Parameter estimation for chaotic systems using the cuckoo search algorithm with an orthogonal learning method

We study the parameter estimation of a nonlinear chaotic system,which can be essentially formulated as a multidimensional optimization problem.In this paper,an orthogonal learning cuckoo search algorithm is used to estimate the parameters of chaotic systems.This algorithm can combine the stochastic exploration of the cuckoo search and the exploitation capability of the orthogonal learning strategy.Experiments are conducted on the Lorenz system and the Chen system.The proposed algorithm is used to estimate the parameters for these two systems.Simulation results and comparisons demonstrate that the proposed algorithm is better or at least comparable to the particle swarm optimization and the genetic algorithm when considering the quality of the solutions obtained.

A Multi-Period Constrained Multi-Objective Evolutionary Algorithm with Orthogonal Learning for Solving the Complex Carbon Neutral Stock Portfolio Optimization Model

Financial market has systemic complexity and uncertainty.For investors,return and risk often coexist.How to rationally allocate funds into different assets and achieve excess returns with effectively controlling risk are main problems to be solved in the field of portfolio optimization(PO).At present,due to the influence of modeling and algorithm solving,the PO models established by many researchers are still mainly focused on single-stage single-objective models or single-stage multiobjective models.PO is actually considered as a multi-stage multi-objective optimization problem in real investment scenarios.It is more difficult than the previous single-stage PO model for meeting the realistic requirements.In this paper,the authors proposed a mean-improved stable tail adjusted return ratio-maximum drawdown rate(M-ISTARR-MD)PO model which effectively characterizes the real investment scenario.In order to solve the multi-stage multi-objective PO model with complex multi-constraints,the authors designed a multi-stage constrained multi-objective evolutionary algorithm with orthogonal learning(MSCMOEA-OL).Comparing with four well-known intelligence algorithms,the MSCMOEA-OL algorithm has competitive advantages in solving the M-ISTARR-MD model on the proposed constructed carbon neutral stock dataset.This paper provides a new way to construct and solve the complex PO model.

Orthogonal nonnegative learning for sparse feature extraction and approximate combinatorial optimization

Nonnegativity has been shown to be a powerful principle in linear matrix decompositions,leading to sparse component matrices in feature analysis and data compression.The classical method is Lee and Seung’s Nonnegative Matrix Factorization.A standard way to form learning rules is by multiplicative updates,maintaining nonnegativity.Here,a generic principle is presented for forming multiplicative update rules,which integrate an orthonormality constraint into nonnegative learning.The principle,called Orthogonal Nonnegative Learning(ONL),is rigorously derived from the Lagrangian technique.As examples,the proposed method is applied for transforming Nonnegative Matrix Factorization(NMF)and its variant,Projective Nonnegative Matrix Factorization(PNMF),into their orthogonal versions.In general,it is well-known that orthogonal nonnegative learning can give very useful approximative solutions for problems involving non-vectorial data,for example,binary solutions.Combinatorial optimization is replaced by continuous-space gradient optimization which is often computationally lighter.It is shown how the multiplicative updates rules obtained by using the proposed ONL principle can find a nonnegative and highly orthogonal matrix for an approximated graph partitioning problem.The empirical results on various graphs indicate that our nonnegative learning algorithms not only outperform those without the orthogonality condition,but also surpass other existing partitioning approaches.