Jul 2026· Annual Conference on Genetic and Evolutionary Computation· pp. 41-49· 1 citation· 35 references
Computer Science
TL;DR
This work proposes a framework for designing both single- and multi-objective benchmark problems with identifiable local optima and controllable landscape features and implies that the landscape features of single-objective MSG landscapes are inherited in multi-objective extensions.
Abstract
The number and arrangement of local optima are crucial for evaluating the exploration-exploitation balance and the ability to discover promising local optima. However, existing benchmark suites rarely provide explicitly defined multi-modal landscapes, especially in multi-objective optimization. To bridge this gap, we propose a framework for designing both single- and multi-objective benchmark problems with identifiable local optima and controllable landscape features. Our approach builds on Max-Set of Gaussians (MSG) landscapes and extends them to the multi-objective domain. To match target landscape features, we optimize Gaussian heights and variances. Empirical results demonstrate that the framework can emulate several function classes from the Black-Box Optimization Benchmarking (BBOB) suite, including separable, multimodal, and ill-conditioned functions. Furthermore, we confirm that the framework can generate problems with Exploratory Landscape Analysis (ELA) feature patterns that are not present in the BBOB suite. Our results also imply that the landscape features of single-objective MSG landscapes are inherited in multi-objective extensions.
Fitness landscape analysis provides insights into optimization problems, informing algorithms' design and identifying properties that influence performance. While understanding global landscape structure is critical, tools for analyzing and visualizing multi-objective, high-dimensional optimization problems remain limited. Recent models, such as Pareto local optima solution networks (PLOS-nets), primarily focus on small instances and binary representations, posing challenges for extension to more complex domains. To address this gap, we introduce mo-LON/D, a decomposition-based local optima network model for multi-objective landscapes. This model partitions a multi-objective problem into scalar sub-problems, constructs standard single-objective local optima networks (LONs) for each, and integrates them via a graph union. We validate mo-LON/D on fully enumerated bi-objective ρmnk-landscapes and contrast its structural features against PLOS-nets both visually and quantitatively. Despite the inherent sampling involved in scalarization, our results indicate that mo-LON/D offers comparable explanatory power (and even higher correlations) with respect to the performance of state-of-the-art algorithms. By harnessing established sampling techniques from single-objective research, mo-LON/D could potentially provide a scalable framework for characterizing complex multi-objective landscapes.
Gabriela Ochoa, Quentin Renau, Arnaud Liefooghe et al.· Annual Conference on Genetic...· 0 citations
Large Language Models (LLMs) are opening new directions for automated heuristic design (AHD), allowing evolutionary methods to create and enhance heuristics for constrained optimization problems (COPs). However, most existing approaches face the challenge of the exploration-exploitation balance, where the evolution needs to escape convergence to homogeneous populations and discover as large a heuristic landscape as possible. To address this challenge, we introduce Quality-Diversity Evolution (QDEvo), a multi-objective framework that integrates Quality-Diversity optimization with LLM-based AHD. At its core, QDEvo employs a semantic survival selection mechanism that clusters algorithms by functional similarity, then applies local Pareto competition. Evaluation on well-known COPs benchmarks and real-world problems shows that our method consistently outperforms the state-of-the-art baseline in both Hypervolume and Inverted Generational Distance metrics. These results facilitate further exploration of the algorithmic design space, while ensuring competitive solution quality and efficiency.
