasks or in other engineering design activities.     

Hybrid evolutionary multi-objective algorithms for integrating assembly sequence planning and assembly line balancing

Assembly sequence planning (ASP) and assembly line balancing (ALB) play critical roles in designing product assembly systems. In view of the trend of concurrent engineering, pondering simultaneously over these two problems in the development of assembly systems is significant for establishing a manufacturing system. This paper contemplates the assembly tool change and the assembly direction as measurements in ASP; and further, Equal Piles assembly line strategy is adopted and the imbalanced status of the system employed as criteria for the evaluation concerning ALB. Focus of the paper is principally on proposing hybrid evolutionary multiple-objective algorithms (HEMOAs) for solutions with regard to integrate the evolutionary multi-objective optimization and grouping genetic algorithms. The results provide a set of objectives and amend Pareto-optimal solutions to benefit decision makers in the assembly plan. In addition, an implemented decision analytic model supports the preference selection from the Pareto-optimal ones. Finally, the exemplifications demonstrate the effectiveness and performance of the proposed algorithm. The consequences definitely illustrate that HEMOAs search out Pareto-optimal solutions effectively and contribute to references for the flexible change of assembly system design.     

Truss topology,shape and sizing optimization by fully stressed design based on hybrid grey wolf optimization and adaptive differential evolution

A hybrid adaptive optimization algorithm based on integrating grey wolf optimization into adaptive differential evolution with fully stressed design (FSD) local search is presented in this article. Hybrid reproduction and control parameter adaptation strategies are employed to increase the performance of the algorithm. The proposed algorithm, called fully stressed design–grey wolf–adaptive differential evolution (FSD-GWADE), is demonstrated to tackle a variety of truss optimization problems. The problems have mixed continuous/discrete design variables that are assigned as simultaneous topology, shape and sizing design variables. FSD-GWADE provides competitive results and gives superior results at a higher success rate than the previous FSD-based algorithm.     

Scalability of surrogate-assisted multi-objective optimization of antenna structures exploiting variable-fidelity electromagnetic simulation models

Multi-objective optimization of antenna structures is a challenging task owing to the high computational cost of evaluating the design objectives as well as the large number of adjustable parameters. Design speed-up can be achieved by means of surrogate-based optimization techniques. In particular, a combination of variable-fidelity electromagnetic (EM) simulations, design space reduction techniques, response surface approximation models and design refinement methods permits identification of the Pareto-optimal set of designs within a reasonable timeframe. Here, a study concerning the scalability of surrogate-assisted multi-objective antenna design is carried out based on a set of benchmark problems, with the dimensionality of the design space ranging from six to 24 and a CPU cost of the EM antenna model from 10 to 20 min per simulation. Numerical results indicate that the computational overhead of the design process increases more or less quadratically with the number of adjustable geometric parameters of the antenna structure at hand, which is a promising result from the point of view of handling even more complex problems.     

结构主动控制的一体化多目标优化研究

基于Pareto多目标遗传算法提出了结构主动控制系统的一体化多目标优化设计方法,对作动器位置与主动控制器进行同步优化设计.外界激励采用平稳过滤白噪声来模拟,在状态空间下通过求解Lyapunov方程,得到结构响应和主动控制力的均方值.主动控制器采用LQG控制算法来进行设计.以结构位移和加速度均方值最大值与相应无控响应均方值的最大值之比,以及所需控制力均方值之和作为多目标同步优化的目标函数.优化过程还考虑了结构与激励参数对优化结果的影响.最后以某6层平面框架有限元模型为例进行了计算机仿真分析,结果表明所提出的主动控制系统多目标一体化优化方法简单,高效,实用,具有较好的普适性.     

Hybrid particle swarm optimizer for a class of dynamic fitness landscape

This article presents the use of particle swarm optimization (PSO) for a class of non-stationary environments. The dynamic problems studied in this work are restricted to one of the possible types of changes that can be produced over the fitness landscape. A hybrid PSO approach (called HPSO_dyn) is proposed, which uses a dynamic macromutation operator to maintain diversity. In order to validate the approach, a test case generator previously proposed in the specialized literature was adopted. Such a test case generator allows the creation of different types of dynamic environments with a varying degree of complexity. The main goals of this research were to analyze the ability of HPSO_dyn to react to the changes in the environment, to study the influence of the dynamic macromutation operator on the algorithm's performance and finally, to analyze the algorithm's behavior in the presence of high multimodality.     

A multi-objective approach for multi-material topology and shape optimization

An automated multi-material approach that integrates multi-objective Topology Optimization (TO) and multi-objective shape optimization is presented. A new ant colony optimization algorithm is presented and applied to solving the TO problem, estimating a trade-off set of initial topologies or distributions of material. The solutions found usually present irregular boundaries, which are not desirable in applications. Thus, shape parameterization of the internal boundaries of the design region, and subsequent shape optimization, is performed to improve the quality of the estimated Pareto-optimal solutions. The selection of solutions for shape optimization is done by using the PROMETHEE II decision-making method. The parameterization process involves identifying the boundaries of different materials and describing these boundaries by non-uniform rational B-spline curves. The proposed approach is applied to the optimization of a C-core magnetic actuator, with two objectives: the maximization of the attractive force on the armature and the minimization of the volume of permanent magnet material.     

