Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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Section: Overall Objectives

Scientific Context

Important problems in various scientific domains like biology, physics, medicine or in industry critically rely on the resolution of difficult numerical optimization problems. Often those problems depend on noisy data or are the outcome of complex numerical simulations such that derivatives are not available or not useful and the function is seen as a black-box.

Many of those optimization problems are in essence multiobjective—one needs to optimize simultaneously several conflicting objectives like minimizing the cost of an energy network and maximizing its reliability—and most of the challenging black-box problems are non-convex, non-smooth and combine difficulties related to ill-conditioning, non-separability, and ruggedness (a term that characterizes functions that can be non-smooth but also noisy or multi-modal). Additionally, the objective function can be expensive to evaluate—a single function evaluation might take several minutes to hours (it can involve for instance a CFD simulation).

In this context, the use of randomness combined with proper adaptive mechanisms has proven to be one key component for the design of robust global numerical optimization algorithms.

The field of adaptive stochastic optimization algorithms has witnessed some important progress over the past 15 years. On the one hand, subdomains like medium-scale unconstrained optimization may be considered as “solved” (particularly, the CMA-ES algorithm, an instance of Evolution Strategy (ES) algorithms, stands out as state-of-the-art method) and considerably better standards have been established in the way benchmarking and experimentation are performed. On the other hand, multiobjective population-based stochastic algorithms became the method of choice to address multiobjective problems when a set of some best possible compromises is sought for. In all cases, the resulting algorithms have been naturally transferred to industry (the CMA-ES algorithm is now regularly used in companies such as Bosch, Total, ALSTOM, ...) or to other academic domains where difficult problems need to be solved such as physics, biology [28], geoscience [23], or robotics [25].

Very recently, ES algorithms attracted quite some attention in Machine Learning with the OpenAI article Evolution Strategies as a Scalable Alternative to Reinforcement Learning. It is shown that the training time for difficult reinforcement learning benchmarks could be reduced from 1 day (with standard RL approaches) to 1 hour using ES [27]. A few years ago, another impressive application of CMA-ES, how “Computer Sim Teaches Itself To Walk Upright” (published at the conference SIGGRAPH Asia 2013) was presented in the press in the UK.

Several of those important advances around adaptive stochastic optimization algorithms are relying to a great extent on works initiated or achieved by the founding members of RandOpt particularly related to the CMA-ES algorithm and to the Comparing Continuous Optimizer (COCO) platform (see Section on Software and Platform).

Yet, the field of adaptive stochastic algorithms for black-box optimization is relatively young compared to the “classical optimization” field that includes convex and gradient-based optimization. For instance, the state-of-the art algorithms for unconstrained gradient based optimization like quasi-newton methods (e.g. the BFGS method) date from the 1970s [20] while the stochastic derivative-free counterpart, CMA-ES dates from the early 2000s [21]. Consequently, in some subdomains with important practical demands, not even the most fundamental and basic questions are answered: