Jul 2026· Annual Conference on Genetic and Evolutionary Computation· pp. 484-492· 0 citations· 37 references
Computer Science
TL;DR
Mo-LON/D, a decomposition-based local optima network model for multi-objective landscapes, is introduced, indicating that mo-LON/D offers comparable explanatory power (and even higher correlations) with respect to the performance of state-of-the-art algorithms.
Abstract
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.
Many real-world problems involve several objectives that conflict with each other. In such cases, the goal is not to find a single best solution, but a set of solutions that represent different trade-offs. Although parameterized complexity is a well-established framework for studying hard optimization problems, it has rarely been applied to multi-objective optimization. In this paper, we study the Multi-Objective Traveling Salesperson Problem (MO-TSP) from a parameterized complexity perspective. We focus on two common operators, namely 2-opt and swap. We consider restricted versions of these operators using a distance parameter r, and define (k,r)-neighborhoods that allow up to k applications of the operator. For both operators, we analyze the problem of finding an improved solution with respect to Pareto dominance. We prove that this problem is fixed-parameter tractable when parameterized by k, r, and the maximum edge weight W. These results provide new insight into the complexity of multi-objective optimization and show that parameterized analysis is a useful tool in this setting.
Many-objective optimization has been a field of interest over the past two decades and several evolutionary optimization algorithms have been introduced to tackle these problems; yet two fundamental questions remain underexplored: (i) What happens when the number of objectives grows beyond the typical many-objective regime of about fifteen and becomes massive? (ii) How do problem characteristics, such as the nature of interactions between objectives, influence algorithmic performance? To answer these questions we employ a diagnostic benchmark suite that allows control over problem characteristics and can be scaled to extremely high objective counts. Using this framework we evaluate several state-of-the-art evolutionary algorithms including NSGA-II, NSGA-III, MOEA/D and lexicase selection across a range of dimensionalities and diagnostic problem landscapes. Our experiments reveal that problem characteristics significantly affect algorithm performance. In particular, the nature of interactions between objectives appears important. These results highlight the importance of understanding these properties before selecting an algorithm for a specific problem. We also show that lexicase selection, an algorithm originally designed for genetic programming, compares favorably with state-of-the-art many-objective optimization algorithms while avoiding the dependence on predefined reference directions.
Shakiba Shahbandegan, Jose Guadalupe Hernandez, Emily L. Dolson· arXiv.org· 0 citations
This work investigates how balancing the number of decomposed subproblems and ants impacts performance under a fixed computational budget and introduces MOEA/D-AM, a hybrid algorithm that adapts this decomposition strategy for partial classification rule induction.
Multi-objective combinatorial optimization arises in a wide range of problems and applications, including the canonical multi-objective MaxCut problem. Differentiable single-instance quadratic methods have recently achieved remarkable performance in single-objective combinatorial optimization. In this paper, we develop a differentiable framework for multi-objective MaxCut by combining an adjacency-based quadratic formulation with linear scalarization, thereby reducing the problem to a preference-conditioned single-objective signed-weight MaxCut problem. Theoretically, we characterize the stationary points of the resulting signed-weight formulation and show how they induce preference-conditioned fixed points on the Pareto front. Computationally, unlike conventional heuristics and branch-and-bound methods, our approach is GPU-parallelizable and can therefore benefit from substantial performance speedups. We term our algorithm Multi-objective QUadratic Combinatorial Optimization (MO-QUCO) and its parallelized variant pMO-QUCO. Empirically, across different multi-layered (and weight distributions) graphs, we show that both our CPU-only and GPU-based algorithms outperform SOTA exact and heuristic methods in terms of wall-clock runtime and objective quality. Despite operating under different computational settings, MO-QUCO also outperforms the SOTA quantum method.
Jinghang Huang, Alvaro Velasquez, Jia Liu et al.· 0 citations
An objective-wise variable analysis method that first evaluates the sensitivity of each objective to all decision variables, and then comprehensively aggregates the sensitivity information across multiple objectives to estimate the overall importance of decision variables is proposed.
Chuanlong Ye, Fazhi He, Xiaoxin Gao et al.· Journal of King Saud Univers...· 0 citations
A unified Parallel Evolutionary Algorithm Framework (PEAF) is proposed, which combines structure-inheriting crossover operators, a hierarchical mutation mechanism based on the Multiple Mutation Heuristic and the Auxiliary Cut Mutation Heuristic, and a diversity-preserving selection strategy.
Sihong Shao, Chuan Yang· 0 citations
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