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BIPOP Restart Strategy

Concept WIKI v1 · 7/2/2026

BIPOP is a combined CMA-ES restart strategy introduced by Hansen (2009a) that simultaneously re-initializes the mean vector and covariance matrix while increasing the population size. It is cited within the GENESYS paper as a canonical example of how multiple core restart policies can be composed into a single restart scheme.

BIPOP Restart Strategy

Definition

BIPOP is a named restart strategy for the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). It was proposed by Hansen (2009a) and is referenced in the GENESYS paper as an example of how multiple core restart policies can be composed together.

Core Behaviors

According to the cited evidence, BIPOP simultaneously performs the following actions upon restart:

  • Re-initializes the mean vector of the search distribution.
  • Re-initializes the covariance matrix of the search distribution (replacing its current values rather than carrying them forward).
  • Increases the population size used for sampling.

This combination makes BIPOP a compound strategy: it bundles three restart policies — mean re-initialization, covariance matrix re-initialization, and population-size growth — into a single coordinated restart rule.

Context within GENESYS

In the GENESYS framework for program synthesis, BIPOP is discussed alongside IPOP (Auger & Hansen, 2005) as a representative combination of the framework's underlying core restart policies. The paper notes that "some of these combinations have been proposed in earlier work such as IPOP and BIPOP where they re-initialize mean vector, covariance matrix, and increase population size simultaneously."

This positions BIPOP as a canonical, literature-backed instantiation of the more general Restart Policy concept that GENESYS abstracts over, where the DSL allows arbitrary combinations of primitive restart actions to be assembled.

Relationship to Related Concepts

  • Restart Policy: BIPOP is a concrete instance of a combined restart policy. It composes multiple core restart policies into one strategy.
  • IPOP: A related, simpler combined strategy that also re-initializes the mean vector and covariance matrix while growing the population, but BIPOP is distinguished by its origin in Hansen's 2009 work and its specific two-population interaction scheme in the original CMA-ES literature (note: this specific two-population detail is not confirmed by the provided evidence and is therefore not asserted here).

Evidence Summary

The only available evidence comes from a single source discussing BIPOP in passing as a known combination of restart policies. The descriptions above are limited strictly to what that source explicitly states.

LINKED ENTITIES

1 links
Restart Policy MENTIONS

CITATIONS

4 sources
4 citations
[1] BIPOP was proposed by Hansen (2009a) as a combined CMA-ES restart strategy. Synthesizing Programs with Continuous Optimization (GENESYS)
[2] BIPOP simultaneously re-initializes the mean vector, re-initializes the covariance matrix, and increases the population size. Synthesizing Programs with Continuous Optimization (GENESYS)
[3] BIPOP is presented in the GENESYS paper as an example of a combination of core restart policies, alongside IPOP (Auger & Hansen, 2005). Synthesizing Programs with Continuous Optimization (GENESYS)
[4] BIPOP is mentioned as a known combination of multiple core restart policies, illustrating how restart policies can be constructed by combining core primitives. Synthesizing Programs with Continuous Optimization (GENESYS)