en Optimal analysis Optimal analysis پژوهشي Research <span style="font-size:11pt"><span style="text-justify:kashida"><span style="text-kashida:0%"><span style="line-height:normal"><span style="font-family:Calibri,sans-serif"><span lang="IT" style="font-size:11.5pt"><span new="" roman="" style="font-family:" times=""><span style="letter-spacing:-.2pt"><span style="layout-grid-mode:line">In this paper, a neural network is trained for optimal nodal ordering of graphs to obtain a small wavefront using soft computing. A preference function consists of six inputs that can be seen as a generalization of Sloan&#39;s function. These six inputs represent the different connection characteristics of graph models. This research is done with the aim of comparing Sloan&#39;s theoretical numbering method with Sloan&#39;s developed method with neural networks and WSA meta-heuristic algorithm. Unlike the Sloan algorithm, which uses two fixed coefficients, six coefficients are used here, based on the evaluation of artificial neural networks. The weight of networks is obtained using Water Strider algorithm. Examples are included to demonstrate the performance of the present hybrid method.</span></span></span></span></span></span></span></span></span> Graph ordering, wavefront, neural network, Metaheuristic algorithm, WSA 647 663 http://ijoce.iust.ac.ir/browse.php?a_code=A-10-6463-14&slc_lang=en&sid=1 A. Kaveh alikaveh@iust.ac.ir 180031947532846002556 180031947532846002556 Yes School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran N. Khavaninzadeh 180031947532846002557 180031947532846002557 No School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran