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

Real-world constrained multi-objective optimization problems (CMOPs) commonly involve multiple constraints, and understanding and exploiting their coupling relationships is crucial for efficient optimization. Recent constraint-decoupling methods handle individual constraints separately, but they generally search only in the evolutionary direction to approximate single-constraint Pareto fronts (SCPFs). In this study, we show that part or all of the constrained Pareto front (CPF) may be unrelated to any SCPF and instead be shaped by the boundaries of infeasible regions. We refer to such a portion as the independent CPF (ICPF) and introduce the reverse CPF (RCPF) to characterize its associated informative infeasible boundaries. Based on these observations, we propose a bidirectional constraint-decoupling coevolutionary algorithm named DCF2D. DCF2D dynamically identifies the constraints obstructing the main population and activates constraint-specific auxiliary populations. These populations adaptively search in the evolutionary direction for the corresponding SCPFs or in the reverse evolutionary direction for the corresponding RCPFs. Its three-stage framework integrates unconstrained global exploration, event-driven bidirectional coevolution, and final convergence refinement. Experiments on 87 benchmark instances from seven test suites and 28 real-world engineering CMOPs demonstrate that DCF2D achieves the best overall performance among nine algorithms. Code available at: https://github.com/RuiqingS/DCF2D.

Constrained Optimization Problems are crucial in fields such as engineering, economics, and robotics, where high-dimensional search spaces and complex objectives and constraints are common. Numerical optimization methods, including Feasible Direction, Interior Point, and Sequential Quadratic Programming, have shown strong performance in finding feasible local optima, but require accurate analytical gradients and effective initialization, which can be challenging in real-world settings. Evolutionary Algorithms, on the other hand, offer gradient-free search and robustness to noisy landscapes, managing to detect global optima more often than numerical methods, but they often suffer from high computational costs and slow convergence. In this work, we propose a Hybrid Augmented Lagrangian (HyAL) method that integrates the AL framework's constraint-handling strengths with the exploratory power of population-based search. Our approach employs evolutionary techniques to solve subproblems within the AL iterations, promoting exploration and aiding in the escape from local optima. We conduct extensive experiments on benchmark optimization problems, comparing our method against state-of-the-art optimizers, including IPOPT and CMA-ES, and a standalone evolutionary optimization baseline (with constraint enforcement via penalties). In addition, we evaluate four population-based methods integrated within the AL framework to study the effect of different evolutionary solvers. Our results show that HyAL consistently produces high-quality solutions across the benchmark suite. It outperforms purely evolutionary approaches and scales more effectively to high-dimensional constrained problems, where evolutionary-only methods often struggle. HyAL also surpasses state-of-the-art numerical optimization algorithms on complex landscapes containing numerous local minima and saddle points.

Multiobjective optimization remains challenging for many scientific and engineering problems due to the need to balance convergence, diversity, and computational efficiency across high-dimensional objective landscapes. This work presents the Multiobjective Animorphic Ensemble Optimization (MAEO) framework, a parallelizable ensemble strategy that unifies state-of-the-art evolutionary algorithms within an island-based architecture, overcoming the limitations of relying on a single optimizer, as implied by the No Free Lunch theorem. MAEO uses a parameter-free hypervolume indicator for island performance assessment and a strict Pareto-rank-based individual scoring formulation that incorporates crowding distance and nadir-point proximity to ensure consistent selection pressure within each front. The framework is initiated using four algorithms (NSGA-III, CTAEA, AGEMOEA2, SPEA2) and evaluated through extensive benchmarking on 12 DTLZ/ZDT functions under 36 dimensionality settings using Wilcoxon signed-rank tests with both hypervolume and inverse generational distance metrics. Results show that MAEO achieves balanced convergence-diversity performance, outperforming or matching some of the leading multiobjective optimization algorithms across different benchmark problems. To demonstrate practical applicability, MAEO is applied to the equilibrium-cycle optimization of a small modular nuclear reactor. Eight discrete design variables (and three objectives (levelized cost of electricity, peak soluble boron concentration, fuel cycle length) are optimized under two safety constraints. The algorithm carried out roughly 40000 evaluations using computer simulations. MAEO identifies core designs that lower both the levelized cost of electricity and the peak boron concentration, while preserving fuel cycle length and meeting all safety constraints.