Computational aspects of the optimal transit path problem
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This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Industrial and Management Optimization 'JIMO' following peer review. The definitive publisher-authenticated version: “Caccetta, Louis and Loosen, Ian and Rehbock, Volker. 2008. Computational aspects of the optimal transit path problem. Journal of Industrial and Management Optimization. Vol. 4 (1): pp. 95-105.” is available online at: <a href="http://aimsciences.org/journals/pdfs.jsp?paperID=3087&mode=full">http://aimsciences.org/journals/pdfs.jsp?paperID=3087&mode=full</a>
In this paper we present a novel method for short term forecast of time series based on Knot-Optimizing Spline Networks (KOSNETS). The time series is first approximated by a nonlinear recurrent system. The resulting recurrent system is then approximated by feedforward B-spline networks, yielding a nonlinear optimization problem. In this optimization problem, both the knot points and the coefficients of the B-splines are decision variables so that the solution to the problem has both optimal coefficients and partition points. To demonstrate the usefulness and accuracy of the method, numerical simulations and tests using various model and real time series are performed. The numerical simulation results are compared with those from a well-known regression method, MARS. The comparison shows that our method outperforms MARS for nonlinear problems.
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