Abstract-Surrogate models have shown to be effective in assisting metaheuristic algorithms for solving computationally expensive complex optimization problems. The effectiveness of existing surrogate-assisted metaheuristic algorithms, however, has only been verified on low-dimensional optimization problems. In this paper, a surrogate-assisted cooperative swarm optimization algorithm is proposed, in which a surrogate-assisted particle swarm optimization algorithm and a surrogate-assisted social learning based particle swarm optimization algorithm cooperatively search for the global optimum. The cooperation between the particle swarm optimization and the social learning based particle swarm optimization consists of two aspects. First, they share promising solutions evaluated by the real fitness function. Second, the social learning based particle swarm optimization focuses on exploration while the particle swarm optimization concentrates on local search. Empirical studies on six 50-dimensional and six 100-dimensional benchmark problems demonstrate that the proposed algorithm is able to find high-quality solutions for high-dimensional problems on a limited computational budget.

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Gaussian processes (GPs) are the most popular model used in surrogate-assisted evolutionary optimization of computationally expensive problems, mainly because GPs are able to measure the uncertainty of the estimated fitness values, based on which certain infill sampling criteria can be used to guide the search and update the surrogate model. However, the computation time for constructing GPs may become excessively long when the number of training samples increases, which makes it inappropriate to use them as surrogates in evolutionary optimization. To address this issue, this paper proposes to use ensembles as surrogates and infill criteria for model management in evolutionary optimization. A heterogeneous ensemble consisting of a least square support vector machine and two radial basis function networks is constructed to enhance the reliability of ensembles for uncertainty estimation. In addition to the original decision variables, a selected subset of the decision variables and a set of transformed variables are used as inputs of the heterogeneous ensemble to further promote the diversity of the ensemble. The proposed heterogeneous ensemble is compared with a GP and a homogeneous ensemble for infill sampling criteria in evolutionary multiobjective optimization. Experimental results demonstrate that the heterogeneous ensemble is competitive in performance compared with GPs and much more scalable in computational complexity to the increase in search dimension.

The recent financial crisis and other major crises have suggested that there are some strong interactions and interdependence between several supply chains and their external environments in various ways. A set of supply chains that are interdependent is called a holistic supply chain network (H-SCN) in this paper. There is a need to focus on building the resilience (in short, the ability of a system to recover from damage or disruption) of an entire H-SCN as it is believed that such a network system is strongly relevant to the recent economic recession that is triggered by financial crises. The objectives of this paper are to provide a classification of different SCNs in literature, leading to the identification of a new type of SCN system, i.e., an H-SCN, and to discuss the state of knowledge on the resilience of SCNs, particularly of an H-SCN. A systematic review approach is applied in this paper. Another contribution of this paper is the provision of a more comprehensive definition and description of resilient systems, including SCN systems. A final contribution of this paper is the proposal of the future directions of research on resilient SCN systems, particularly resilient H-SCN systems. Manuscript

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