Multi-objective evolutionary algorithm

Key words Multi-objective molecular library design, multi-objective evolutionary algorithm,... 

Multi-Objective Evolutionary Algorithms A Review of the State-of-the-Art and some of their Applications in Chemical Engineering... 

The first multi-objective evolutionary algorithms (MOEAs) were introduced in the 1980s (Schaffer, 1985), but they became popular only in the mid 1990s. Nowadays, the use of MOEAs in all disciplines has become widespread (see for example (Coello Coello and Lamont, 2004)), and chemical engineering is, by no means, an exception. 

Coello Coello, C. A. and Lament, G. B. (eds.) (2004). Applications of Multi-Objective Evolutionary Algorithms (World Scientific, Singapore), ISBN 981-256-106-4. 

Rudolph, G. (1998). On a multi-objective evolutionary algorithm and its convergence to the Pareto set, in Proceedings of the 5th IEEE Conference on Evolutionary Computation (IEEE Press, Piscataway, New Jersey), pp. 511-516. 

Keywords Multi-objective Evolutionary Algorithm, Feed Optimization, Fluidized Catalytic Cracking... 

Tan, K. C., Lee, T. H., Khoo, D. and Khor, E. F. (2001a). A Multi-objective Evolutionary Algorithm Toolbox for Computer-Aided Multi-objective Optimization, IEEE Transactions on System, Man and Cybernetics Part B, 31(4) 537-556. 

Datta, D., Deb, K., Fonseca, K.M., Lobo, F. and Condado, P. (2006). Multi-objective evolutionary algorithm for land-use management problem. KanGAL Report number 2006005. 

Jaimes, A.L. and Coello Coello C.A. (2008). Multi-objective Evolutionary Algorithms A Review of the State-of-the-Art and some of their Applications in Chemical Engineering, in Rangaiah, G.P. (editor). Multi-objective Optimization Techniques and Applications in Chemical Engineering, World Scientific. 

Van Veldhuizen, D. (1999). Multi-objective evolutionary algorithms classifications, analyses, and new innovations, PhD Thesis, Dayton, Ohio Air Force Institute of Technology. 

The first chapter of the book provides an introduction to MOO with a realistic application, namely, the alkylation process optimization for two objectives. The second chapter reviews nearly 100 chemical engineering applications of MOO since the year 2000 to mid-2007. The next 5 chapters are on the selected MOO techniques they include (1) review of multi-objective evolutionary algorithms in the context of chemical engineering, (2) multi-objective genetic algorithm and simulated... 

Of course, all these measures based upon the ROC curve require knowledge of the ROC curve, which hitherto has been unavailable for the STCA system. In this section we show how multi-objective evolutionary algorithms may be used to derive the ROC curve for the STCA system optimised over all possible parameter values. That is, we seek to discover the set of parameters that simultaneously minimise F 0) and maximise T 0). 

Anastasio Kupinski [13] and Anastasio, Kupinski Nishikawa [3] introduced the use of multi-objective evolutionary algorithms to optimise ROC curves, illustrating the method on a synthetic data and for medical imaging problems. 

Multi-Objective Evolutionary Algorithm (MOEA) Toolbox... 

In terms of dealing with multi-objective problems, many different types of GA have been proposed, for example, vector-optimised evolution strategy, weight-based GA, niched-Pareto GA, predator-prey evolution strategy, Rudolph s elitist multi-objective evolutionary algorithm and distance-based Pareto AG. However, there is probably... 

Optimizing Feed-Forward Neural Network Topology by Multi-objective Evolutionary Algorithms A Comparative Study on Biomedical Datasets... 

Keywords Artificial Neural Networks Multi-Objective Evolutionary Algorithms Akaike Information Criterion... 

In this paper, we follow up on [3] by performing an extensive comparison of a whole set of Multi-Objective Evolutionary Algorithms (MOEAs) on two different datasets, namely the aforementioned WBCD and the Hepatitis Dataset (HD) [5]. First, we try to obtain on each dataset the best possible accuracy, by minimizing at the same time the validation and test error. In a second set of experiments, we try to identify the best trade-off between accuracy and network complexity in this latter case, the optimization criteria are the minimization of (1) the validation error, and (2) a measure of the network complexity, i.e. the Akaike Information Criterion [6] (rather than an explicit minimization of the number of hidden layers and hidden nodes per layer). 

As mentioned earlier, the main idea of this study is to formulate the problem of the definition of an optimal ANN for a specific dataset in a multi-objective fashion. For example, in order to maximize the accuracy, a Multi-Objective Evolutionary Algorithm can be used to minimize the validation error while minimizing the test error. However, depending on the requirements one could also include different optimization criteria in the problem formulation, such as a measure of complexity of the classifier ANN. We will show this in the next section. 

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