Solving nonlinear equations systems with a new approach based on invasive weed optimization algorithm and clustering

Pourjafari, Ebrahim; Mojallali, Hamed

doi:10.1016/j.swevo.2011.12.001

Cited by 93 publications

(50 citation statements)

References 16 publications

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“…Other type of penalty term aiming to create a repulsion area around a previously computed minimizer, say ξi, but with a distinctive behavior, is presented in [19]:…”

Section: Repulsion Merit Functionsmentioning

confidence: 99%

“…Similar arguments may be used to create a sequence of global minimization problems based on the modified merit function ¯ [19] which creates repulsion areas around the located global minimizers ξi, i = 1 ,... ,k so that the solver will not converge again to the same solutions:…”

Section: Repulsion Merit Functionsmentioning

confidence: 99%

“…The algorithms were coded in Matlab Version 8.0.0.783 (R2012b). In this study, the thirteen problems used for benchmark [16,17,19,20,22,23] are listed in Table 2 that also contains the number of roots in the search space Ω. These are the values set to the parameters: ϵ = 0.005, Itmax = 30, HMS=10 when n = 1, 2 and 12 for n = 3, 4, HMCR=0.95, PARmin=0.35, PARmax = 0.99, BWmin = 10 −6 and BWmax = 5 [8].…”

Section: Computational Experimentsmentioning

confidence: 99%

“…However, the same solutions may be located over and over again along the iterations and the computational effort turns out to be quite heavy. Other approaches that combine metaheuristics with techniques that modify the objective function in problem (2) have been reported in the literature [17,18,19,20]. The technique in [20] relies on the assignment of a penalty term to each previously computed root so that a repulsion area around the root is created.…”

Section: Introductionmentioning

confidence: 99%

“…The technique in [20] relies on the assignment of a penalty term to each previously computed root so that a repulsion area around the root is created. In [19], an evolutionary optimization algorithm is used together with a type of polarization technique to create a repulsion area around each previously computed root. The repulsion areas force the algorithm to move to other areas of the search space and look for other roots thus avoiding repeated convergence to already located solutions.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multiple Roots of Systems of Equations by Repulsion Merit Functions

Ramadas

Fernandes

Rocha

2014

Computational Science and Its Applications – ICCSA 2014

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Abstract. In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several iterations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.

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“…Other type of penalty term aiming to create a repulsion area around a previously computed minimizer, say ξi, but with a distinctive behavior, is presented in [19]:…”

Section: Repulsion Merit Functionsmentioning

confidence: 99%

Section: Repulsion Merit Functionsmentioning

confidence: 99%

Section: Computational Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multiple Roots of Systems of Equations by Repulsion Merit Functions

Ramadas

Fernandes

Rocha

2014

Computational Science and Its Applications – ICCSA 2014

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Weed colonization‐based performance improvement opportunities in dual‐mixed refrigerant natural gas liquefaction process

Qyyum

Qadeer

Khan

et al. 2020

Energy Science & Engineering

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Dual‐mixed refrigerant (DMR) process is a promising candidate for liquefying the natural gas (LNG) at onshore as well as offshore sites, thanks to its higher liquefaction capacity and flexibility in using full gas turbines. DMR involves two mixed refrigerant cycles to perform precooling and subcooling of natural gas (NG), and these refrigerant compositions need constant tweaking to match the ever‐changing NG cooling curve, as it is obtained from different gas fields. Mismatching of cooling curves often results in suboptimal operation, which ultimately leads to an increase in the overall energy consumption. Thus, this study is aimed at making DMR liquefaction operation close to optimal using the invasive‐weed paradigm. At first, the decision variables for performance improvement were determined using degrees of freedom analysis then through invasive‐weed paradigm the best set of parameters that results in minimal overall energy consumption were obtained. For the given set of conditions, it was found that after optimization, the DMR process can produce LNG using 16.2% less compression power compared to the published optimized DMR process. Taking into account the higher sensitivity of the DMR process against NG feed conditions, the IWO approach was also examined to find the multiple optimal solutions corresponding to different sets of feed conditions. The thermodynamic evaluation revealed that the mixed refrigerant involves in NG subcooling and interstage coolers have the highest level of exergy destruction. After successful performance improvement of the DMR process, it is also found that still, 62% improvement potential (based on avoidable/unavoidable exergy destruction analysis) is available in the DMR process that can be attained through either sole optimization or optimal retrofitting/revamping.

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An adaptive learning rate backpropagation‐type neural network for solving n × n systems on nonlinear algebraic equations

Goulianas

Margaris

Refanidis

et al. 2015

Math Methods in App Sciences

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This paper presents an MLP‐type neural network with some fixed connections and a backpropagation‐type training algorithm that identifies the full set of solutions of a complete system of nonlinear algebraic equations with n equations and n unknowns. The proposed structure is based on a backpropagation‐type algorithm with bias units in output neurons layer. Its novelty and innovation with respect to similar structures is the use of the hyperbolic tangent output function associated with an interesting feature, the use of adaptive learning rate for the neurons of the second hidden layer, a feature that adds a high degree of flexibility and parameter tuning during the network training stage. The paper presents the theoretical aspects for this approach as well as a set of experimental results that justify the necessity of such an architecture and evaluate its performance. Copyright © 2015 John Wiley & Sons, Ltd.

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Solving nonlinear equations systems with a new approach based on invasive weed optimization algorithm and clustering

Cited by 93 publications

References 16 publications

Multiple Roots of Systems of Equations by Repulsion Merit Functions

Multiple Roots of Systems of Equations by Repulsion Merit Functions

Weed colonization‐based performance improvement opportunities in dual‐mixed refrigerant natural gas liquefaction process

An adaptive learning rate backpropagation‐type neural network for solving n × n systems on nonlinear algebraic equations

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