Number Of Objective Function Evaluations Research Articles

A novel multi-objective optimization strategy based on vibrating particle system algorithm applied to chemical process design

Chemical process design is a highly interesting field within the chemical engineering community due to the numerous potential applications it offers. Traditionally, this problem involves multiple objectives and constraints related to mass, energy, and momentum balances, as well as limitations based on environmental, physical, and operating conditions. Over the past few decades, various multi-objective optimization strategies incorporating evolutionary algorithms have been proposed and tested using test cases of varying complexity. In this study, we propose a new Multi-objective Optimization Vibrating Particle System (MOVPS) algorithm. This numerical strategy extends the Vibrating Particle System Algorithm to a multi-objective context by incorporating three operators into the original algorithm: Pareto dominance, crowding distance, and a mutation strategy. To expedite the convergence process and avoid local optima, an external repository is considered. We evaluate the performance of the proposed methodology by applying it to mathematical functions (ZDT functions) and chemical process design problems. Regarding the ZDT functions, the computational cost (number of objective function evaluations and the processing time) was not increased considering the proposed methodology, as well as the values of convergence and diversity metrics are in agreement with those calculated considering other multi-objective optimization strategies. For most engineering case studies, it was possible to verify that the proposed methodology was able to obtain good estimates for the Pareto curve without increasing the computational cost. However, for the industrial styrene reactor problem it was possible to improve the Pareto curve and reduce the computational cost in relation to other multi-objective optimization algorithms.

Hybrid Bird Mating Optimizer for Welded Beam Design Optimization Problem

This study introduces a hybridization of the Bird Mating Optimizer (BMO) with Differential Evolution (DE). The Bird Mating Optimizer exhibits certain limitations, such as a slow convergence rate and a tendency to become trapped in local optima. To address these issues, a new method, BMO-DE, is proposed to enhance the performance of the BMO swarm intelligence algorithm. BMO-DE is a versatile swarm intelligence algorithm applicable to various engineering problems. In this research, it is specifically employed in the optimization of welded beam design, a type of problem characterized by numerous constraints. The penalty function approach is used to handle the constraints associated with welded beam design. Comparative analysis indicates that the proposed BMO-DE method outperforms other swarm intelligence algorithms in tackling this category of problems. Notably, the method demonstrates efficacy in finding optimal solutions with a low number of objective function evaluations, making it a potent and promising approach for addressing such problems.

Multi-Objective Bayesian Optimization Design of Elliptical Double Serpentine Nozzle

The use of traditional optimization methods in engineering design problems, specifically in aerodynamic and infrared stealth optimization for engine nozzles, requires a large number of objective function evaluations, therefore introducing a considerable challenge in terms of time constraints. In this paper, this limitation is addressed by using a sample-efficient multi-objective Bayesian optimization that takes Kriging as a surrogate model and Expected Hypervolume Improvement as the infill criterion. Using this approach, the probabilistic model is continuously established and updated, and the approximate Pareto front is obtained at a relatively small computational budget. The objective of this work is to evaluate the applicability of employing a multi-objective Bayesian optimization framework for the aerodynamic-infrared shape optimization of an elliptical double serpentine nozzle at 6 km flight condition, where the objective functions are evaluated by means of high-fidelity computational fluid dynamics and reversed Monte Carlo ray tracing simulations. We achieve good results in both infrared radiation signature reduction and aerodynamic performance improvement with a reasonable number of evaluations, indicating that the proposed method is effective and efficient for tackling the computationally intensive optimization challenges in the aircraft design.

Using Gaussian Processes for Metamodeling in Robust Optimization Problems


 This article proposes an approach based on Gaussian Processes for building metamodels for robust optimization problems that seek to reduce the computational effort required to quantify uncertainties. The approach is applied to two cases: a low-dimensional benchmark problem and a high-dimensional structural design, which consists of minimizing the mass of a structure formed by bars of different materials and diameters, subjected to point loads in different locations. The cases are modeled as robust optimization problems, where the objective function is estimated by a Gaussian Process and the optimization procedure uses a population meta-heuristic. The results indicate that the proposed approach is effective in reducing the number of objective function evaluations required to obtain a robust solution, with no significant statistical differences in the quality of solutions achieved.