Nam Do Khanh, Nhat Nguyen Tran Minh, Dat Pham Vu Tuan et al.· Proceedings of the Genetic a...· 1 citation
We address the problem of achieving convergence and diversity in many-objective problems, focusing on continuous and unconstrained functions. It is known that with increasing numbers of objectives (say from 4 to 20) even modern many-objective Evolutionary Algorithms (EAs) may struggle to converge to, and fully distribute across the Pareto front. This paper presents a general and modular hybrid approach that integrates local search into reference-vector-based Many-Objective Evolutionary Algorithms (MaOEAs), addressing issues such as weakened selection pressure and the increasing complexity of exploring high-dimensional objective spaces. The hybrid approach employs Sequential Quadratic Programming (SQP) guided by achievement scalarizing directions, derived from either the Weighted Achievement Scalarizing Function (W-ASF) or the Penalty-based Boundary Intersection (PBI) schemes, depending on the decomposition strategy of the underlying MaOEA. It is designed to be broadly applicable with limited parameter tuning, facilitating integration with algorithms from the NSGA-III and MOEA-DD families. The effectiveness of the proposed approach is demonstrated through extensive experiments on standard continuous-variable many-objective benchmark problems as well as on representative real-world case studies. Results show that integrating local search significantly enhances performance, while a principled method for setting hybrid parameters ensures robustness and reproducibility. Although limited to an empirical study over a (large) test function suite, these findings highlight the potential of combining mathematical programming techniques with evolutionary algorithms for high-dimensional many-objective optimization problems.
Regina C. L. C. de Sousa, Dênis E. C. Vargas, Elizabeth F. Wanner et al.· Journal of Heuristics· 0 citations
The evaluation of heuristic optimizers on test problems, better known as benchmarking, is a cornerstone of research in multiobjective optimization. However, many frequently used test problems either feature a limited degree of optimization challenges or have poorly understood reference solutions. Here, we present an overview of BONO-Bench [5], a recently proposed problem generator and benchmark set for bi-objective numerical optimization. Building on convex-quadratic problems, it features diverse challenges ranging from different levels of conditioning, shapes of Pareto set and front as well as plateaus to different structured and unstructured multimodality patterns. Furthermore, we enable best practices for empirical runtime analysis of optimizers using reference solutions that can be approximated to an arbitrary degree, resulting in precise target values for the hypervolume and exact R2 indicators.
Lennart Schäpermeier, P. Kerschke· Proceedings of the Genetic a...· 0 citations
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. In this paper, we extend the concept of structural bias to the multi-objective setting and propose a methodology to study it in isolation from fitness-driven guidance. We introduce a suite of synthetic multi-objective test problems with analytically controlled Pareto fronts and deliberately uninformative objective values. These problems are designed to decouple algorithmic behaviour from problem structure, allowing bias induced purely by algorithmic operators and design choices to be observed. The test suite covers a range of Pareto front shapes, densities and noise levels, enabling systematic analysis of different manifestations of structural bias. We discuss methodological challenges specific to the multi-objective case and outline how existing SB detection approaches can be adapted. This work provides a first step towards behaviour-based benchmarking of multi-objective optimisers, complementing performance-based evaluation and informing more robust algorithm design.
Jakub Kůdela, Niki van Stein, T. Bäck et al.· Annual Conference on Genetic...· 0 citations
A continuous development of metaheuristics necessitates a deeper understanding of internal search mechanisms, specifically the transition between exploration and exploitation, which is often overlooked in favour of final fitness values. This study introduces a standardized framework based on a Normalized Positional Diversity Index (D*) to quantify optimizer behaviour. We demonstrate that D* is a geometric generalization of existing measures, such as the one proposed by Hussain et al. [1], by replacing stochastic, path-dependent historical maximums with a fixed global upper bound anchored to the search space geometry. This transformation eliminates post-hoc bias and provides a scale-independent diagnostic. From D*, additional metrics including Area Under the Curve (AUC) and crossover point (txover) are derived to identify exact phase transitions. We evaluate five optimizers (GWO, DE, PSO, AGOA, and EES) across CEC 2020 benchmarks. Results confirm that D* offers consistent diversity monitoring with lower Coefficients of Variation compared to existing measures. Code and supplementary materials are available at: [https://github.com/saiddddd/D-Star-Metric-Optimization].
Said Gani, A. Bhat· Proceedings of the Genetic a...· 0 citations