In solving many real-world optimization problems, neither mathematical functions nor numerical simulations are available for evaluating the quality of candidate solutions. Instead, surrogate models must be built based on historical data to approximate the objective functions and no new data will be available during the optimization process. Such problems are known as offline data-driven optimization problems. Since the surrogate models solely depend on the given historical data, the optimization algorithm is able to search only in a very limited decision space during offline data-driven optimization. This paper proposes a new offline data-driven evolutionary algorithm to make the full use of the offline data to guide the search. To this end, a surrogate management strategy based on ensemble learning techniques developed in machine learning is adopted, which builds a large number of surrogate models before optimization and adaptively selects a small yet diverse subset of them during the optimization to achieve the best local approximation accuracy and reduce the computational complexity. Our experimental results on the benchmark problems and a transonic airfoil design example show that the proposed algorithm is able to handle offline data-driven optimization problems with up to 100 decision variables.

Model management plays an essential role in surrogate-assisted evolutionary optimization of expensive problems, since the strategy for selecting individuals for fitness evaluation using the real objective function has substantial influences on the final performance. Among many others, infill criterion driven Gaussian process assisted evolutionary algorithms have been demonstrated competitive for optimization of problems with up to 50 decision variables. In this paper, a multi-objective infill criterion that considers the approximated fitness and the approximation uncertainty as two objectives is proposed for a Gaussian process assisted social learning particle swarm optimization algorithm. The multi-objective infill criterion uses non-dominated sorting for model management, thereby avoiding combining the approximated fitness and the approximation uncertainty into a scalar function, which is shown to be particularly important for high-dimensional problems, where the estimated uncertainty becomes less reliable. Empirical studies on 50-and 100-dimensional benchmark problems and a synthetic problem constructed from four real-world optimization problems demonstrate that the proposed multi-objective infill criterion is more effective than existing scalar infill criteria for Gaussian process assisted optimization given a limited computational budget.

The balance between the exploration and the exploitation plays a significant role in the meta-heuristic algorithms, especially when they are used to solve large-scale optimization problems. In this paper, we propose a multiple-strategy learning particle swarm optimization algorithm, called MSL-PSO, to solve problems with large-scale variables, in which different learning strategies are utilized in different stages. At the first stage, each individual tries to probe some positions by learning from the demonstrators who have better performance on the fitness value and the mean position of the population. All the best probed positions, each of which has the best fitness among all positions probed by its corresponding individual, will compose a new temporary population. The temporary population will be sorted on the fitness values in a descending order, and will be used for each individual to find its demonstrators, which is based on the rank of the best probed solution in the temporary population and the rank of the individual in the current population, to learn using a new strategy in the second stage. The first stage is used to improve the exploration capability, and the second one is expected to balance the convergence and diversity of the population. To verify the effectiveness of MSL-PSO for solving large-scale optimization problems, some empirical experiments are conducted, which include CEC2008 problems with 100, 500, and 1000 dimensions, and CEC2010 problems with 1000 dimensions. Experimental results show that our proposed MSL-PSO is competitive or has a better performance compared with ten state-of-the-art algorithms.

Many evolutionary algorithms have been proposed for multi-/many-objective optimization problems; however, the tradeoff of convergence and diversity is still the challenge for optimization algorithms. In this paper, we propose a modified particle swarm optimization based on decomposition framework with different ideal points on each reference vector, called MPSO/DD, for many-objective optimization problems. In the MPSO/DD algorithm, the decomposition strategy is used to ensure the diversity of the population, and the ideal point on each reference vector can draw the population converge faster to the optimal front. The position of each individual will be updated by learning the demonstrators in its neighborhood that have less distance to the ideal point along the reference vector. Eight state-of-the-art evolutionary multi-/many-objective optimization algorithms are adopted to compare the performance with MPSO/DD for solving many-objective optimization problems. The experimental results on seven DTLZ test problems with 3, 5, 8, 10, 15 and 20 objectives, respectively, show the efficiency of our proposed method on solving problems with high-dimensional objective space.