Towards Self-Adaptive Efficient Global Optimization

Algorithms and the Foundations of Software technolog

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Algorithms and the Foundations of Software technolog

Multi-Objective Bayesian Global Optimization using expected hypervolume improvement gradient

The Expected Hypervolume Improvement (EHVI) is a frequently used infill criterion in Multi-Objective Bayesian Global Optimization (MOBGO), due to its good ability to lead the exploration. Recently, the computational complexity of EHVI calculation is reduced to O(n log n) for both 2-D and 3-D cases. However, the optimizer in MOBGO still requires a significant amount of time, because the calculation of EHVI is carried out in each iteration and usually tens of thousands of the EHVI calculations are required. This paper derives a formula for the Expected Hypervolume Improvement Gradient (EHVIG) and proposes an efficient algorithm to calculate EHVIG. The new criterion (EHVIG) is utilized by two different strategies to improve the efficiency of the optimizer discussed in this paper. Firstly, it enables gradient ascent methods to be used in MOBGO. Moreover, since the EHVIG of an optimal solution should be a zero vector, it can be regarded as a stopping criterion in global optimization, e.g., in Evolution Strategies. Empirical experiments are performed on seven benchmark problems. The experimental results show that the second proposed strategy, using EHVIG as a stopping criterion for local search, can outperform the normal MOBGO on problems where the optimal solutions are located in the interior of the search space. For the ZDT series test problems, EHVIG still can perform better when gradient projection is applied.Algorithms and the Foundations of Software technolog

Dominance-based variable analysis for large-scale multi-objective problems

Optimization problems with multiple objectives and many input variables inherit challenges from both large-scale optimization and multi-objective optimization. To solve the problems, decomposition and transformation methods are frequently used. In this study, an improved control variable analysis is proposed based on dominance and diversity in Pareto optimization. Further, the decomposition method is used in a cooperative coevolution framework with orthogonal sampling mutation. The algorithm's performances are compared against the weighted optimization framework. The results show that the proposed decomposition method has much better accuracy compared to the traditional method. The results also show that the cooperative coevolution framework with a good grouping is very competitive. Additionally, the number of search directions in orthogonal sampling can be easily configured. A small number of search directions will reduce the search space greatly while also restricting the area that can be explored and vice versa.Algorithms and the Foundations of Software technolog

Preference-Based Evolutionary Many-Objective Optimization for Agile Satellite Mission Planning

With the development of aerospace technologies, the mission planning of agile earth observation satellites has to consider several objectives simultaneously, such as profit, observation task number, image quality, resource balance, and observation timeliness. In this paper, a five-objective mixed-integer optimization problem is formulated for agile satellite mission planning. Preference-based multi-objective evolutionary algorithms, i.e., T-MOEA/D-TCH, T-MOEA/D-PBI, and T-NSGA-III are applied to solve the problem. Problem-specific coding and decoding approaches are proposed based on heuristic rules. Experiments have shown the advantage of integrating preferences in many-objective satellite mission planning. A comparative study is conducted with other state-of-the-art preference-based methods (T-NSGA-II, T-RVEA, and MOEA/D-c). Results have demonstrated that the proposed T-MOEA/D-TCH has the best performance with regard to IGD and elapsed runtime. An interactive framework is also proposed for the decision maker to adjust preferences during the search. We have exemplified that a more satisfactory solution could be gained through the interactive approach.Algorithms and the Foundations of Software technolog

The set-based hypervolume Newton method for bi-objective optimization

Algorithms and the Foundations of Software technolog

Towards Multi-objective Mixed Integer Evolution Strategies

Many problems are of a mixed integer nature, rather than being restricted to a single variable type. Although mixed integer algorithms exist for the single-objective case, work on the multi-objective case remains limited. Evolution strategies are stochastic optimisation algorithms that feature step size adaptation mechanisms and are typically used in continuous domains. More recently they were generalised to mixed integer problems. In this work, first steps are taken towards extending the single-objective mixed integer evolution strategy for the multi-objective case. First results are promising, but step size adaptation for the multi-objective case can likely be improved.Algorithms and the Foundations of Software technolog

Cluster-based Kriging approximation algorithms for complexity reduction

Kriging or Gaussian Process Regression is applied in many fields as a non-linear regression model as well as a surrogate model in the field of evolutionary computation. However, the computational and space complexity of Kriging, that is cubic and quadratic in the number of data points respectively, becomes a major bottleneck with more and more data available nowadays. In this paper, we propose a general methodology for the complexity reduction, called cluster Kriging, where the whole data set is partitioned into smaller clusters and multiple Kriging models are built on top of them. In addition, four Kriging approximation algorithms are proposed as candidate algorithms within the new framework. Each of these algorithms can be applied to much larger data sets while maintaining the advantages and power of Kriging. The proposed algorithms are explained in detail and compared empirically against a broad set of existing state-of-the-art Kriging approximation methods on a well-defined testing framework. According to the empirical study, the proposed algorithms consistently outperform the existing algorithms. Moreover, some practical suggestions are provided for using the proposed algorithms.Algorithms and the Foundations of Software technolog

Super-structure and super-structure free design search space representations for a building spatial design in multi-disciplinary building optimisation

In multi-disciplinary building optimisation, solutions depend on the representation of the design search space, the latter being a collection of all solutions. This paper presents two design search space representations and discusses their advantages and disadvantages: The first, a super-structure approach, requires all possible solutions to be prescribed in a so-called super-structure. The second approach, super-structure free, uses dynamic data structures that offer freedom in the range of possible solutions. It is concluded that both approaches may supplement each other, if applied in a combination of optimisation methods. A method for this combination of optimisation methods is proposed. The method includes the transformation of one representation into the other and vice versa. Finally, therefore in this paper these transformations are proposed, implemented, and verified as well.Algorithms and the Foundations of Software technolog