Real-world Design Optimization Problems Research Articles

Surrogate-assisted hybrid evolutionary algorithm with local estimation of distribution for expensive mixed-variable optimization problems

Some real-world design optimization problems can be formulated as expensive mixed-variable optimization problems (EMVOPs), which involve both continuous and discrete decision variables and expensive function evaluations. The main challenges for solving EMVOPs are the handling of mixed variables, limited number of function evaluations and multiple disconnected regions in the search space. In this work, we propose a novel algorithm with global and local search strategies for improving the search ability on disconnected regions, and it only consumes hundreds of function evaluations. The global module employs hybrid evolutionary operators and a Gower distance based surrogate model for handling mixed variables. The local estimation of distributions in different local regions performs in a competitive switching way to combine their advantages, and local surrogate models trained with selected samples improve the accuracy of approximated evaluations for the locally generated solutions. In the late stage, a local continuous search module is executed for refining the continuous decision variables. Verification results on the artificial benchmarks demonstrate that our proposed algorithm is competitive and works effectively. To verify the practicability of the algorithm, it is applied on a convolutional neural network hyperparameter optimization problems and obtains satisfactory results.

A dynamic adaptive hybrid surrogate-assisted particle swarm optimization algorithm for complex system design optimization

PurposeSurrogate-assisted evolutionary algorithms (SAEAs) are the most popular algorithms used to solve design optimization problems of expensive and complex engineering systems. However, it is difficult for fixed surrogate models to maintain their accuracy and efficiency in the face of different issues. Therefore, the selection of an appropriate surrogate model remains a significant challenge. This paper aims to propose a dynamic adaptive hybrid surrogate-assisted particle swarm optimization algorithm (AHSM-PSO) to address this issue.Design/methodology/approachA dynamic adaptive hybrid selection method (AHSM) is proposed. This method can identify multiple ensemble models formed by integrating different numbers of excellent individual surrogate models. Then, according to the minimum root-mean-square error, the best suitable surrogate model is dynamically selected in each generation and is used to assist PSO.FindingsExperimental studies on commonly used benchmark problems, and two real-world design optimization problems demonstrate that, compared with existing algorithms, the proposed algorithm achieves better performance.Originality/valueThe main contribution of this work is the proposal of a dynamic adaptive hybrid selection method (AHSM). This method uses the advantages of different surrogate models and eliminates the shortcomings of experience selection. Furthermore, the empirical results of the comparison of the proposed algorithm (AHSM-PSO) with existing algorithms on commonly used benchmark problems, and two real-world design optimization problems demonstrate its competitiveness.

Hybrid Taguchi-Lévy flight distribution optimization algorithm for solving real-world design optimization problems

Abstract The Lévy flight distribution optimization algorithm is a recently developed meta-heuristic. In this study, the Lévy flight distribution optimization algorithm and the Taguchi method are hybridized to solve the shape optimization problem, which is the final step in developing optimum structural components. The new method is termed the hybrid Lévy flight distribution and Taguchi (HLFD-T) algorithm. Geometric dimensions are used as design variables in the optimization, and the problem is aimed at mass minimization. The constraint in the problem is the maximum stress value. The well-known Kriging meta-modeling approach and a specifically developed hybrid approach have been coupled in this paper to find the component’s optimal geometry. The results show that the proposed hybrid algorithm (HLFD-T) has more robust features than the ant lion algorithm, the whale algorithm, and the Lévy flight distribution optimization algorithm for obtaining an optimal component geometry.

Design optimization of water distribution networks: real-world case study with penalty-free multi-objective genetic algorithm using pressure-driven simulation

Water distribution systems are an integral part of the economic infrastructure of modern-day societies. However, previous research on the design optimization of water distribution systems generally involved few decision variables and consequently small solution spaces; piecemeal-solution methods based on pre-processing and search space reduction; and/or combinations of techniques working in concert. The present investigation was motivated by the desire to address the above-mentioned issues including those associated with the lack of high-performance computing (HPC) expertise and limited access in developing countries. More specifically, the article’s aims are, firstly, to solve a practical water distribution network design optimization problem and, secondly, to develop and demonstrate a generic multi-objective genetic algorithm capable of achieving optimal and near-optimal solutions on complex real-world design optimization problems reliably and quickly. A multi-objective genetic algorithm was developed that applies sustained and extensive exploration of the active constraint boundaries. The computational efficiency was demonstrated by the small fraction of 10-245 function evaluations relative to the size of the solution space. Highly competitive solutions were achieved consistently, including a new best solution. The water utility’s detailed distribution network model in EPANET 2 was used for the hydraulic simulations. Therefore, with some additional improvements, the optimization algorithm developed could assist practitioners in day-to-day planning and design.

