We rediscovered the idea of gradient based evolution presented in Nature-Inspired Algorithms for Optimisation by Thomas Weise, Michael Zapf, Raymond Chiong, Antonio J. Nebro, Raymond Chiong in the chapter The Evolutionary-Gradient-Search Procedure in Theory and Practice. The basic motivation is to improve each step of the evolution by approximating the gradients using some function (black box) calls. We also show that this idea works better for many experiments we have done.
For the theory and basic algorithm, please refer to algorithm.pdf A very rough proof for local convergence is available in the proof.xopp file. We are planning to upload a more formal proof in the future.
lander results after 80 iterations
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walker results after 80 iterations
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Benchmarking results on Restrigin function and Image Reconstruction are available in algorithm.pdf.