Abstract-We propose a surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive optimization problems with more than three objectives. The proposed algorithm is based on a recently developed evolutionary algorithm for many-objective optimization that relies on a set of adaptive reference vectors for selection. The proposed surrogateassisted evolutionary algorithm 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 surrogate-assisted evolutionary algorithms on a number of benchmark problems demonstrate the competitiveness of the proposed algorithm.

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.

Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008-2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation based algorithms. We also compare these algorithms based on different criteria such as metamodelling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive mmultiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.

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 twelve 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.KEYWORDS: blast furnace, ironmaking, metamodeling, multi-objective optimization, model management, data-driven optimization, Pareto optimality INTRODUCTIONIron blast furnace is an immensely complex reactor and running it in an optimized fashion is a very complex task [1] . Although analytical models exist for this type of 2 reactors that produces hot metal [2] , such models are often quite cumbersome and of limited applicability in a real-life industrial scenario. In addition, a complete understanding of the blast furnace process involves handling several objectives together, which so far has been only marginally successful [3] . Thus, it is extremely complex, if not impossible, to build a simulator for blast furnace optimization and one has to rely upon limited amount of noisy data collected in daily operations to perform optimization.Another challenge in optimization of blast furnaces is that it involves multiple conflicting objectives, which is often known as multiobjective optimization [4] . The evolutionary algorithms have been widely used to solve multiobjective optimization problems [5] .However, the efficacy of most multiobjective evolutionary algorithms deteriorates as the number of objectives becomes more than four [4] , which makes them less suited for blast furnace optimization. Fortunately, many-objective optimization to solve problems with more than three objectives, has received increasing attention recently and many evolutionary algorithms have been developed for such problems [3,6] .Purely data-driven evolutionary optimization has received little attention with few exceptions. Most recently, Wang et al. [7] have also categorized data-driven optimization into two types: on-line and off-line. In on-line optimization, small amount of new data is available during the optimization while in off-line optimization, no extra data other than those in hands is available. The authors have also proposed a surrogate-based data-driven approach, capable of optimizing a trauma system involving two conflicting objectives in an evolutionary way. Although trauma system optimization belongs to offline data-driven 3 optimization [7] , there are a large amount of data available. By contrast, as indicated by Guo et al. [8] , off-line optimization becomes extremely challenging, when amount of historical data is small and noisy. Unfortunately, blast furnace optimization that is being...

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