Michael T. M. Emmerich

Multiobjective evolutionary algorithms based on target region preferences

Abstract Incorporating decision makers preferences is of great significance in multiobjective optimization. Target region-based multiobjective evolutionary algorithms (TMOEAs), aiming at a well-distributed subset of Pareto optimal solutions within the user-provided region(s), are extensively investigated in this paper. An empirical comparison is performed among three TMOEA instantiations: T-NSGA-II, T-SMS-EMOA and T-R2-EMOA. Experimental results show that T-SMS-EMOA has the best overall performance regarding the hypervolume indicator within the target region, while T-NSGA-II is the fastest algorithm. We also compare TMOEAs with other state-of-the-art preference-based approaches, i.e., DF-SMS-EMOA, RVEA, AS-EMOA and R-NSGA-II to show the advantages of TMOEAs. A case study in the mission planning of earth observation satellite is carried out to verify the capabilities of TMOEAs in the real-world application. Experimental results indicate that preferences can improve the searching ability of MOEAs, and TMOEAs can successfully find nondominated solutions preferred by the decision maker.

Quadcriteria optimization of binary classifiers: error rates, coverage, and complexity

This paper presents a 4-objective evolutionary multiobjective optimization study for optimizing the error rates (false positives, false negatives), reliability, and complexity of binary classifiers. The example taken is the email anti-spam filtering problem.

Coupling between a building spatial design optimisation toolbox and BouwConnect BIM

This paper presents a framework in which a building spatial design optimisation toolbox and a building information modelling environment are coupled. The coupling is used in a case study to investigate the possible challenges that hamper the interaction between a designer and an optimisation method within a BIM environment. The following challenges are identified: Accessibility of optimisation methods; Discrepancies in design representations; And, data transfer between BIM models. Moreover, the study provides insights for the application of optimisation in BIM.

Application of portfolio optimization to drug discovery

Abstract In this work, a problem of selecting a subset of molecules, which are potential lead candidates for drug discovery, is considered. Such molecule subset selection problem is formulated as a portfolio optimization, well known and studied in financial management. The financial return, more precisely the return rate, is interpreted as return rate from a potential lead and calculated as a product of gain and probability of success (probability that a selected molecule becomes a lead), which is related to performance of the molecule, in particular, its (bio-)activity. The risk is associated with not finding active molecules and is related to the level of diversity of the molecules selected in portfolio. It is due to potential of some molecules to contribute to the diversity of the set of molecules selected in portfolio and hence decreasing risk of portfolio as a whole. Even though such molecules considered in isolation look inefficient, they are located in sparsely sampled regions of chemical space and are different from more promising molecules. One way of computing diversity of a set is associated with a covariance matrix, and here it is represented by the Solow-Polasky measure. Several formulations of molecule portfolio optimization are considered taking into account the limited budget provided for buying molecules and the fixed size of the portfolio. The proposed approach is tested in experimental settings for three molecules datasets using exact and/or evolutionary approaches. The results obtained for these datasets look promising and encouraging for application of the proposed portfolio-based approach for molecule subset selection in real settings.

Multiobjective sparse ensemble learning by means of evolutionary algorithms

Abstract Ensemble learning can improve the performance of individual classifiers by combining their decisions. The sparseness of ensemble learning has attracted much attention in recent years. In this paper, a novel multiobjective sparse ensemble learning (MOSEL) model is proposed. Firstly, to describe the ensemble classifiers more precisely the detection error trade-off (DET) curve is taken into consideration. The sparsity ratio (sr) is treated as the third objective to be minimized, in addition to false positive rate (fpr) and false negative rate (fnr) minimization. The MOSEL turns out to be augmented DET (ADET) convex hull maximization problem. Secondly, several evolutionary multiobjective algorithms are exploited to find sparse ensemble classifiers with strong performance. The relationship between the sparsity and the performance of ensemble classifiers on the ADET space is explained. Thirdly, an adaptive MOSEL classifiers selection method is designed to select the most suitable ensemble classifiers for a given dataset. The proposed MOSEL method is applied to well-known MNIST datasets and a real-world remote sensing image change detection problem, and several datasets are used to test the performance of the method on this problem. Experimental results based on both MNIST datasets and remote sensing image change detection show that MOSEL performs significantly better than conventional ensemble learning methods.

Multi-Objective Bayesian Global Optimization using expected hypervolume improvement gradient

Abstract 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.

On Gradient-Based and Swarm-Based Algorithms for Set-Oriented Bicriteria Optimization

This paper is about the numerical solution of multiobjective optimization problems in continuous spaces. The problem is to define a search direction and a dynamical adaptation scheme for sets of vectors that serve as approximation sets. Two algorithmic concepts are compared: These are stochastic optimization algorithms based on cooperative particle swarms, and a deterministic optimization algorithm based on set-oriented gradients of the hypervolume indicator. Both concepts are instantiated as algorithms, which are deliberately kept simple in order to not obfuscate their discussion. It is shown that these algorithms are capable of approximating Pareto fronts iteratively. The numerical studies of the paper are restricted to relatively simple and low dimensional problems. For these problems a visualization of the convergence dynamics was implemented that shows how the approximation set converges to a diverse cover of the Pareto front and efficient set. The demonstration of the algorithms is implemented in Java Script and can therefore run from a website in any conventional browser. Besides using it to reproduce the findings of the paper, it is also suitable as an educational tool in order to demonstrate the idea of set-based convergence in Pareto optimization using stochastic and deterministic search.

Towards many-objective optimization of eigenvector centrality in multiplex networks

Network centrality plays an important role in network analysis — especially in social and economic network analysis such as identification of the most popular actor and artist in the Hollywood community, or to find the most influential scientist in a citation network, or politician in democratic elections. Furthermore, finding an important player for the growth of economics in a region can be important to improve future welfare, or to find important hubs for spreading an important message in crisis management. Many algorithms have been proposed to identify a set of key players in a single network. But in the real world with more complicated data sets we need not only to identify a single player but a set of key players. Moreover, we may have to use different types of links simultaneously, e.g., different social networks, in order to define how influential a node is. This situation can be modelled by multiplex network data. For a multiplex network the set of nodes stays the same, while there are multiple sets of edges. The utilization of such information can be viewed as a multiple objective decision analysis problem. In this paper, we propose a new approach in identifying a network centrality based on a many-objective optimization approach, where the nodes are the potential points to be selected and the objectives are their centrality in the different layers of the network. This yields a new approach to analyse network centrality in multiplex network. For this approach, we propose to compute the Pareto fronts of network centrality of nodes, where maximization of centrality in layer defines its own objective. As a case study, we compute the Pareto fronts for model problems with artificial network and real networks for economic data sets to show on how to find the network centrality trade-offs between different layers and identify efficient sets of key nodes.