Structural bias (SB) refers to systematic preferences of an optimisation algorithm for particular regions of the search space that arise independently of the objective function. While SB has been studied extensively in single-objective optimisation, its role in multi-objective optimisation remains largely unexplored. This is problematic, as dominance relations, diversity preservation and Pareto-based selection mechanisms may introduce or amplify structural effects.

A reliable benchmark library is essential for advancing research in global optimization by enabling fair comparisons and rigorous testing of optimization algorithms across diverse problem landscapes. In this article, we focus on instance selection methods, which aim to choose representative problems for evaluating algorithm performance. We present a comprehensive review of existing instance selection methods, highlighting their strengths and limitations, particularly in balancing the consideration of algorithm performance and the analysis of problem characteristics using exploratory landscape analysis. Building on these insights, we introduce two novel instance selection methods that leverage both algorithm performance data and landscape analysis information to construct diverse and informative benchmark sets. For evaluation, we benchmark our approaches against four existing instance selection methods on the recently expanded DIRECTGOLib v2.0 library. Our results demonstrate that the proposed methods effectively identify representative instances that capture a wide range of problem characteristics, enabling a more comprehensive evaluation of algorithm performance. These findings have significant implications for the development and assessment of new optimization algorithms, ultimately contributing to more reliable and robust solutions for real-world optimization problems.

The Unmanned Aerial Vehicle (UAV) path planning problem is a complex optimization problem in the field of robotics. In this paper, we investigate the possible utilization of this problem in benchmarking global optimization methods. We devise a problem instance generator and pick 56 representative instances, which we compare to established benchmarking suits through Exploratory Landscape Analysis to show their uniqueness. For the computational comparison, we select fourteen well-performing global optimization techniques from both subfields of stochastic algorithms (evolutionary computation methods) and deterministic algorithms (Dividing RECTangles, or DIRECT-type methods). The experiments were conducted in settings with varying dimensionality and computational budgets. The results were analyzed through several criteria (number of best-found solutions, mean relative error, Friedman ranks) and utilized established statistical tests. The best-ranking methods for the UAV problems were almost universally the top-performing evolutionary techniques from recent competitions on numerical optimization at the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation. Lastly, we discussed the variable dimension characteristics of the studied UAV problems that remain still largely under-investigated. The code and results are available at a Zenodo repository https://doi.org/10.5281/zenodo.15424080 .

This paper addresses the challenge of selecting the most suitable optimization algorithm by presenting a comprehensive computational comparison between stochastic and deterministic methods. The complexity of algorithm selection arises from the absence of a universal algorithm and the abundance of available options. Manual selection without comprehensive studies can lead to suboptimal or incorrect results. In order to address this issue, we carefully selected twenty-five promising and representative state-of-the-art algorithms from both aforementioned classes. The evaluation with up to the twenty dimensions and large evaluation budgets (105×n) was carried out in a significantly expanded and improved version of the DIRECTGOLib v2.0 library, which included ten distinct collections of primarily continuous test functions. The evaluation covered various aspects, such as solution quality, time complexity, and function evaluation usage. The rankings were determined using statistical tests and performance profiles. When it comes to the problems and algorithms examined in this study, EA4eig, EBOwithCMAR, APGSK-IMODE, 1-DTC-GL, OQNLP, and DIRMIN stand out as superior to other derivative-free solvers in terms of solution quality. While deterministic algorithms can locate reasonable solutions with comparatively fewer function evaluations, most stochastic algorithms require more extensive evaluation budgets to deliver comparable results. However, the performance of stochastic algorithms tends to excel in more complex and higher-dimensional problems. These research findings offer valuable insights for practitioners and researchers, enabling them to tackle diverse optimization problems effectively.

Surrogate-assisted evolutionary algorithms (SAEAs) are currently among the most widely researched techniques for their capability to solve expensive real-world optimization problems. The development of these techniques and their bench-marking with other methods still relies almost exclusively on artificially created problems. In this paper, we use a real-world problem of optimizing the parameters of a hospital resource planning tool to compare the performance of nine state-of-the-art single-objective SAEAs. We find that there are significant differences between the performance of the compared methods on the selected instances, making the problems suitable for benchmarking SAEAs.

