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In this paper, we target the problems of finding a global minimum of nonlinear and stochastic programming problems. To solve this type of problem, we propose new approaches based on combining direct search methods with Evolution Strategies (ESs) and Scatter Search (SS) metaheuristics approaches. First, we suggest new designs of ESs and SS with a memory-based element called Gene Matrix (GM) to deal with those type of problems. These methods are called Directed Evolution Strategies (DES) and Directed Scatter Search (DSS), respectively, and they are able to search for a global minima. Moreover, a faster convergence can be achieved by accelerating the evolutionary search process using GM, and in the final stage we apply the Nelder-Mead algorithm to find the global minimum from the solutions found so far. Then, the variable-sample method is invoked in the DES and DSS to compose new stochastic programming techniques. Extensive numerical experiments have been applied on some well-known functions to test the performance of the proposed methods.

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Electrical Capacitance Tomography (ECT) is a well-established industrial process tomography technique. Image reconstruction for the ECT is a nonlinear problem, and the inverse problem is usually ill-posed and ill-conditioned. Hence, the solutions for the ECT are not unique and highly sensitive to the measurement noise. In this paper, a novel tuned fuzzy algorithm is proposed for reconstructing accurate images to monitor the distribution of the multi-phase flow in the industrial process. The proposed algorithm utilizes a Tuned Fuzzy Inference System (TFIS) to overcome the nonlinear characteristics of the ECT system. The optimal parameters of the fuzzy membership functions are obtained using the Particle Swarm Optimization (PSO) technique. In the past few decades, the naturally inspired intelligent swarm algorithms got more attention due to their wide spectrum of research for real-world complex problems optimization. The proposed PSO-tuned fuzzy algorithm is fast since it does not require solving the forward problem to update the sensitivity matrix. Comparing the results with traditional reconstruction algorithms, the proposed algorithm performs better in visual effects and imaging quality, since the image edges and details are better preserved.