Real-world Optimization Problems Research Articles

Self-learning salp swarm algorithm for global optimization and its application in multi-layer perceptron model training

Optimization problems are common across various fields, and one effective solution is the swarm intelligence algorithm.It is essential for the algorithm to deliver high-quality solutions for problems with varying characteristics. However, most existing swarm intelligence rely on fixed and monotonic search strategies, which limits their ability to handle the diverse and complex situations encountered when solving real-world optimization problems with unknown fitness landscapes. To extend the applicability of swarm intelligence and thus offer users an efficient black-box optimizer for various applications, a novel self-learning mechanism is proposed and applied to the Salp Swarm Algorithm (SSA) to develop the self-learning salp swarm algorithm (SLSSA) in this paper. In SLSSA, four distinct search strategies, including a novel multiple food sources search strategy, are adopted to strengthen the search agents’ abilities to conquer various difficulties in the search space. To improve the efficiency of the search process, the self-learning strategy dynamically determines the execution probability of each search strategy according to the quality of solutions it produced previously. Moreover, a parameter setting method is proposed in this paper, which eliminates the need for a trial-and-error approach and allows for straightforward configuration of the parameters that optimize the performance of SLSSA. In comparison with several highly regarded state-of-the-art peer algorithms, the performance of SLSSA in solving the CEC2014 benchmark functions was thoroughly examined. Subsequently, SLSSA was applied to train multi-layer perceptron classifiers and test on the UCI machine-learning datasets. The experimental results and analysis on benchmark functions and multi-layer perceptron classifier training problems demonstrate that SLSSA outperforms the competing algorithms in terms of solution accuracy, stability, and overall convergence speed. Moreover, computational time comparisons reveal that SLSSA achieves significant performance improvement with only a marginal increase in time cost compared to the original SSA.

Efficient Constrained Real-World Problem-Solving Using Gradient-Based Mutation Manta Ray Foraging Optimization (GM-MRFO)

This paper presents a Gradient-based Mutation Manta ray foraging optimization (GM-MRFO) that is designed to solve real-world optimization problems with constraints. GM-MRFO combines the basic strategy of MRFO with the Gradient-based Mutation (GM) strategy, which is a feasibility-and-solution repair strategy adopted from the ϵ-Matrix-Adaptation Evolution Strategy ( MAgES). MRFO algorithm is not immune to the common problems confronted by constrained optimization algorithms where constraints in the optimization problem are incompatible, and a solution that satisfies all constraints does not exist. In such cases, the MRFO algorithm may not be able to find a feasible solution. Another challenge is the optimization algorithm converges to a solution that is not globally optimal. By introducing the GM strategy and using Jacobian approximation in finite differences, GM-MRFO can improve the feasibility of solutions throughout the search process, which enables it to handle constraints more effectively than its predecessor. The proposed algorithm's performance is evaluated by assessing the accuracy of the best solution produced, the feasibility rate, mean of violation, success rate, and the ranking based on a ranking scheme in the Congress on Evolutionary Computation 2020 (CEC2020). Specifically, GM-MRFO achieved a feasibility rate of 100% on 47 out of 57 CEC2020 real-world problems and improved adequately best-known solutions.

Differential evolution with multi-strategies for UAV trajectory planning and point cloud registration

