Fig. 2

Performance of DOPS and other meta-heuristics for the Ackley and Rastrigin functions. a: Mean scaled error versus the number of function evaluations for the 10-dimensional Ackley function. DOPS, DDS and ESS find optimal or near optimal solutions within the specified number of function evaluations. b: Mean scaled error versus the number of function evaluations for the 10-dimensional Rastrigin function. Nearly all the techniques find optimal or near optimal solutions within the specified number of function evaluations. c: Mean scaled error versus the number of function evaluations for the 300-dimensional Rastrigin function. DOPS is the only algorithm that finds an optimal or near optimal solution within the specified number of function evaluations. In all cases, the maximum number of function evaluations was \(\mathcal {N}\) = 4000. Mean and standard deviation were calculated over \(\mathcal {T}\) = 25 trials. A star denotes that the average value was less than 1E-6