Wolf-Bird Optimizer (WBO): A Novel Metaheuristic Algorithm for Building Information Modeling-based Resource Tradeoff

In the animal kingdom, a mutually-beneficial ecosystemic coexistence and partnership in predation between wolves and ravens, known as the wolf-bird relationship, is observed in various cultures. The Wolf-Bird Optimizer (WBO), a novel metaheuristic algorithm inspired by this natural zoological relationship, is proposed. This method is developed based on the foraging behaviors of ravens and wolves, wherein the intelligence of ravens in finding prey and sending signals to wolves for assistance in hunting is considered. Furthermore, a framework for resource tradeoffs in project scheduling using metaheuristic algorithms and the Building Information Modeling (BIM) approach is established in this research. For statistical analysis, the algorithms are independently run 30 times with a preset stopping condition, enabling the calculation of descriptive statistical metrics such as mean, standard deviation (SD), and the required number of objective function evaluations. To ensure the statistical significance of the results, several inferential statistical methods, including the Kolmogorov-Smirnov, Wilcoxon, Mann-Whitney, and Kruskal-Wallis tests, are employed. Additionally, the capability of the proposed algorithm in solving resource tradeoff problems in four construction projects is assessed. The performance of the WBO algorithm is also evaluated in two benchmark construction projects, with the results indicating the algorithm's ability to produce competitive and exceptional outcomes regarding tradeoffs.

A standard benchmarking suite for structural optimization algorithms: ISCSO 2016–2022

Benchmarking is an essential part of developing efficient structural optimization techniques. Despite the advent of numerous metaheuristic techniques for solving truss optimization problems, benchmarking new algorithms is often carried out using a selection of classic test examples which are indeed unchallenging for contemporary sophisticated optimization algorithms. Furthermore, the limited optimization results available in the literature on new test examples are usually not accurately comparable. This is typically due to the lack of infromation about the performance of the investigated algorithms and the inconsistencies between the studies in terms of adopted test examples for benchmarking, optimization problem formulation, maximum number of objective function evaluations and other similar issues. Accordingly, there exists a need for developing new standard test suites composed of easily reproducible challenging test examples with rigorous and comparable performance evaluation results of algorithms on these test suites. To this end, the present work aims to propose a new baseline for benchmarking structural optimization algorithms, using a set of challenging sizing and shape optimization problems of truss structures selected from the international student competition in structural optimization (ISCSO) instances. The most recent six structural optimization examples from the ISCSO are tackled using a representative metaheuristic structural optimization algorithm. The statistical results of all the optimization runs using the proposed benchmarking suite are provided to pave the way for more rigorous benchmarking of structural optimization algorithms.

Energy valley optimizer: a novel metaheuristic algorithm for global and engineering optimization

In this paper, Energy Valley Optimizer (EVO) is proposed as a novel metaheuristic algorithm inspired by advanced physics principles regarding stability and different modes of particle decay. Twenty unconstrained mathematical test functions are utilized in different dimensions to evaluate the proposed algorithm's performance. For statistical purposes, 100 independent optimization runs are conducted to determine the statistical measurements, including the mean, standard deviation, and the required number of objective function evaluations, by considering a predefined stopping criterion. Some well-known statistical analyses are also used for comparative purposes, including the Kolmogorov–Smirnov, Wilcoxon, and Kruskal–Wallis analysis. Besides, the latest Competitions on Evolutionary Computation (CEC), regarding real-world optimization, are also considered for comparing the results of the EVO to the most successful state-of-the-art algorithms. The results demonstrate that the proposed algorithm can provide competitive and outstanding results in dealing with complex benchmarks and real-world problems.

Damping optimization of the excited mechanical system using dimension reduction

We consider a mechanical system excited by a periodic external force. The main problem is to determine the best damping matrix to be able to minimize the system average displacement amplitude. Damping optimization usually includes optimization of damping positions and corresponding damping viscosities. Since the objective function is non-convex, a standard optimization approach requires a large number of objective function evaluations. We first propose a dimension reduction approach that calculates approximation of the average displacement amplitude and additionally we efficiently use a low rank update structure that appears in the external damping matrix. Moreover, an error bound which allows determination of appropriate approximation orders is derived and incorporated within the optimization method. We also present a theoretical error bound that allows determination of effective damping positions. The methodology proposed here provides a significant acceleration of the optimization process. The gain in efficiency is illustrated in numerical experiments.

Analysis of Surrogate-Assisted Information-Geometric Optimization Algorithms

Surrogate functions are often employed to reduce the number of objective function evaluations in a continuous optimization. However, their effects have seldom been investigated theoretically. This paper analyzes the effect of a surrogate function in the information-geometric optimization (IGO) framework, which includes as an algorithm instance a variant of the covariance matrix adaptation evolution strategy—a widely used solver for black-box continuous optimization. We derive a sufficient condition on the surrogate function for the parameter update in the IGO algorithms to point to a descent direction of the objective function expected over the search distribution. The condition is expressed in terms of three measures of correlation between the objective function and the surrogate function. Our result constitutes a partial justification for the use of a surrogate function in IGO algorithms.