The present study introduces a novel adaptive algorithm, MELSHADE-cnEpSin, which aims to enhance the performance of LSHADE-cnEpSin, which is not only stands out as one of the most competitive versions of differential evolution but also holds the distinction of being one of the CEC winner algorithms. Compared to the original methodology, four main distinctions are presented. To begin with, we adopt an adaptive selection mechanism (ASM) of crossover rate Cr value based on the external archive to rechoose a suitable value. In the next place, a nonlinear population reduction strategy using Sigmoid function is employed to improve population distribution. Additionally, a restart strategy is implemented to mitigate the risk of algorithmic convergence towards suboptimal solutions. Furthermore, the performance of MELSHADE-cnEpSin was evaluated using standard CEC2017 and CEC2022 test suites in conjunction with nine CEC-winning algorithms (L-SHADE, EBOwithCMAR, AGSK, LSHADE-SPACMA, LSHADE-cnEpSin, ELSHADE-SPACMA, EA4eig, MadDE and APGSK-IMODE) as well as two novel algorithms (ACD-DE and MIDE). Furthermore, MELSHADE-cnEpSin was effectively employed to address the challenge of UAV trajectory planning in intricate mountainous terrain and underwent simulation with point cloud registration cases utilizing a rapid global registration dataset, thereby showcasing the potential of MELSHADE-cnEpSin in tackling real-world optimization problems.

Research on hybrid strategy Particle Swarm Optimization algorithm and its applications

The increasing complexity and high-dimensional nature of real-world optimization problems necessitate the development of advanced optimization algorithms. Traditional Particle Swarm Optimization (PSO) often faces challenges such as local optima entrapment and slow convergence, limiting its effectiveness in complex tasks. This paper introduces a novel Hybrid Strategy Particle Swarm Optimization (HSPSO) algorithm, which integrates adaptive weight adjustment, reverse learning, Cauchy mutation, and the Hook-Jeeves strategy to enhance both global and local search capabilities. HSPSO is evaluated using CEC-2005 and CEC-2014 benchmark functions, demonstrating superior performance over standard PSO, Dynamic Adaptive Inertia Weight PSO (DAIW-PSO), Hummingbird Flight patterns PSO (HBF-PSO), Butterfly Optimization Algorithm (BOA), Ant Colony Optimization (ACO), and Firefly Algorithm (FA). Experimental results show that HSPSO achieves optimal results in terms of best fitness, average fitness, and stability. Additionally, HSPSO is applied to feature selection for the UCI Arrhythmia dataset, resulting in a high-accuracy classification model that outperforms traditional methods. These findings establish HSPSO as an effective solution for complex optimization and feature selection tasks.

Solving higher dimensional expensive black box global optimization problems using sparse directional search on surrogates

We present a new algorithm Directional Optimization Search with Surrogate (DOSS), for optimizing problems with box constraints and a computationally expensive black-box objective function. DOSS is a radial basis function (RBF) based method that mainly focuses on higher dimensional and computationally expensive objective functions that can be multimodal. DOSS introduces three new techniques not previously used in earlier RBF algorithms, including using a combination of the coordinates knowledge level, fewer initial sampling points, and the surrogate’s gradient information. Numerical results on a test set including 14 test problems with 36, 48, and 60 dimensions show that DOSS outperforms two recently published algorithms RBFOpt and TuRBO, and earlier RBF algorithms such as DYCORS. TuRBO is a Gaussian process based optimization algorithm, which outperformed earlier state-of-the-art methods. DOSS algorithm also has a good performance on real-world optimization problems, including robot pushing and rover trajectory planning problems. Almost sure convergence for the DOSS algorithm is also proven in this paper. An implementation of DOSS is available at https://doi.org/10.5281/zenodo.13731558.

A comparative study of evolutionary algorithms and particle swarm optimization approaches for constrained multi-objective optimization problems

