A Comparative Study of PSO and CMA-ES Algorithms on Black-box Optimization Benchmarks

Abstract

Numerous practical engineering applications can be formulated as non-convex, non-smooth, multi-modal and ill-conditioned optimization problems. Classical, deterministic algorithms require an enormous computational effort, which tends to fail as the problem size and its complexity increase, which is often the case. On the other hand, stochastic, biologically-inspired techniques, designed for global optimum calculation, frequently prove successful when applied to real life computational problems. While the area of bio-inspired algorithms (BIAs) is still relatively young, it is undergoing continuous, rapid development. Selection and tuning of the appropriate optimization solver for a particular task can be challenging and requires expert knowledge of the methods to be considered. Comparing the performance of viable candidates against a defined test bed environment can help in solving such dilemmas. This paper presents the benchmark results of two biologically inspired algorithms: covariance matrix adaptation evolution strategy (CMA-ES) and two variants of particle swarm optimization (PSO). COCO (COmparing Continuous Optimizers) -a platform for systematic and sound comparisons of real-parameter global optimization solvers was used to evaluate the performance of CMA-ES and PSO methods. Particular attention was paid to the efficiency and scalability of both techniques.

Optimization of an Oil and Gas Separation Plant for Different Reservoir Fluids Using an Evolutionary Algorithm

“…The CMA-ES algorithm is very convenient since it has minimal parameters to be set by the user, can be run with default settings with good results, and does not require parameter tuning. In addition, the CMA-ES has been used for a similar application with success and studies also indicate that CMA-ES has good performance compared to other algorithms. , The strength of the method relies on a smart generation of phase space points (seeds) applied to probe the phase space in an effective way in search of local/global maxima. Briefly, a population of phase space points (seeds) are iteratively generated by sampling from a multivariate normal distributionwith its corresponding mean and covariance matrix updated at each step in the iteration processuntil the method converges to a local maximum or to the global maximum.…”

“…In addition, the CMA-ES has been used for a similar application with success 9 and studies also indicate that CMA-ES has good performance compared to other algorithms. 25,26 The strength of the method relies on a smart generation of phase space points (seeds) applied to probe the phase space in an effective way in search of local/ global maxima. Briefly, a population of phase space points (seeds) are iteratively generated by sampling from a multivariate normal distributionwith its corresponding mean and covariance matrix updated at each step in the iteration processuntil the method converges to a local maximum or to the global maximum.…”

Aberration correction for multiphoton microscopy using covariance matrix adaptation evolution strategy

“…Here, we propose a new approach to indirect AO based on an algorithm called covariance matrix adaptation evolution strategy (CMA-ES) [15] . The CMA-ES is a widely used algorithm for black-box optimization problems and has proved to be very effective [16] . Through both numerical simulation and experiment, we show that the CMA-ES has a faster convergence speed and higher accuracy than the GA in indirect AO, which provides a new approach for fast in vivo aberration correction and provides the possibility of further improving the maximum multi-photon imaging depth.…”

“…are stochastic search methods inspired by the principles of biological evolution typically using a multivariate normal mutation distribution. The CMA-ES is considered to be one of the best choices against ill-conditioned, non-convex black-box optimization problems in the continuous domain [16] . The core idea of the CMA-ES is to deal with the dependence between variables and scaling by adjusting the covariance matrix in the normal distribution [15] .…”

Learning causal theories with non-reversible MCMC methods

“…Hansen et al (2016);Szynkiewicz (2018);Dolan and More (2001);More and Wild (2009) we use empirical cumulative distribution function (ECDF) (seeVaart, 1998) to display the proportion of trials which achieved accuracy ǫ ∈ {1, 2, 3, 5, 8, 10}. Figures, depicting ECDF curves prove that the Q 1 algorithm outperforms the Q 2 algorithm in all the phases considered.…”