Finding All Solutions of Systems of Nonlinear Equations Using Spiral Dynamics Inspired Optimization with Clustering

Sidarto, Kuntjoro Adji; Kania, Adhe

doi:10.20965/jaciii.2015.p0697

Cited by 19 publications

(19 citation statements)

References 5 publications

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“…No timing figures reported for CDFPA to compare against. x 1 2 -2x 1 +3x 2 = −1 2x 1 2 -3.9999x 1 +6.0001x 2 = − 1.9999 0 13615 ≈ 0 - Table 6: the performance of our algorithm versus CDFPA Finally we compare our algorithm with the one proposed in [20]. Table 7 shows the systems of equations and the performance of our algorithm compared to that of the algorithm in [20].…”

Section: Problem (2)mentioning

confidence: 99%

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Probability-Directed Problem Optimization Technique for Solving Systems of Linear and Non-Linear Equations

Al-Muhammed¹

2019

Computer Science &Amp; Information Technology (CS &Amp; IT )

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Although many methods have been proposed for solving linear or nonlinear systems of equations, there is always a pressing need for more effective and efficient methods. Good methods should produce solutions with high precision and speed. This paper proposed an innovative method for solving systems of linear and nonlinear equations. This method transforms the problem into an optimization problem and uses a probability guided search technique for solving this optimization problem, which is the solution for the system of equations. The transformation results in an aggregate violation function and a criterion function. The aggregation violation function is composed of the constraints that represent the equations and whose satisfaction is a solution for the system of equations. The criterion function intelligently guides the search for the solution to the aggregate violation function by determining when the constraints must be checked; thereby avoiding unnecessary, timeintensive checks for the constraints. Experiments conducted with our prototype implementation showed that our method is effective in finding solutions with high precision and efficient in terms of CPU time.

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Section: Problem (2)mentioning

confidence: 99%

“…Clearly our approach produced better precision. No timing numbers are reported in [20] to compare against. 3.93E−07 Table 7: The performance of our algorithm verses [20].…”

Section: Problem (2)mentioning

confidence: 99%

Probability-Directed Problem Optimization Technique for Solving Systems of Linear and Non-Linear Equations

Al-Muhammed¹

2019

Computer Science &Amp; Information Technology (CS &Amp; IT )

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“…Luo, et al [6] proposed a hybrid approach using a chaos optimization algorithm and the quasi-Newton method, while Burden and Faires [7] used a combination of the steepest descent method and the Newton method for solving the nonlinear equation system. The latest approach is given by Sidarto & Kania in [8]. Because solving nonlinear equation systems is related to the pressure distribution in gas pipeline distribution networks, Sidarto, et al [9,10] have proposed a genetic algorithm optimization method combined with the Newton method.…”

Section: Introductionmentioning

confidence: 99%

“…However, for large systems it is observed that the convergence of the optimization process before applying the Newton-type method is rather slow. Detailed information on converting the root finding problem to an optimization process can be found in [8].…”

Section: Introductionmentioning

confidence: 99%

Determination of Gas Pressure Distribution in a Pipeline Network using the Broyden Method

Sidarto

Kania

Mucharam

et al. 2017

J. Eng. Technol. Sci.

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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.

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“…The results show a better performance in finding an optimal solution for the benchmark functions in comparison with other SDA approaches. The paper [1] and this paper propose an improvement by implementing the clustering technique. There is also a new technique in this paper in dealing with more general multimodal optimization problems, where their differential form of the objective functions is not existing or difficult to obtain.…”

Section: Introductionmentioning

confidence: 99%

Finding Multiple Solutions of Multimodal Optimization Using Spiral Optimization Algorithm with Clustering

Sidarto¹,

Kania²,

Sumarti³

2017

mendel

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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.

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Finding All Solutions of Systems of Nonlinear Equations Using Spiral Dynamics Inspired Optimization with Clustering

Cited by 19 publications

References 5 publications

Probability-Directed Problem Optimization Technique for Solving Systems of Linear and Non-Linear Equations

Probability-Directed Problem Optimization Technique for Solving Systems of Linear and Non-Linear Equations

Determination of Gas Pressure Distribution in a Pipeline Network using the Broyden Method

Finding Multiple Solutions of Multimodal Optimization Using Spiral Optimization Algorithm with Clustering

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