MSC-CMA-ES boosts optimization with 2.7x better coverage on complex functions
New restart strategy finds better solutions faster on multimodal landscapes
CMA-ES is a powerful local optimizer, but its performance on multimodal problems relies on restart strategies like IPOP and BIPOP, which restart uniformly and ignore previous evaluations. MSC-CMA-ES, developed by Dimitar Nedanovski, Svetoslav Nenov, and Dimitar Pilev, makes restarts structure-aware: in alternating cycles, a Sobol pre-sample is partitioned into approximate basins of attraction via nearest-better clustering. Restarts are then seeded basin by basin with locally scaled step sizes and population sizes, redundant basin visits are excluded, and the remaining budget is spent on local refinement of the best solution found.
The method was evaluated on four CEC benchmark suites (2014, 2017, 2020, 2022) across ten (suite, dimension) cells with dimensions 5–30 and 51 runs per function, against BIPOP-CMA-ES and five differential evolution algorithms. On composition functions—the hardest class—MSC-CMA-ES achieved the best value on all four aggregate measures, with 2.7× the fixed-budget target coverage of BIPOP-CMA-ES, the highest of any algorithm. On basic functions, it produced the lowest median error, though deep-target coverage was slightly lower due to budget spent on landscape discovery. On hybrid functions, both CMA variants trailed leading DE algorithms, indicating a family-wide limitation. All results and code are publicly available.
- MSC-CMA-ES uses cyclic nearest-better clustering to identify and seed restart basins intelligently, avoiding redundant evaluations.
- Achieves 2.7× the fixed-budget target coverage of BIPOP-CMA-ES on composition functions across CEC2014–2022.
- Outperforms all algorithms on composition functions while maintaining best median error on basic functions, with open-source code.
Why It Matters
Smarter restart strategies can dramatically improve real-world optimization efficiency for complex engineering and AI problems.