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A FLEXIBLE OBJECTIVE-CONSTRAINT APPROACH AND A NEW ALGORITHm FOR CONSTRUCTING THE PARETO FRONT OF mULTIOBJECTIVE OPTImIZATION PROBLEmS

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Acta mathematica Scientia 2024年第2期44卷 702-720页

作者： N.HOSEINPOOR m.ghaznavi Faculty of mathematical Sciences Shahrood University of TechnologyShahroodIran

In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.

关键词： multiobjective optimization Pareto front scalarization objective-constraint approach proper efficient solution

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Visualising data distributions with kernel density estimation and reduced chi-squared statistic

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Geoscience Frontiers 2017年第6期8卷 1247-1252页

作者： C.J.Spencer C.Yakymchuk m.ghaznavi Earth Dynamics Research Group The Institute of Geoscience ResearchDepartment of Applied GeologyCurtin UniversityPerthAustralia Department of Earth and Environmental Sciences University of WaterlooWaterlooCanada David R.Cheriton School of Computer Science University of WaterlooWaterlooCanada

The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret *** commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted *** to the wide applicability of these tools,we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.

关键词： Data visualisation Kernel density estimation Reduced chi-squared statistic mean square weighted deviation Geostatistics

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