Many real-world optimization problems contain multiple conflicting objectives as well as additional problem constraints. These problems are referred to as constrained multi-objective optimization problems (CMOPs). Many meta-heuristics for solving CMOPs, called constrained multi-objective meta-heuristics (CMOMHs) have been introduced in the literature, including those using particle swarm optimization (PSO)(Kennedy and Eberhart, 1995), genetic algorithms (GAs)(Man et al., 1996), and differential evolution (DE)(Storn and Price, 1997). CMOMHs can be grouped into four different classes: classic CMOMHs, co-evolutionary approaches, multi-stage approaches, and multi-tasking approaches. An extensive comparative study of twenty different CMOMHs on a wide variety of test problems, including real-world CMOPs in the fields of science and engineering, is conducted. A multi-swarm PSO approach called constrained multi-guide particle swarm optimization (ConMGPSO) is introduced and compared to the best-performing previous approaches according to the comparative study. The performance of each algorithm was found to be problem dependent, however the best overall approaches were ConMGPSO, paired-offspring constrained evolutionary algorithm (POCEA)(He et al., 2021), adaptive non-dominated sorting genetic algorithm III (A-NSGA-III)(Jain and Deb, 2014), and constrained multi-objective framework using Q-learning and evolutionary multi-tasking (CMOQLMT)(Ming and Gong, 2023). ConMGPSO and POCEA had the best performance on the CF benchmark set, which contains examples of bi-objective and tri-objective CMOPs with disconnected CPOFs. The CMOQLMT approach had the best performance on the DAS-CMOP benchmark set, which contain additional difficulty in terms of feasibility-, convergence-, and diversity-hardness. For the selected real-world CMOPs, A-NSGA-III had the best performance overall. ConMGPSO was shown to have the best performance on the process, design, and synthesis problems, and had competitive performance for the power system optimization problems.

A nonlinear randomly reuse-based mutated whale optimization algorithm and its application for solving engineering problems

The whale optimization algorithm (WOA) is a meta-heuristic optimization algorithm inspired by the social behavior of whale hunting. However, the WOA has the defects of easily falling into local optimum and slow convergence speed. Therefore, to overcome the shortcomings of the original WOA, a novel variant of WOA called nonlinear randomly reuse-based mutated whale optimization algorithm (NRRMWOA) is proposed in this study. In detail, the proposed NRRMWOA includes three novel strategies as compared with original WOA. Firstly, a nonlinear adaptive parameter strategy is introduced to achieve nonlinear adjustment of search pattern along with the iteration time. The second improvement is the random reuse strategy, which can fully utilize the current optimal whale to improve the solution accuracy. The thirdly proposed late disturbance mutation strategy has the function of increasing population diversity in the later stage of iteration. The three proposed strategies complement each other and significantly improve the convergence efficiency and global exploration capability of WOA. To verify the superiority of the proposed NRRMWOA, a series of typical benchmark functions are utilized to conduct comprehensive numerical experiments. Compared with three sets of comparison algorithms (five variants of WOA, five advanced algorithms, and five well-known algorithms), the ARVs (average ranking values) obtained by NRRMWOA are 1.4667, 1.9167, and 2.1333, respectively. The rankings are all the best in the corresponding group. The detailed experimental and statistics results indicate that the presented NRRMWOA has higher convergence speed and better solution quality compared with the three sets of existing algorithms. In addition, 15 real-world optimization problems are employed to further test the performance of NRRMWOA for solving engineering optimization problems. For the results of 15 real-world optimization problems, the proposed NRRMWOA achieves the best results including 8 best “Mean”, 10 best “Min.”, and 7 best “Max.”. As a conclusion, the proposed NRRMWOA is a promising and excellent algorithm.

Scheduling of memory chips for final testing on parallel machines considering power constraints and deteriorating effects

This paper delves into the intricate scheduling strategies crucial for the final testing phase of memory chip manufacturing within the semiconductor industry and other related sectors. It specifically addresses the complex serial-batching scheduling problem, where memory chips are tested on parallel machines under power constraints and chip deterioration effects. The processing time for each chip is significantly influenced by both the cumulative processing time of preceding chips and the power requirements for testing. We formulate this real-world optimization problem using a mixed integer nonlinear programming model. Exact solutions for small instances are obtained using a commercial solver. However, due to the model's complexity, we also develop heuristic solutions to efficiently handle larger instances. Based on the derivation of structural properties, we develop two tailored heuristic algorithms to determine the schedule for the final testing of memory chips. Additionally, we propose a refined Variable Neighborhood Search algorithm (VNS-H) that seamlessly integrates five local search strategies with two supplementary heuristic algorithms, dynamically alternating between them to ensure a balance between computational efficiency and the quality of the solutions obtained. Additionally, we establish a lower bound to validate the effectiveness of these solutions, particularly for large-scale instances. To validate the efficacy and robustness of our proposed metaheuristic algorithm, we conduct a rigorous comparison of the VNS-H algorithm with five other metaheuristic algorithms that have promising performance in various optimization problems. The results highlight the superior performance of the VNS-H algorithm. In small-scale instances, our VNS-H algorithm achieves an average makespan that is 5.52% lower compared to the original VNS. For large-scale instances, the VNS-H algorithm reduces the average makespan by 13.46% compared to VNS. Finally, we discuss the managerial implications of our findings, providing insights specifically tailored to semiconductor manufacturing enterprises based on the outcomes of this study.

