Nowadays the root finding problem for nonlinear system equations is still one of the difficult problems in computational sciences. Many attempts using deterministic and meta-heuristic methods have been done with their advantages and disadvantages, but many of them have fail to converge to all possible roots. In this paper, a novel method of locating and finding all of the real roots from the system of nonlinear equations is proposed mainly using the spiral dynamics inspired optimization by Tamura and Yasuda [1]. The method is improved by the usage of the Sobol sequence of points for generating initial candidates of roots which are uniformly distributed than of pseudo-random generated points. Using clustering technique, the method localizes all potential roots so the optimization is conducted in those points simultaneously. A set of problems as the benchmarks from the literature is given. Having only a single run for each problem, the proposed method has successfully found all possible roots within a bounded domain.

No abstract

No abstract

Abstract.A potential problem in natural gas pipeline networks is bottlenecks occurring in the flow system due to unexpected high pressure at the pipeline network junctions resulting in inaccurate quantity and quality (pressure) at the end user outlets. The gas operator should be able to measure the pressure distribution in its network so the consumers can expect adequate gas quality and quantity obtained at their outlets. In this paper, a new approach to determine the gas pressure distribution in a pipeline network is proposed. A practical and userfriendly software application was developed. The network was modeled as a collection of node pressures and edge flows. The steady state gas flow equations Panhandle A, Panhandle B and Weymouth to represent flow in pipes of different sizes and a valve and regulator equation were considered. The obtained system consists of a set of nonlinear equations of node pressures and edge flowrates. Application in a network in the field involving a large number of outlets will result in a large system of nonlinear equations to be solved. In this study, the Broyden method was used for solving the system of equations. It showed satisfactory performance when implemented with field data.

Multimodal optimization is one of the interesting problems in optimization which arises frequently in a widerange of engineering and practical applications. The goal of this problem is to find all of optimum solutions in a single run. Some algorithms fail to find all solutions that have been proven their existence analytically. In our paper [1], a method is proposed to find the roots of a system of non-linear equations using a clustering technique that combine with Spiral Optimization algorithm and Sobol sequence of points. An interesting benefit using this method is that the same inputs will give the same results. Most of the time this does not happen in meta-heuristic algorithms using random factors. Now the method is modified to find solutions of multimodal optimization problems. Generally in an optimization problem, the differential form of the objective function is needed. In this paper, the proposed method is to find optimum points of general multimodal functions that its differential form is not required. Several problems with benchmark functions have been examined using our method and they give good result.