Box constraint handling

[nomuramasahir0]

Motivation

I would like to empirically investigate reasonable box constraint handling in the continuous and discrete case in the CMA-ES. This issue is related to https://github.com/CyberAgentAILab/cmaes/pull/136.

[nomuramasahir0]

I found several related papers, which draws the following opinions.

• From [1], the current implementation of cmaes using resampling is somewhat reasonable.
• However, from [2], the performance of resampling becomes much worse when the optimum lies on near the boundary, compared to penalty-based methods. (But it is difficult to use penalty method for us, as ask-and-tell interface urges us to use the same points between the evaluation and the update.)

In conclusion, using resampling is not bad choice for now, but it may be a good idea to allow the use of the penalty method when the ask-and-tell interface is not used.

[1] Handling bound constraints in CMA-ES: An experimental study, Rafał Biedrzycki, Swarm and Evolutionary Computation, 2020. [2] Adaptive Ranking-Based Constraint Handling for Explicitly Constrained Black-Box Optimization, Naoki Sakamoto, Youhei Akimoto, Evolutionary Computation, 2022.