Blast furnace charging optimization using multi-objective evolutionary and genetic algorithms

Charging programs giving rise to desired burden and gas distributions in the ironmaking blast furnace were detected through an evolutionary multi-objective optimization strategy. The Pareto optimality condition traditionally used in such studies was substituted by a recently developed k-optimality criterion that allowed for simultaneous optimization of a large number of objectives, leading to a significant improvement over the results of earlier studies. A large number of optimum charging strategies were identified through this procedure and thoroughly analyzed, in view of an efficient blast furnace operation.     

A global single-loop deterministic approach for reliability-based design optimization of truss structures with continuous and discrete design variables

A single-loop deterministic method (SLDM) has previously been proposed for solving reliability-based design optimization (RBDO) problems. In SLDM, probabilistic constraints are converted to approximate deterministic constraints. Consequently, RBDO problems can be transformed into approximate deterministic optimization problems, and hence the computational cost of solving such problems is reduced significantly. However, SLDM is limited to continuous design variables, and the obtained solutions are often trapped into local extrema. To overcome these two disadvantages, a global single-loop deterministic approach is developed in this article, and then it is applied to solve the RBDO problems of truss structures with both continuous and discrete design variables. The proposed approach is a combination of SLDM and improved differential evolution (IDE). The IDE algorithm is an improved version of the original differential evolution (DE) algorithm with two improvements: a roulette wheel selection with stochastic acceptance and an elitist selection technique. These improvements are applied to the mutation and selection phases of DE to enhance its convergence rate and accuracy. To demonstrate the reliability, efficiency and applicability of the proposed method, three numerical examples are executed, and the obtained results are compared with those available in the literature.     

A new multi-objective optimization model for preventive maintenance and replacement scheduling of multi-component systems

In this article, a new multi-objective optimization model is developed to determine the optimal preventive maintenance and replacement schedules in a repairable and maintainable multi-component system. In this model, the planning horizon is divided into discrete and equally-sized periods in which three possible actions must be planned for each component, namely maintenance, replacement, or do nothing. The objective is to determine a plan of actions for each component in the system while minimizing the total cost and maximizing overall system reliability simultaneously over the planning horizon. Because of the complexity, combinatorial and highly nonlinear structure of the mathematical model, two metaheuristic solution methods, generational genetic algorithm, and a simulated annealing are applied to tackle the problem. The Pareto optimal solutions that provide good tradeoffs between the total cost and the overall reliability of the system can be obtained by the solution approach. Such a modeling approach should be useful for maintenance planners and engineers tasked with the problem of developing recommended maintenance plans for complex systems of components.     

A Comparative Study of the Mechanical Performance and Cost of Metal, FRP, and Hybrid Beams

Aluminum, FRP, and aluminum/FRP hybrid box beams designed for minimum weight are compared. The FRP beams consist of ±45° angle-ply windings with an intercalated unidirectional layer in the flanges. The hybrid beams consist of aluminum for the predominantly shear-loaded webs and part of the flange, and FRP in the parts of the flange with the maximum tensile or compressive stresses. All-CFRP beams have the lowest weight for a desired stiffness or strength, providing up to nearly 70% weight saving compared to aluminum beams. Hybrid beams are slightly heavier than all-composite beams, with up to 56% weight saving compared to aluminum, but they are easier and less expensive to produce. A hybrid beam can be produced at the same cost as an equivalent aluminum beam at a higher, more realistic CFRP price than an all-CFRP beam. Other advantages of aluminum/CFRP hybrids are increased ductility, a high fatigue resistance, and joining using conventional techniques for metals.     

Enhanced particle swarm optimization for size and shape optimization of truss structures

This article presents an enhanced particle swarm optimization (EPSO) algorithm for size and shape optimization of truss structures. The proposed EPSO introduces a particle categorization mechanism into the particle swarm optimization (PSO) to eliminate unnecessary structural analyses during the optimization process and improve the computational efficiency of the PSO-based structural optimization. The numerical investigation, including three benchmark truss optimization problems, examines the efficiency of the EPSO. The results demonstrate that the particle categorization mechanism greatly reduces the computational requirements of the PSO-based approaches while maintaining the original search capability of the algorithms in solving optimization problems with computationally cheap objective function and expensive constraints.     

A multicriteria evolutionary algorithm for mechanical design optimization with expert rules

This paper addresses the problem of optimizing mechanical components during the first stage of the design process. While a previous study focused on parameterized designs with fixed configurations—which led to the development of the PAMUC (Preferences Applied to Multiobjectivity and Constraints) method, to tackle constraints and preferences in evolutionary algorithms (EAs)—, the models to be considered in this work are enriched by the presence of topological variables. In this context, in order to create optimal but also realistic designs, i.e. fulfilling not only technical requirements but also technological constraints (more naturally expressed in terms of rules), a novel approach is proposed: PAMUC II. It consists in integrating an inference engine within the EA to repair the individuals violating the user‐defined rules. PAMUC II is tested on mechanical benchmarks, and provides very satisfactory results in comparison with a weighted sum method with penalization to deal with the constraints. Copyright © 2004 John Wiley & Sons, Ltd.