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243 | 243 | "source": [ |
244 | 244 | "Second is the hybrid single/multi objective CMA strategy. It is tasked with both:\n", |
245 | 245 | "- minimizing the fitness computed as the sum of the scores \n", |
246 | | - "- maximizimg the hyper-volume of the Pareto front formed by the current population of models.\n", |
| 246 | + "- maximizing the hyper-volume of the Pareto front formed by the current population of models.\n", |
247 | 247 | "\n", |
248 | 248 | "At each generation, all models in the population are ranked for both criteria, and a mixed rank is obtained following the formula:\n", |
249 | 249 | "\n", |
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324 | 324 | "\n", |
325 | 325 | "From a theoretical point of view, the advantages of the CMA strategy seem strong:\n", |
326 | 326 | "- In IBEA, the creation of a new generation is performed through random mating and mutation. However, due to the lack of a learning rate, this leads to a lack of convergence in the latter stage of the optimisation as the models will jump around an optimal solution without being able to reach it. In CMA, the `sigma` parameter, which is the width of the distribution from which the models should be drawn, decreases once the optimisation finds a bassin in the fitness landscape, leading to smoother convergence.\n", |
327 | | - "- In IBEA, as the new generation only depends on the latest one, the knowledge contained in the previous generations is almost completely lost. In CMA, the covariance matrix continusly evolves, taking into account the results of each generation, leading to an accumulation of past knowledge about the shape of the local fitness landscape.\n", |
| 327 | + "- In IBEA, as the new generation only depends on the latest one, the knowledge contained in the previous generations is almost completely lost. In CMA, the covariance matrix continuously evolves, taking into account the results of each generation, leading to an accumulation of past knowledge about the shape of the local fitness landscape.\n", |
328 | 328 | "- The ideal CMA population size, computed as int(4 + 3 * log(dimension_parameter_space)) is often one or two order of magnitude smaller than the population size needed by IBEA to reach the same results. This results in less compute per generation for the CMA strategy.\n", |
329 | 329 | "\n", |
330 | 330 | "However, CMA is not without drawbacks:\n", |
331 | 331 | "- It is frequent for the CMA strategy (especially the SO-CMA) to converge too quickly and thus get stuck in sub-optimal minima. Therefore, to achieve the exploration level displayed by the IBEA strategy, it might be needed to run several CMA optimisations in parallel and pool the results.\n", |
332 | | - "- Although the population size is much smaller when using the CMA strategy, a proper convergence might require many more generations than for the IBEA strategy, thus nulliying the advantage of the small generation in term of compute.\n", |
| 332 | + "- Although the population size is much smaller when using the CMA strategy, a proper convergence might require many more generations than for the IBEA strategy, thus nullifying the advantage of the small generation in term of compute.\n", |
333 | 333 | "\n", |
334 | 334 | "Overall, CMA makes a more clever use of the information available, but IBEA is not to be neglected, especially if more compute power is available." |
335 | 335 | ] |
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