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.

In this paper, we discuss the idea of incorporating preference information into evolutionary multi-objective optimization and propose a preference-based evolutionary approach that can be used as an integral part of an interactive algorithm. One algorithm is proposed in the paper. At each iteration, the decision maker is asked to give preference information in terms of his or her reference point consisting of desirable aspiration levels for objective functions. The information is used in an evolutionary algorithm to generate a new population by combining the fitness function and an achievement scalarizing function. In multi-objective optimization, achievement scalarizing functions are widely used to project a given reference point into the Pareto optimal set. In our approach, the next population is thus more concentrated in the area where more preferred alternatives are assumed to lie and the whole Pareto optimal set does not have to be generated with equal accuracy. The approach is demonstrated by numerical examples.

Evolutionary multi-objective optimization algorithms are widely used for solving optimization problems with multiple conflicting objectives. However, basic evolutionary multi-objective optimization algorithms have shortcomings, such as slow convergence to the Pareto optimal front, no efficient termination criterion, and a lack of a theoretical convergence proof. A hybrid evolutionary multi-objective optimization algorithm involving a local search module is often used to overcome these shortcomings. But there are many issues that affect the performance of hybrid evolutionary multi-objective optimization algorithms, such as the type of scalarization function used in a local search and frequency of a local search. In this paper, we address some of these issues and propose a hybrid evolutionary multi-objective optimization framework. The proposed hybrid evolutionary multi-objective optimization framework has a modular structure, which can be used for implementing a hybrid evolutionary multi-objective optimization algorithm. A sample implementation of this framework considering NSGA-II, MOEA/D, and MOEA/D-DRA as evolutionary multi-objective optimization algorithms is presented. A gradient-based sequential quadratic programming method as a single objective optimization method for solving a scalarizing function used in a local search is implemented. Hence, only continuously differentiable functions were considered for numerical experiments. The numerical experiments demonstrate the usefulness of our proposed framework.