Seagull optimization algorithm for solving real-world design optimization problems

Abstract In this research paper, a new surrogate-assisted metaheuristic for shape optimization is proposed. A seagull optimization algorithm (SOA) is used to solve the shape optimization of a vehicle bracket. The design problem is to find structural shape while minimizing structural mass and meeting a stress constraint. Function evaluations are carried out using finite element analysis and estimated by using a Kriging model. The results show that SOA has outstanding features just as the whale optimization algorithm and salp swarm optimization algorithm for designing optimal components in the industry.

Seagull optimization algorithm for solving real-world design optimization problems

AbstractIn this research paper, a new surrogate-assisted metaheuristic for shape optimization is proposed. A seagull optimization algorithm (SOA) is used to solve the shape optimization of a vehicle bracket. The design problem is to find structural shape while minimizing structural mass and meeting a stress constraint. Function evaluations are carried out using finite element analysis and estimated by using a Kriging model. The results show that SOA has outstanding features just as the whale optimization algorithm and salp swarm optimization algorithm for designing optimal components in the industry.

Artificial algae algorithm (AAA) for nonlinear global optimization

In this study, a novel bio-inspired metaheuristic optimization algorithm called artificial algae algorithm (AAA) inspired by the living behaviors of microalgae, photosynthetic species, is introduced. The algorithm is based on evolutionary process, adaptation process and the movement of microalgae. The performance of the algorithm has been verified on various benchmark functions and a real-world design optimization problem. The CEC’05 function set was employed as benchmark functions and the test results were compared with the algorithms of Artificial Bee Colony (ABC), Bee Algorithm (BA), Differential Evolution (DE), Ant Colony Optimization for continuous domain (ACOR) and Harmony Search (HSPOP). The pressure vessel design optimization problem, which is one of the widely used optimization problems, was used as a sample real-world design optimization problem to test the algorithm. In order to compare the results on the mentioned problem, the methods including ABC and Standard PSO (SPSO2011) were used. Mean, best, standard deviation values and convergence curves were employed for the analyses of performance. Furthermore, mean square error (MSE), root mean square error (RMSE) and mean absolute percentage error (MAPE), which are computed as a result of using the errors of algorithms on functions, were used for the general performance comparison. AAA produced successful and balanced results over different dimensions of the benchmark functions. It is a consistent algorithm having balanced search qualifications. Because of the contribution of adaptation and evolutionary process, semi-random selection employed while choosing the source of light in order to avoid local minima, and balancing of helical movement methods each other. Moreover, in tested real-world application AAA produced consistent results and it is a stable algorithm.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

An Evolutionary Algorithm Based Approach to Design Optimization Using Evidence Theory

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.

A Memetic Algorithm for Global Optimization in Chemical Process Synthesis Problems

Design optimization problems in chemical engineering and in many other engineering domains are characterized by the presence of a large number of discrete and continuous decision variables, complex nonlinear models that restrict the search space, nonlinear cost functions, and the presence of many local optima. The classical approach to such problems are mixed integer nonlinear program solvers that work on a superstructure formulation which explicitly represents all design alternatives. The structural decisions lead to a large number of discrete variables and an exponential increase in the computational effort. The mathematical programming (MP) methods which are usually employed to solve the continuous subproblems that arise by fixing the discrete variables provide only one local optimum which depends strongly on the initialization. Thus standard methods may not find the global optimum despite long computation times. In this contribution we introduce a memetic algorithm (MA) for the global optimization of a computational demanding real-world design problem from the chemical engineering domain. The MA overcomes the problem of getting stuck in local optima by the use of an evolution strategy (ES) which addresses the global optimization of the design decisions, whereas a robust MP solver is used to handle complex nonlinear constraints as well as to improve the individuals of the ES by performing a local search in continuous sub-spaces in an integrated fashion. The MA is discussed in detail, the novel decomposition of the problem class at hand is analyzed and the MA is tested for the example of the optimal design of a reactive distillation column with several thousand decision variables. The MA is the only algorithm that finds the global solution in reasonable computation times. The introduction of structural decisions and additional constraints and discontinuous penalty terms lead only to a moderate increase in the computational effort which demonstrates the potential of this class of memetic algorithms in real-world design optimization problems.