P‐122: Bayesian Optimization with Gradients for OLED Efficiency Enhancement

In order to enhance Organic Light‐Emitting Diode (OLED) efficiency, typically a multitude of devices are fabricated to test the many possible permutations of materials and layer thicknesses. Simulation can be used to predict device performance in advance, reducing the trial and error in specifying test cells. For example, a dipole emission model can be used to predict outcoupling efficiency and color characteristics with ease, but predicting device efficiency is more challenging because it depends on both optical cavity effects as well as charge transport. Accurate models for charge/exciton transport with carefully calibrated material parameters are required. In this work, assuming well characterized material parameters, we turn to the task of optimizing the design of an OLED device in order to maximize efficiency. A Bayesian Optimization algorithm that incorporates gradient information is applied to globally maximize OLED efficiency with minimal computational cost. In contrast, conventional optimization approaches, such as the Response Surface Methodology (RSM) and Particle Swarm Optimization (PSO), require a large number of objective function evaluations (with each evaluation demanding one device simulation).

A diversity preservation method for expensive multi-objective combinatorial optimization problems using Novel-First Tabu Search and MOEA/D

Expensive multi-objective combinatorial optimization problems have constraints in the number of objective function evaluations due to time, financial, or resource restrictions. As most combinatorial problems, they are subject to a high number of duplicated solutions. Given the fact that expensive environments limit the number of objective function evaluations, the existence of duplicated solutions heavily impacts the optimization process due to poor diversity and low convergence speed. This paper proposes the Novel-First Tabu Search, a greedy-strategy mechanism that uses Knowledge-Assisted Local Search methods to preserve the population diversity and increase the exploration and exploitation ability of MOEA/D. Experiments are conducted on constrained, unconstrained, multimodal, deceptive, linear, convex, and non-convex Pareto Front multi-objective combinatorial optimization benchmark problems. This paper also conducts an experiment on the real-world, expensive problem of Well Placement Optimization using a benchmark case based on the Namorado oil field, located in the Campos Basin, Brazil. The experimental results and performance comparison with state-of-the-art algorithms demonstrate that the proposed design significantly preserves diversity and increases convergence without violating the constraint in the number of objective function evaluations.

An enhanced genetic algorithm for path planning of autonomous UAV in target coverage problems

Unmanned aerial vehicles (UAV) have become an important and integral part of military and civilian operations in recent years. In many UAV missions, the main purpose is to visit some predetermined checkpoints in operational space. If the number of checkpoints and constraints increases, finding a feasible solution may take up too much time. In this paper; the path planning problem of autonomous UAV in target coverage problems is solved by using artificial intelligent methods including genetic algorithm (GA), ant colony optimizer (ACO), Voronoi diagram, and clustering methods. The main contribution of this article is to propose initial population enhancement methods in GA, and thus accelerate convergence process. The first common enhancement to basic GA structure is to generate a sub-optimal path by implementing ACO. A sub-optimal path can be used to generate initial individuals. However, sub-optimal paths may have the problem that is collision with terrain. To avoid a UAV from any crash three approaches are integrated into an initial population phase of genetic algorithm. The first approach includes Voronoi vertices as additional waypoints to keep clear of trouble. The second approach consists of cluster centers which forms Voronoi vertices as supplemental waypoints. The final proposal comprises again cluster centers but based on a set of collision points. The proposed methods are tested in different three dimensional (3D) environments and the results are compared. Performance results show that collision with terrain surface is a local phenomenon and solving this issue by using the cluster center of collision points provides the best result including at least 70% or much more decrease in the required number of objective function evaluations.

Bayesian optimization of riser configurations

Optimizing the configuration of risers is a challenging task. It requires numerous nonlinear dynamic finite element analyses to evaluate each candidate configuration regarding its structural behavior. In such an optimization procedure, the computational time is commonly dominated by the structural analysis step. Therefore, reducing the number of simulations required to find feasible candidates is paramount to reduce the overall computational cost. In this work, we propose applying the Bayesian Optimization (BO) algorithm to optimize steel risers’ initial configuration efficiently. The performance of BO, measured as the number of objective function evaluations, is shown to be competitive in selected problems of steel lazy-wave risers and catenary risers with hydrodynamic dampers, compared to other optimization methods found in the literature (i.e., MIDACO commercial code, globalized bounded Nelder–Mead and genetic algorithms). In particular, we demonstrate the superior performance of BO compared to genetic algorithms, the most commonly found method in riser literature. Representative examples, which illustrate the capabilities of the proposed strategy, are presented and discussed.

