Function evaluations (FEs) of many real-world optimization problems are time or resource consuming, posing a serious challenge to the application of evolutionary algorithms (EAs) to solve these problems. To address this challenge, the research on surrogate-assisted EAs has attracted increasing attention from both academia and industry over the past decades. However, most existing surrogate-assisted EAs (SAEAs) either still require thousands of expensive FEs to obtain acceptable solutions, or are only applied to very low-dimensional problems. In this paper, a novel surrogate-assisted particle swarm optimization (PSO) inspired from committee-based active learning (CAL) is proposed. In the proposed algorithm, a global model management strategy inspired from CAL is developed, which searches for the best and most uncertain solutions according to a surrogate ensemble using a PSO algorithm and evaluates these solutions using the expensive objective function. In addition, a local surrogate model is built around the best solution obtained so far. Then, a PSO algorithm searches on the local surrogate to find its optimum and evaluates it. The evolutionary search using the global model management strategy switches to the local search once no further improvement can be observed, and vice versa. This iterative search process continues until the computational budget is exhausted. Experimental results comparing the proposed algorithm with a few state-of-the-art SAEAs on both benchmark problems up to 30 decision variables as well as an airfoil design problem demonstrate that the proposed algorithm is able to achieve better or competitive solutions with a limited budget of hundreds of exact FEs.
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.
Many real-world optimization problems involve computationally intensive numerical simulations to accurately evaluate the quality of solutions. Usually the fidelity of the simulations can be controlled using certain parameters and there is a trade-off between simulation fidelity and computational cost, i.e., the higher the fidelity, the more complex the simulation will be. To reduce the computational time in simulation-driven optimization, it is a common practice to use multiple fidelity levels in search for the optimal solution. So far, not much work has been done in evolutionary optimization that considers multiple fidelity levels in fitness evaluations. In this work, we aim to develop test suites that are able to capture some important characteristics in real-world multi-fidelity optimization, thereby offering a useful benchmark for developing evolutionary algorithms for multi-fidelity optimization. To demonstrate the usefulness of the proposed test suite, three strategies for adapting the fidelity level of the test problems during optimization are suggested and embedded in a particle swarm optimization algorithm. Our simulation results indicate that the use of changing fidelity is able to enhance the performance and reduce the computational cost of the particle swarm optimization, which is desired in solving expensive optimization problems.
Minimax optimization is a widely-used formulation for robust design in multiple operating or environmental scenarios, where the worst-case performance among multiple scenarios is the optimization objective requiring a large number of quality assessments. Consequently, minimax optimization using evolutionary algorithms becomes prohibitive when each quality assessment involves computationally expensive numerical simulations or costly physical experiments. This work employs evolutionary multitasking optimization and surrogate techniques to address the challenges of the high-dimensional search space and high computation cost. To this end, finding the worst-case scenario for different candidate solutions is considered as the optimization of multiple problems that can be solved simultaneously using the evolutionary multi-tasking optimization approach. In order to further speed up the proposed algorithm, a surrogate model in the joint space of the decision and scenario spaces is built to replace part of the expensive function evaluations. A generation-based model management strategy using a statistical hypothesis test is designed to manage the surrogate model. Experimental results on both benchmark problems and an airfoil design application indicate that the proposed algorithm can find satisfactory solutions with a very limited computational budget.
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