More effective parallel hybrid optimization algorithm for matched field inversion

Existing algorithms for matched field inversion are, in our opinion, still not quite effective. To overcome this shortcoming, we develop a hybrid optimization algorithm, which combines differential evolution (DE) algorithm and downhill simplex (DHS) algorithm, and apply it to the problem of determining seabed properties by minimizing the mismatch between measured and modeled acoustic fields. The DE is a global optimization algorithm, which is effective in the first step optimization, but its effectiveness is not sustainable and drops rapidly. we explain in much detail the combination of DHS algorithm and DE algorithm into what we call a more effective DHSDE algorithm. We deduce a mechanism for detecting efficiency fall of DE algorithm and apply it to combining DE and DHS into DHSDE. The DHS algorithm is a local optimization algorithm sensitive to gradient information of objective function, via which the parameter vector is compressed. The ability of parameter vector compression of DHS provides sufficient information for effective running of DE. For the numerical simulation example, our DHSDE algorithm gives 4.0×10^-6 as the final value of objective function; compared with 0.66 for DHS and 3.7×10^-3 for DE, our 4.0×10^-6 is much lower. One of the 13 parameters gives the biggest deviation of DHSDE from the true value: (1600.77-1603)/l603=-0.139%. This deviation is much smaller in absolute value than (1619.7-1603)/1603=1.042% for DHS and (1617.13-1603)/1603=0.881% for DE. These results show preliminarily that our hybrid DHSDE is more effective.