![]() The contribution of the family mechanism always increases the performance of both SSGA and ViE respect to their versions without family mechanism (, except when comparing ViE and ViE-noF in DTLZ1:, Wilcoxon rank sum test). ![]() ViE-noF can discover more unique target solutions than SSGA on three benchmarks (FletcherPowell: Griewangk: Rastrigin:, Wilcoxon rank sum test), displaying similar performance in the other benchmark problems. ![]() ViE can discover more unique target solutions than SSGA-F in three benchmark problems (Langerman and FletcherPowell: Hump:, Wilcoxon rank sum test), displaying similar performance in the other benchmark problems. Each plot shows results for 50 repetitions of the experiments on each function (, otherwise, Wilcoxon rank-sum test N.S. ViE can discover more unique solution than SSGA-FS in all benchmarks ( Shubert:, Wilcoxon rank sum test) except for Rastrigin, where results are not significantly different.įigure S10: Number of unique target solutions discovered by SSGA, ViE, SSGA equipped with the family mechanism (SSGA-F) and Viability Evolution without the family mechanism (ViE-noF) on single- and multi-objective problems. The niche-radius is computed using, where is the number of parameters, and are the decision space boundaries of each parameter and is the number of peaks (in our case disconnected target areas) in the fitness landscape. ![]() Niche-radius values for each benchmark problems are reported in Table S5. We set the niche-radius parameter as suggested in. As SSGA was originally designed to discover optimal solutions and not to maximize the number of unique solutions discovered at the final generation, we equipped it with a traditional diversity preservation mechanism, fitness sharing, obtaining a modified version of SSGA named SSGA-FS. Finally, S represents the desired value for the maximum amplitude of any stop band ripple.įigure S6: Number of unique target solutions discovered by SSGA-FS and ViE on single-objective problems. The maximum deviation from G is defined by specifying a lower bound L and upper bound U. The desired cutoff frequency f and output amplitude G are shown. (B) A typical frequency response of a low pass filter. The SPICE models for the operational trans-conductance amplifiers (OTAs) used to build the filter circuit are available from. The performance of each candidate solution is obtained from simulations of the filter circuit using the SPICE circuit simulator. The three constraints on the frequency response characteristics of the filter are set such that there are approximately 300 (296, due to the quantization resolution introduced by the fixed bitstring encoding on possible values) bias current pair values that satisfy all three constraints. Hence, a solution to this problem is a pair of bias current values and the goal of an evolutionary algorithm is to find values for these two bias currents, assuming the fixed topology filter circuit, such that the specified low pass filter functionality is obtained. The filter functionality is specified using constraints on three frequency response characteristics, namely gain-bandwidth product, pass band flatness and stop band attenuation. ![]() This circuit topology allows the filter functionality to be modified using two bias current inputs (Bias-1 and Bias-2). (A) A low-pass filter was evolved using the circuit topology derived from (depicted in figure). ![]()
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