A Multi-objective Exploratory Procedure for Regression Model Selection

Variable selection is recognized as one of the most critical steps in statistical modeling. The problems encountered in engineering and social sciences are commonly characterized by over-abundance of explanatory variables, non-linearities and unknown interdependencies between the regressors. An added difficulty is that the analysts may have little or no prior knowledge on the relative importance of the variables. To provide a robust method for model selection, this paper introduces the Multi-objective Genetic Algorithm for Variable Selection (MOGA-VS) that provides the user with an optimal set of regression models for a given data-set. The algorithm considers the regression problem as a two objective task, and explores the Pareto-optimal (best subset) models by preferring those models over the other which have less number of regression coefficients and better goodness of fit. The model exploration can be performed based on in-sample or generalization error minimization. The model selection is proposed to be performed in two steps. First, we generate the frontier of Pareto-optimal regression models by eliminating the dominated models without any user intervention. Second, a decision making process is executed which allows the user to choose the most preferred model using visualisations and simple metrics. The method has been evaluated on a recently published real dataset on Communities and Crime within United States.Comment: in Journal of Computational and Graphical Statistics, Vol. 24, Iss. 1, 201

Fidelity Between Unitary Operators and the Generation of Gates Robust Against Off-Resonance Perturbations

We perform a functional expansion of the fidelity between two unitary matrices in order to find the necessary conditions for the robust implementation of a target gate. Comparison of these conditions with those obtained from the Magnus expansion and Dyson series shows that they are equivalent in first order. By exploiting techniques from robust design optimization, we account for issues of experimental feasibility by introducing an additional criterion to the search for control pulses. This search is accomplished by exploring the competition between the multiple objectives in the implementation of the NOT gate by means of evolutionary multi-objective optimization

A predictive strategy based on special points for evolutionary dynamic multi-objective optimization

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI linkThere are some real-world problems in which multiple objectives conflict with each other and the objectives change with time. These problems require an optimization algorithm to track the moving Pareto front or Pareto set over time. In this paper, we propose a predictive strategy based on special points (SPPS) which consists of three mechanisms. The first one is that the non-dominated set is predicted directly by feed-forward center points, which can eliminate many useless individuals predicted by traditional prediction using feed-forward center points. The second one is that a special point set(such as boundary point, knee point, etc.) is introduced into the predicted population which can track Pareto front or Pareto set more accurately. The third one is the adaptive diversity maintenance mechanism based on boundary points and center points. The mechanism can introduce diverse individuals of the corresponding number according to the degree of difficulty of the problem to keep the diversity of the population. The number of these diverse individuals is strongly related to the center points. Then, they are generated evenly throughout the decision space between the boundary points. The proposed strategy is compared with the four other state-of-the-art strategies. The experimental results show that SPPS can do well for dynamic multi-objective optimization