Most evolutionary optimization algorithms assume that the evaluation of the objective and constraint functions is straightforward. In solving many real-world optimization problems, however, such objective functions may not exist. Instead, computationally expensive numerical simulations or costly physical experiments must be performed for fitness evaluations. In more extreme cases, only historical data are available for performing optimization and no new data can be generated during optimization. Solving evolutionary optimization problems driven by data collected in simulations, physical experiments, production processes, or daily life are termed data-driven evolutionary optimization. In this paper, we provide a taxonomy of different data driven evolutionary optimization problems, discuss main challenges in data-driven evolutionary optimization with respect to the nature and amount of data, and the availability of new data during optimization. Real-world application examples are given to illustrate different model management strategies for different categories of data-driven optimization problems.

We propose a surrogate-assisted reference vector guided evolutionary algorithm (EA) for computationally expensive optimization problems with more than three objectives. The proposed algorithm is based on a recently developed EA for many-objective optimization that relies on a set of adaptive reference vectors for selection. The proposed surrogate-assisted EA (SAEA) uses Kriging to approximate each objective function to reduce the computational cost. In managing the Kriging models, the algorithm focuses on the balance of diversity and convergence by making use of the uncertainty information in the approximated objective values given by the Kriging models, the distribution of the reference vectors as well as the location of the individuals. In addition, we design a strategy for choosing data for training the Kriging model to limit the computation time without impairing the approximation accuracy. Empirical results on comparing the new algorithm with the state-of-the-art SAEAs on a number of benchmark problems demonstrate the competitiveness of the proposed algorithm.

Many-objective optimization problems (MaOP) contain four or more conflicting objectives to be optimized. A number of efficient decomposition-based evolutionary algorithms have been developed in the recent years to solve them. However, computationally expensive MaOPs have been scarcely investigated. Typically, surrogate-assisted methods have been used in the literature to tackle computationally expensive problems, but such studies have largely focused on problems with 1-3 objectives. In this study, we present an approach called HSMEA to solve computationally expensive MaOPs. The key features of the approach include (a) the use of multiple surrogates to effectively approximate a wide range of objective functions, (b) use of two sets of reference vectors for improved performance on irregular Pareto fronts, (c) effective use of archive solutions during offspring generation and (d) a local improvement scheme for generating high quality infill solutions. Furthermore, the approach includes constraint handling which is often overlooked in contemporary algorithms. The performance of the approach is benchmarked extensively on a set of unconstrained and constrained problems with regular and irregular Pareto fronts. A statistical comparison with the existing techniques highlights the efficacy and potential of the approach.

A new data-driven reference vector-guided evolutionary algorithm has been successfully implemented to construct surrogate models for various objectives pertinent to an industrial blast furnace. A total of eight objectives have been modeled using the operational data of the furnace using 12 process variables identified through a principal component analysis and optimized simultaneously. The capability of this algorithm to handle a large number of objectives, which has been lacking earlier, results in a more efficient setting of the operational parameters of the furnace, leading to a precisely optimized hot metal production process.

We tackle three different challenges in solving a real-world industrial problem: formulating the optimization problem, connecting different simulation tools and dealing with computationally expensive objective functions. The problem to be optimized is an air intake ventilation system of a tractor and consists of three computationally expensive objective functions. We describe the modeling of the system and its numerical evaluation with a commercial software. To obtain solutions in few function evaluations, a recently proposed surrogate-assisted evolutionary algorithm K-RVEA is applied. The diameters of four different outlets of the ventilation system are considered as decision variables. From the set of nondominated solutions generated by K-RVEA, a decision maker having substance knowledge selected the final one based on his preferences. The final selected solution has better objective function values compared to the baseline solution of the initial design. A comparison of solutions with K-RVEA and RVEA (which does not use surrogates) is also performed to show the potential of using surrogates.