Multi-Objective Efficient Global Optimization Method With Truncated Expected Improvement Matrix-Based Infill Criterion for Problems With Prior Knowledge on Objective Bounds

An Evolution Algorithm with Objective-Wise Variable Analysis for Sparse Large-Scale Multi-Objective Optimization

Sparse large-scale multiobjective optimization problems are widely encountered in scientific research and engineering applications. However, the enormous search space and the intrinsic sparsity of the Pareto-optimal solutions substantially increase the difficulty of the optimization process. Different from existing approaches that directly rely on all objective values, this paper proposes an objective-wise variable analysis method. Specifically, the analysis method 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. As a result, critical variables can be accurately identified to generate initial population, enabling the population to focus on the critical decision subspace efficiently. Furthermore, a non-coordinated mask-real evolution strategy is proposed to fully exploit the potential of mask vector and reduce the interference of real vectors. In this strategy, mask vector and real component evolve at separate update frequencies. This non-coordinate updating mechanism enables the mask structure to better match the corresponding real number vector. Experimental results demonstrate that the proposed algorithm significantly outperforms several state-of-the-art algorithms on the SMOP benchmark suite and exhibits promising potential in four practical real-world applications.

A new dual-population constrained multi-objective evolutionary optimization algorithm with repair constraint handling for structural optimization

Structural optimization problems often involve a large number of decision variables and highly non-convex feasible regions, making convergence to the true Pareto front extremely challenging. Even when convergence is achievable, it typically requires thousands of function evaluations, resulting in significant computational cost. This highlights the need for efficient and robust optimization algorithms for real-world engineering applications. In this study, we introduce a novel constrained multi-objective evolutionary algorithm, termed DPCME. The algorithm employs two interacting populations that exchange information, enabling effective global exploration and reducing the risk of convergence to local optima. To further enhance performance, a recent repair-based constraint-handling technique is incorporated, and alternative repair approaches are proposed and systematically evaluated. The proposed algorithm is tested on three engineering problems: the 72-bar truss, the 120-bar truss, and a chemical tanker structure, each involving hundreds of nonlinear failure constraints. Its performance is evaluated against state-of-the-art constrained multi-objective optimization algorithms from the latest PlatEMO package. A total of 43 algorithms are initially tested, from which the 12 best-performing methods are selected for detailed comparison. The results demonstrate that DPCME achieves superior or competitive convergence and diversity across all test cases, and that the inclusion of repair-based constraint handling further improves its performance.

A general hybrid framework for many-objective optimization: integrating local search into reference-vector-based evolutionary algorithms

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.

Efficient Hessian-Free Methods for Multi-Objective Bilevel Optimization with Nonconvex Lower Level

This work proposes a class of Multi-Objective Moreau Envelope based Hessian-free Algorithms (MOMEHA) to solve the multi-objective bilevel learning problems with nonconvex lower level and proposes a momentum-based variant of MOMEHA (i.e., MB-MOMEHA) method to solve the stochastic multi-objective bilevel learning problems.

Hot off the Press: Superior Runtime Guarantees for the MOEA/D Multi-Objective Optimizer via Weighted-Sum Decomposition

The MOEA/D is the most popular decomposition-based evolutionary algorithm to solve multi-objective optimization problems. However, among the two common decomposition approaches, weighted-sum and Tchebycheff, the existing theoretical research almost exclusively focuses on the latter one. In this first complete mathematical runtime analysis for the MOEA/D using the original weighted-sum decomposition, we show that this variant of the algorithm solves the classic OneMinMax benchmark considerably faster than both the MOEA/D with Tchebycheff decomposition and many other classic algorithms such as the NSGA-II, NSGA-III, SMS-EMOA, and SPEA2. More precisely, we show that already a logarithmic number of subproblems suffices for the algorithm to be efficient, and then typically O(n log2 n) function evaluations suffice to compute the full Pareto front. This beats the other algorithms by a factor of Θ(n/log n). For a second benchmark, the OneJumpZeroJump problem, we show a speed-up by a factor of Θ(n). Overall, this work shows that a further development of the weighted-sum approach might be fruitful. This paper summarizes the work Danyang Zhang, Zerong Zhong, Weijie Zheng, and Benjamin Doerr. 2026. Superior Runtime Guarantees for the MOEA/D Multi-Objective Optimizer via Weighted-Sum Decomposition. In AAAI Conference on Artificial Intelligence, AAAI 2026. AAAI Press, 37187–37194 [14].

A survey of a posteriori multi-objective multidisciplinary optimisation methods and benchmarks