Surrogate-assisted push and pull search for expensive constrained multi-objective optimization problems

In many real-world engineering optimizations, a large number of objective and constraint function values often need to be obtained through simulation software or physical experiments, which incurs significant computational costs and/or time expenses. These problems are known as expensive constraint multi-objective optimization problems (ECMOPs). This paper combines the push and pull search (PPS) framework and proposes a surrogate-assisted evolutionary algorithm to solve ECMOPs through Bayesian active learning, naming it the surrogate-assisted PPS (SA-PPS). Specifically, during the push search stage, candidate solutions are selected based on two indicators: hypervolume improvement and objective uncertainty. These aim to quickly guide the population towards the unconstrained Pareto front while ensuring diversity. During the pull search stage, the population is partitioned into many subregions through reference vectors, and different selection strategies are assigned to each subregion based on its state, aiming to guide the population towards the constrained Pareto front while ensuring diversity. Furthermore, we introduce a batch data selection strategy that utilizes Bayesian active learning to enable the surrogate model to focus on regions of interest in the pull search stage. Extensive experimental results have shown that the proposed SA-PPS algorithm exhibits superior convergence and diversity compared to 9 state-of-the-art algorithms across a variety of benchmark problems and a real-world optimization problem.

Improved multi-strategy adaptive Grey Wolf Optimization for practical engineering applications and high-dimensional problem solving

The Grey Wolf Optimization (GWO) is a highly effective meta-heuristic algorithm leveraging swarm intelligence to tackle real-world optimization problems. However, when confronted with large-scale problems, GWO encounters hurdles in convergence speed and problem-solving capabilities. To address this, we propose an Improved Adaptive Grey Wolf Optimization (IAGWO), which significantly enhances exploration of the search space through refined search mechanisms and adaptive strategy. Primarily, we introduce the incorporation of velocity and the Inverse Multiquadratic Function (IMF) into the search mechanism. This integration not only accelerates convergence speed but also maintains accuracy. Secondly, we implement an adaptive strategy for population updates, enhancing the algorithm's search and optimization capabilities dynamically. The efficacy of our proposed IAGWO is demonstrated through comparative experiments conducted on benchmark test sets, including CEC 2017, CEC 2020, CEC 2022, and CEC 2013 large-scale global optimization suites. At CEC2017, CEC 2020 (10/20 dimensions), CEC 2022 (10/20 dimensions), and CEC 2013, respectively, it outperformed other comparative algorithms by 88.2%, 91.5%, 85.4%, 96.2%, 97.4%, and 97.2%. Results affirm that our algorithm surpasses state-of-the-art approaches in addressing large-scale problems. Moreover, we showcase the broad application potential of the algorithm by successfully solving 19 real-world engineering challenges.