Several real-world applications introduce derivativefree optimization problems, called variable dimension problems, where the problem's dimension is not known in advance. Despite their importance, no unified framework for developing, comparing, and benchmarking variable dimension problems exists. The robot arm controlling problem is a variable dimension problem where the number of joints to optimize defines the problem's dimension. For a holistic study of global optimization methods, we studied 14 representative methods from 4 different categories, i.e., (i) local search optimization techniques with random restarts, (ii) state-of-the-art DIRECT-type methods, (iii) established Evolutionary Computation approaches, and (iv) state-of-the-art Evolutionary Computation approaches. To investigate the effect of the problem's dimensionality on the solution we generated 20 instances of various combinations among the number of predefined and open decision variables, and we performed experiments for various computational budgets. The results attest that the robot arm controlling problem provides a proper benchmark for variable dimensions. Furthermore, methods in-corporating local search techniques have dominant performance for higher dimensionalities of the problem, while state-of-the-art EC methods dominate in the lower dimensionalities.

The aim of this paper is to show the possibility of generating general semi-stable periodic orbits using genetic programming (GP). This concept is a GP design of a perturbation sequence that forces a defined dynamical system to behave periodically. Recall that periodic orbits in deterministic chaotic systems are trajectories along which the system moves at regular intervals. Despite the chaotic nature of these systems, periodic orbits represent the repetition of certain states of the system over time. In chaotic systems, these orbits are usually surrounded by complex, irregular trajectories, but are themselves defined by regularity and predictability. We should add that periodic orbits are important to chaos theory because they provide a basis for understanding the internal structure of chaotic systems. Although chaos is defined by unpredictability based on initial conditions and the complexity, these periodic orbits represent islands of predictability that can be analyzed and modeled. GP and its symbolic regression capability is an ideal tool for finding both stable periodic orbits defined by stable points and general periodic orbits that rebuild attractive periodic states for the system. The objective function is also crucial for finding periodic orbits using GP. This function has been designed to achieve stable regions as well as the possibility of choosing the degree of the orbital. The test problem will consist of four systems of deterministic chaos, the so-called chaotic maps - the logistic map, the Henon map, the Lozi map and the Burgers map.

Several researchers have turned their attention to the structural components of Evolutionary Computation and Swarm Intelligence-oriented approaches. This direction offers various opportunities, such as developing automatic design and configuration frameworks and integrating operators and mechanisms addressing known limitations. This work lists recent operators and discusses promising mechanisms found in existing atureinspired approaches. It also discusses how these algorithmic components can be integrated into modular frameworks and how they can be assessed and benchmarked. The work aims to emphasize the importance of the research direction about nature-inspired mechanisms and operators in the Evolutionary Computation field.

Inverse heat transfer problems are ill-posed problems and their solution is challenging. Conventional (hard computing) solution methods were developed for this purpose in the past, but they are not well applicable in cases including phase change, which contain strong non-linearity and bring additional computational difficulties. Soft computing methods, which currently experience very rapid development, are a promising tool for the solution of such problems. This paper addresses an inverse heat transfer problem with phase change, in which the boundary heat flux is estimated. Four methods based on distinct mathematical principles are applied to this problem and thoroughly compared. These methods include a conventional Levenberg–Marquardt method (LMM), a predictive fuzzy logic (PFL)-based method, a population-based meta-heuristic method called LSHADE (a state-of-the-art differential evolution variant), and a recently developed surrogate-assisted method coupled with differential evolution, referred to as LSADE method. Furthermore, a reformulation of the problem was developed, utilising a dimension reduction scheme and a decomposition scheme that led to sub-problems with different time frames. This reformulation brought extensive computational improvements. Results of the comparison of the methods then showed that the LMM and the PFL behave well in case without phase change but their performance deteriorates substantially in case with phase change. The LSHADE and the LSADE showed superior performance in the solution of the inverse problem with the phase change. Moreover, their performance was rather stable and insensitive to the location of the temperature sensor , which was the source of data for the estimation.

The development and comparison of new optimization methods in general, and evolutionary algorithms in particular, rely heavily on benchmarking. In this paper, the construction of novel zigzag-based benchmark functions for bound constrained single objective optimization is presented. The new benchmark functions are non-differentiable, highly multimodal, and have a built-in parameter that controls the complexity of the function. To investigate the properties of the new benchmark functions two of the best algorithms from the CEC'20 Competition on Single Objective Bound Constrained Optimization, as well as one standard evolutionary algorithm, were utilized in a computational study. The results of the study suggest that the new benchmark functions are very well suited for algorithmic comparison.