Recently, a local-search heuristic algorithm called extremal optimization (EO) has been proposed and successfully applied in some NP-hard combinatorial optimization problems. This paper presents an investigation on the fundamentals of EO with its applications in discrete and numerical optimization problems. The EO was originally developed from the fundamental of statistic physics. However, in this study we also explore the mechanism of EO from all three aspects: statistical physics, biological evolution or co-evolution and ecosystem. Furthermore, we introduce our contributions to the applications of EO in solving traveling salesman problem (TSP) and production scheduling, and multi-objective optimization problems with novel perspective in discrete and continuous search spaces, respectively. The simulation results demonstrate the competitive performance with EO optimization solutions due to its extremal dynamics mechanism

Based on the critical position of the endpoint quality prediction for basic oxygen furnaces (BOFs) in steelmaking, and the latest results in computational intelligence (CI), this paper deals with the development of a novel memetic algorithm (MA) for neural network (NN) learning. Included in this is the integration of extremal optimization (EO) and Levenberg-Marquardt (LM) gradient search, and its application in BOF endpoint quality prediction. The fundamental analysis reveals that the proposed EO-LM algorithm may provide superior performance in generalization, computation efficiency, and avoid local minima, compared to traditional NN learning methods. Experimental results with production-scale BOF data show that the proposed method can effectively improve the NN model for BOF endpoint quality prediction.

This paper presents a novel approach to automatic design of a robust optimal controller for interval plants with Genetic Programming based on Kharitonov Theorem (KT), which provides a theoretical foundation in the design of robust controller for interval plants. The structure and parameters of the robust optimal controller for interval plants are optimized by Genetic Programming and the Generalized KT related stability criteria are integrated into the solution to guarantee the stability of the closed-loop system. Consequently, the evolved controller not only minimizes time-weighted absolute error (ITAE) of the closed-loop system, but also stabilizes the whole interval plant family robustly. Finally, the simulations on a benchmark problem show that the proposed method can effectively generate a robust optimal controller for interval plants.

Gradient search based neural network training algorithm may suffer from local optimum, poor generalization and slow convergence. In this study, a novel Memetic Algorithm based hybrid method with the integration of “extremal optimization” and “Levenberg–Marquardt” is proposed to train multilayer perceptron (MLP) networks. Inheriting the advantages of the two approaches, the proposed “EO-LM” method can avoid local minima and improve MLP network learning performance in generalization capability and computation efficiency. The experimental tests on two benchmark problems and an application example for the end-point-prediction of basic oxygen furnace in steelmaking show the effectiveness of the proposed EO-LM algorithm.