SDO: A novel sled dog-inspired optimizer for solving engineering problems

A new bio-inspired meta-heuristic algorithm, named Sled Dog Optimizer (SDO), is proposed in this paper. The inspiration for SDO is primarily drawn from the various behavioral patterns of sled dogs. It focuses on constructing mathematical models by simulating the process of dog sledding, training and retiring behaviors. The mutual constraints of multiple steps and the variation of several parameters make the exploitation and exploration capabilities of SDO well balanced. To test the ability of SDO, this paper sets up several different sets of experiments to be analyzed from a number of different aspects. First, SDO is qualitatively analyzed through several performance metrics, which include search history, search trajectory and population diversity. Second, SDO is compared with several novel and excellent metaheuristics at CEC 2017 as well as CEC 2020. The results show that SDO has extremely good performance in solving unconstrained optimization problems. SDO is then further applied to the CEC 2020 real-world problem test set to test its ability to solve real-world optimization problems with constraints. Finally, this paper extends and proposes a new path planning model to which SDO is applied. In these problems with constraints, SDO performs well and has a promising application. SDO demonstrates outstanding control of exploration and exploitation capabilities in all experiments. It can be said that SDO promotes the progress of meta-heuristic algorithms and provides another new powerful technology for complex optimization problems in the real world.

An improved differential evolution with adaptive population allocation and mutation selection

In order to improve the performance of differential evolution (DE) for different optimization problems, an improved DE with adaptive population allocation and mutation selection (iDE-APAMS) is proposed. First, different mutation strategies are selected to constitute the exploration strategy pool and the exploitation strategy pool. The exploration strategy pool is mainly used for global search to increase the population diversity; the exploitation strategy pool is primarily used for local search to accelerate the convergence and improve the solution accuracy. Second, different mutation strategies obtain population resources dynamically through cooperation and competition. Mutation strategies in the same strategy pool first compete for population resources with mutation strategies in the other strategy pool through cooperation, and in this way the population is allocated between the two strategy pools. Then within each strategy pool, different mutation strategies compete with each other to obtain corresponding population resources. Third, mutation scale factor and crossover rate are adaptively adjusted based on population diversity and fitness improvement. Finally, the Levy random walk is applied to individuals with better fitness at the later stage of the iteration to avoid falling into local optima and further improve the accuracy of the solution. The iDE-APAMS is compared with 4 classical DE variants and 11 state-of-the-art algorithms on the CEC2013, CEC2014, and CEC2017 benchmark test suites respectively, and it is also tested on 22 real-world optimization problems in CEC2011. The results show that iDE-APAMS can improve the convergence of the algorithm and the stability of the solution, and it is statistically significantly better than the comparison algorithms.

An in-depth survey of the artificial gorilla troops optimizer: outcomes, variations, and applications

A recently developed algorithm inspired by natural processes, known as the Artificial Gorilla Troops Optimizer (GTO), boasts a straightforward structure, unique stabilizing features, and notably high effectiveness. Its primary objective is to efficiently find solutions for a wide array of challenges, whether they involve constraints or not. The GTO takes its inspiration from the behavior of Gorilla Troops in the natural world. To emulate the impact of gorillas at each stage of the search process, the GTO employs a flexible weighting mechanism rooted in its concept. Its exceptional qualities, including its independence from derivatives, lack of parameters, user-friendliness, adaptability, and simplicity, have resulted in its rapid adoption for addressing various optimization challenges. This review is dedicated to the examination and discussion of the foundational research that forms the basis of the GTO. It delves into the evolution of this algorithm, drawing insights from 112 research studies that highlight its effectiveness. Additionally, it explores proposed enhancements to the GTO’s behavior, with a specific focus on aligning the geometry of the search area with real-world optimization problems. The review also introduces the GTO solver, providing details about its identification and organization, and demonstrates its application in various optimization scenarios. Furthermore, it provides a critical assessment of the convergence behavior while addressing the primary limitation of the GTO. In conclusion, this review summarizes the key findings of the study and suggests potential avenues for future advancements and adaptations related to the GTO.