IGS-CMAES: A Two-Stage Optimization for Ground Deformation and DEM Error Estimation in Time Series InSAR Data

Interferometric synthetic aperture radar (InSAR) has become an increasingly recognized remote sensing technology for earth surface monitoring. Slow and subtle terrain displacements can be estimated using time-series InSAR (TSInSAR) data. However, a substantial increase in the availability of exclusive time series data necessitates the development of more efficient and effective algorithms. Research in these areas is usually carried out by solving complicated optimization problems, which is very computationally expensive and time-consuming. This work proposes a two-stage black-box optimization framework to jointly estimate the average ground deformation rate and terrain digital elevation model (DEM) error. The method performs an iterative grid search (IGS) to acquire coarse candidate solutions, and then a covariance matrix adaptive evolution strategy (CMAES) is adopted to obtain the final local results. The performance of our method is evaluated using both simulated and real datasets. Both quantitative and qualitative comparisons using different optimizers support the reliability and effectiveness of our work. The proposed IGS-CMAES achieves higher accuracy with a significantly fewer number of objective function evaluations than other established algorithms. It offers the possibility for wide-area monitoring, where high precision and real-time processing is essential.

An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems

We present an efficient descent method for unconstrained, locally Lipschitz multiobjective optimization problems. The method is realized by combining a theoretical result regarding the computation of descent directions for nonsmooth multiobjective optimization problems with a practical method to approximate the subdifferentials of the objective functions. We show convergence to points which satisfy a necessary condition for Pareto optimality. Using a set of test problems, we compare our method with the multiobjective proximal bundle method by Mäkelä. The results indicate that our method is competitive while being easier to implement. Although the number of objective function evaluations is larger, the overall number of subgradient evaluations is smaller. Our method can be combined with a subdivision algorithm to compute entire Pareto sets of nonsmooth problems. Finally, we demonstrate how our method can be used for solving sparse optimization problems, which are present in many real-life applications.

How Does the Number of Objective Function Evaluations Impact Our Understanding of Metaheuristics Behavior?

Comparing various metaheuristics based on an equal number of objective function evaluations has become standard practice. Many contemporary publications use a specific number of objective function evaluations by the benchmarking sets definitions. Furthermore, many publications deal with the recurrent theme of late stagnation, which may lead to the impression that continuing the optimization process could be a waste of computational capabilities. But is it? Recently, many challenges, issues, and questions have been raised regarding fair comparisons and recommendations towards good practices for benchmarking metaheuristic algorithms. The aim of this work is not to compare the performance of several well-known algorithms but to investigate the issues that can appear in benchmarking and comparisons of metaheuristics performance (no matter what the problem is). This article studies the impact of a higher evaluation number on a selection of metaheuristic algorithms. We examine the effect of a raised evaluation budget on overall performance, mean convergence, and population diversity of selected swarm algorithms and IEEE CEC competition winners. Even though the final impact varies based on current algorithm selection, it may significantly affect the final verdict of metaheuristics comparison. This work has picked an important benchmarking issue and made extensive analysis, resulting in conclusions and possible recommendations for users working with real engineering optimization problems or researching the metaheuristics algorithms. Especially nowadays, when metaheuristic algorithms are used for increasingly complex optimization problems, and meet machine learning in AutoML frameworks, we conclude that the objective function evaluation budget should be considered another vital optimization input variable.

Solving structural optimization problems with discrete variables using interactive fuzzy search algorithm

The current investigation deals with assessing the search performance of a recently developed, parameter-free, and self-adaptive search algorithm so-called Interactive Fuzzy Search Algorithm (IFSA) in solving weight minimization of the constrained structural optimization problems with discrete variables. The proposed IFSA combines the navigation pattern of the Interactive Search Algorithm (ISA) with the decision-making competence of fuzzy reasoning. The fuzzy module of the proposed IFSA permanently monitors the search process and adjusts each agent's search behavior by considering the governing condition of the current problem. In structural optimization, due to construction limitations, it is more realistic to select the sizing variables from a discrete domain. Thus, in this study, to empirically evaluate the search capability of the IFSA, it is applied to solve a suite of structural optimization problems with the discrete design variables. The attained outcomes are compared with the ISA and some other related methods addressed in the relevant literature. The acquired accuracy level and demanded number of objective function evaluations indicates that the IFSA, comparatively, using lower computational cost could found lighter structural systems. Also, the comparison of the attained standard deviation values shows that the IFSA demonstrates higher stability during the optimization process. These superior outcomes designate that the fuzzy decision-making mechanism of the IFSA could work properly in dynamically adapting the search behavior of the algorithm with the governing condition of the current problem. Consequently, the promising gained results reveal that IFSA can effectively be applied in solving the structural optimization problems with discrete search domains.

