This paper presents a simple multiobjective evolutionary algorithm and considers its application to two-objective optimization problems in design of digital maps. The algorithm is based on the MOEA/D and uses mutation operators in reproduction of potential solutions. The digital map is defined on a set of points and can generate various periodic spike-trains. The algorithm is applied to two simple problems that require optimization of autocorrelation of periodic spike-trains and distribution of inter spike intervals. The first problem has a trade-off between two objective functions and the algorithm can find an approximated Pareto front. The second problem does not have a trade-off and the algorithm can find an approximated utopia point. The algorithm performance is confirmed in elementary numerical experiments.

Nested-layer particle swarm optimization (NLPSO) is a powerful method to detect bifurcation parameters in discrete-time dynamical systems. Although NLPSO requires no carefully set initial system parameters, Lyapunov exponents or derivation of objective functions, the method can quickly and accurately detect the bifurcation parameter. Previous studies have proven the effectiveness of NLPSO for discrete-time dynamical systems, but they have not demonstrated the effectiveness of continuous dynamical systems. This study proposes an NLPSO-based method to detect bifurcation parameters in non-autonomous continuous-time dynamical systems and applies the method to the Duffing equation. By adding Poincaré maps computation to the algorithm, the NLPSO accurately detected period-doubling and saddle-node bifurcation parameters in the non-autonomous dynamical systems and the discrete-time dynamical systems, without a change in objective functions.