Population diversity control based differential evolution algorithm using fuzzy system for noisy multi-objective optimization problems

The objective measurements of the real-world optimization problems are mostly subject to noise which occurs due to several reasons like human measurement or environmental factors. The performance of the optimization algorithm gets affected if the effect of noise is higher than the negligible limit. The previous noise handling optimization algorithms use a large population size or multiple sampling at same region which increases the total count of function evaluations, and few methods work for a particular problem type. To address the above challenges, a Differential Evolution based Noise handling Optimization algorithm (NDE) to solve and optimize noisy bi-objective optimization problems is proposed. NDE is a Differential Evolution (DE) based optimization algorithm where the strategies for trial vector generation and the control parameters of DE algorithm are self-adapted using fuzzy inference system to improve the population diversity along the evolution process. In NDE, explicit averaging based method for denoising is used when the noise level is higher than negligible limit. Extending noise handling method enhances the performance of the optimization algorithm in solving real world optimization problems. To improve the convergence characteristics of the proposed algorithm, a restricted local search procedure is proposed. The performance of NDE algorithm is experimented using DTLZ and WFG problems, which are benchmark bi-objective optimization problems. The obtained results are compared with other SOTA algorithm using modified Inverted Generational Distance and Hypervolume performance metrics, from which it is confirmed that the proposed NDE algorithm is better in solving noisy bi-objective problems when compared to the other methods. To further strengthen the claim, statistical tests are conducted using the Wilcoxon and Friedman rank tests, and the proposed NDE algorithm shows significance over the other algorithms rejecting the null hypothesis.

Integer programming using a single atom

Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form through the use of binary variables, which is an indirect and resource-consuming way of solving it. We develop an algorithm that maps and solves an IP problem in its original form to any quantum system possessing a large number of accessible internal degrees of freedom that are controlled with sufficient accuracy. This work leverages the principle of superposition to solve the optimization problem. Using a single Rydberg atom as an example, we associate the integer values to electronic states belonging to different manifolds and implement a selective superposition of different states to solve the full IP problem. The optimal solution is found within a few microseconds for prototypical IP problems with up to eight variables and four constraints. This also includes non-linear IP problems, which are usually harder to solve with classical algorithms when compared to their linear counterparts. Our algorithm for solving IP is benchmarked by a well-known classical algorithm (branch and bound) in terms of the number of steps needed for convergence to the solution. This approach carries the potential to improve the solutions obtained for larger-size problems using hybrid quantum–classical algorithms.

Optimization modeling and verification from problem specifications using a multi-agent multi-stage LLM framework

This paper explores the use of Large Language Models (LLMs) in modeling real-world optimization problems. We concretely define the task of translating natural language descriptions into optimization models (NL2OPT) and provide criteria for classifying optimization problems for the NL2OPT task. Our novel multi-agent modeling framework leverages relations identifier agents and a multi-agent verification mechanism, eliminating the need for solver execution. Additionally, we introduce a straightforward and practical evaluation framework, offering a more effective assessment method compared to traditional execution-based evaluations. We have created a unique dataset tailored for optimization modeling, featuring Problem Specifications as a structured representation of optimization problems. Through comprehensive experiments, our study compares our modeling framework with existing LLM reasoning strategies, highlighting their relative effectiveness in optimization modeling tasks. We also perform ablation studies to explore the effect of different components of our modeling framework. Experimental results demonstrate that our multi-agent framework outperforms many common LLM prompting strategies.

An Improved Football Team Training Algorithm for Global Optimization.

The football team training algorithm (FTTA) is a new metaheuristic algorithm that was proposed in 2024. The FTTA has better performance but faces challenges such as poor convergence accuracy and ease of falling into local optimality due to limitations such as referring too much to the optimal individual for updating and insufficient perturbation of the optimal agent. To address these concerns, this paper presents an improved football team training algorithm called IFTTA. To enhance the exploration ability in the collective training phase, this paper proposes the fitness distance-balanced collective training strategy. This enables the players to train more rationally in the collective training phase and balances the exploration and exploitation capabilities of the algorithm. To further perturb the optimal agent in FTTA, a non-monopoly extra training strategy is designed to enhance the ability to get rid of the local optimum. In addition, a population restart strategy is then designed to boost the convergence accuracy and population diversity of the algorithm. In this paper, we validate the performance of IFTTA and FTTA as well as six comparison algorithms in CEC2017 test suites. The experimental results show that IFTTA has strong optimization performance. Moreover, several engineering-constrained optimization problems confirm the potential of IFTTA to solve real-world optimization problems.