Optimal GENCO's bidding strategy in a power exchange facilitating combined power and emission trading using Intelligent Programmed Genetic Algorithm

Currently, for developing optimal bidding strategy considering carbon credit trading, Generating Company (GENCO) separately participates in electric power and emission market. Recently, researchers proposed a new scheme in which emission trading is facilitated within Power Exchange (PX). Developing optimal GENCO's bidding strategy considering carbon credit trading within PX is a complex single-objective optimization problem with generator's surplus as the main objective function. Obtaining its solution using a simple evolutionary optimization algorithm is difficult and time-consuming. Therefore, this paper presents an application of Intelligent Programmed Genetic Algorithm (IPGA) equipped with advanced deterministic diversity creating operator for solving optimal GENCO's bidding strategy problem with minimum number of objective function evaluations. The performance of IPGA is first tested on three different categories of standard test functions by comparing its simulation results with that obtained using binary-coded GA, simulated annealing, particle swarm optimization, biogeography-based optimization, teaching learning-based optimization, and differential evolution-based hybrid GA. A system comprising of six GENCOs and two buyers is used to validate the applicability of IPGA. IPGA along with other algorithms was used to obtain optimal bidding curve for 24 hours for GENCO GC-1. Simulation results clearly show much faster convergence for IPGA in terms of the number of objective function evaluations required to reach optima. Result also shows that GENCO GC-1 can obtain much higher GC-1 surplus, carbon credit limit, and social welfare by utilizing the obtained bidding strategy using IPGA as compared with the bidding strategy obtained by other algorithms.

An Intelligent Programmed Genetic Algorithm with advanced deterministic diversity creating operator using objective surface visualization

This paper presents a new fast Intelligent Programmed Genetic Algorithm (IPGA) based evolutionary optimization algorithm which requires lesser number of objective function evaluation for reaching optima. The proposed algorithm, apart from using probabilistic genetic operator, i.e. crossover and mutation, also uses a deterministic diversity creating operator for generating new solution in the current population. This is done by first projecting objective surface from higher dimension to lower dimension for visualization purpose and then deterministically generates new solution using some predefined rules in the region with higher objective function value. As the newly generated solution is in lower-dimensional space, these solutions are again projected back to higher dimensional space and then the objective function is evaluated at that point. The proposed IPGA is tested on three different categories of standard test functions viz. Unimodal function (2 Test Function), Unrotated Multimodal function (6 Test Function) and Rotated Multimodal function (5 Test Function). Simulation results were compared with that obtained using Binary Coded GA, Real Coded GA, recently proposed GA with Differential Evolution crossover operator (GA–DEx) and another success-history-based adaptive GA with aging mechanism (GA–aDExSPS) in terms of mean and standard deviation of the objective function, average number of objective function evaluation required to reach optima and algorithmic complexity. Simulation results clearly demonstrate better performance of the proposed IPGA when compared with other variants of GAs.

ESTUDIO COMPARATIVO DE ALGORITMOS DE OPTIMIZACIÓN CON OBJETIVOS MÚLTIPLES PARA UN MODELO DE AUTÓMATA CELULAR

Cellular Automata (CA) models can represent dynamic systems which are discrete in space and time that reflects the effect of intrinsic parameters where individual events are considered to occur from randomness. A CA model of two agents' chemical kinetics has been optimized earlier using NSGA-II based on Evolutionary Algorithm (EA). But the stochastic nature of the CA model along with its high sensitivity on the model parameters requires extensive investigation using different optimization algorithms. For this purpose, in the current study, four more recently developed and popular optimization algorithms based on EA, called NSGA-IIr, NSGA-IIa, AbYSS and MOEA/D, have been considered for investigation based on various performance measuring parameters. The study also compares the performances of the algorithms for different computational efforts with an objective to minimize the required number of objective function evaluations. Simulation results and Friedman rank statistical test show NSGA-IIa and NSGA-IIr as the best choices to optimize the CA stochastic model across any number of objective function evaluations. Though the choice of optimization algorithm does not change with function evaluations, higher function evaluations improve the pseudo-pareto front for the CA optimization problem. Such results will facilitate the use of stochastic CA models to represent complex (bio)-chemical networks.