Metaheuristics for variable-size mixed optimization problems: A unified taxonomy and survey

Many real world optimization problems are formulated as mixed-variable optimization problems (MVOPs) which involve both continuous and discrete variables. MVOPs including dimensional variables are characterized by a variable-size search space. Depending on the values of dimensional variables, the number and type of the variables of the problem can vary dynamically. MVOPs and variable-size MVOPs (VMVOPs) are difficult to solve and raise a number of scientific challenges in the design of metaheuristics. Standard metaheuristics have been first designed to address continuous or discrete optimization problems, and are not able to tackle VMVOPs in an efficient way. The development of metaheuristics for solving such problems has attracted the attention of many researchers and is increasingly popular. However, to our knowledge there is no well established taxonomy or comprehensive survey for handling this important family of optimization problems. This paper presents an unified taxonomy for metaheuristic solutions for solving VMVOPs in an attempt to provide a common terminology and classification mechanisms. It provides a general mathematical formulation and concepts of VMVOPs, and identifies the various solving methodologies than can be applied in metaheuristics. The advantages, the weaknesses and the limitations of the presented methodologies are discussed. The proposed taxonomy also allows to identify some open research issues which needs further in-depth investigations.

Optimization of electric vehicle design problems using improved electric eel foraging optimization algorithm

Abstract This paper introduces a novel approach, the Modified Electric Eel Foraging Optimization (EELFO) algorithm, which integrates artificial neural networks (ANNs) with metaheuristic algorithms for solving multidisciplinary design problems efficiently. Inspired by the foraging behavior of electric eels, the algorithm incorporates four key phases: interactions, resting, hunting, and migrating. Mathematical formulations for each phase are provided, enabling the algorithm to explore and exploit solution spaces effectively. The algorithm’s performance is evaluated on various real-world optimization problems, including weight optimization of engineering components, economic optimization of pressure handling vessels, and cost optimization of welded beams. Comparative analyses demonstrate the superiority of the MEELFO algorithm in achieving optimal solutions with minimal deviations and computational effort compared to existing metaheuristic methods.

Imprecise Bayesian optimization

Bayesian optimization (BO) with Gaussian processes (GPs) surrogate models is widely used to optimize analytically unknown and expensive-to-evaluate functions. In this paper, we propose a robust version of BO grounded in the theory of imprecise probabilities: Prior-mean-RObust Bayesian Optimization (PROBO). Our method is motivated by an empirical and theoretical analysis of the GP prior specifications’ effect on BO’s convergence. A thorough simulation study finds the prior’s mean parameters to have the highest influence on BO’s convergence among all prior components. We thus turn to this part of the prior GP in more detail. In particular, we prove regret bounds for BO under misspecification of GP prior’s mean parameters. We show that sublinear regret bounds become linear under GP misspecification but stay sublinear if the misspecification-induced error is bounded by the variance of the GP. In response to these empirical and theoretical findings, we introduce PROBO as a univariate generalization of BO that avoids prior mean parameter misspecification. This is achieved by explicitly accounting for prior GP mean imprecision via a prior near-ignorance model. We deploy our approach on graphene production, a real-world optimization problem in materials science, and observe PROBO to converge faster than classical BO.11Open Science: Implementations of PROBO and reproducible scripts for the experimental analysis as well as all reported data are available at: https://github.com/rodemann/imprecise-bayesian-optimization.22Some parts of an earlier version of this work have been presented at the Ninth International Symposium on Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM) and published in the corresponding proceedings [1], see Appendix D for details.