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“…Other scholars had also done a lot of valuable work [3], [4], [15], but their methods still ask to solve a global optimization problem via two-phases cycle. In addition, Zhu proposed a globally concavized filled function in [13] as follows:…”

confidence: 98%

“…Other scholars had also done a lot of valuable work [3], [4], [15], but their methods still ask to solve a global optimization problem via two-phases cycle. In addition, Zhu proposed a globally concavized filled function in [13] as follows:…”

confidence: 98%

“…The global minima: x * = (4,4,4,4). The function may be flat; thus, the gradient of the function also is very small in the region outside of very small neighbors of the stationary points, we let initial parameter A enough small, i.e., A = 1, and the initial step size of the local search be enough small.…”

confidence: 99%

“…The optimization of the transportation problem is posed as below: A search for the solution for the dual version of the problem was attempted since this formulation results in a reduced number of variables (seven) but with increased number of constraints (twelve). The 3 n enumeration algorithm in [46] provides virtually instantly the global optimum (23,25,8,12,7,12,0) with function value of 84000. The primal solution (850,350,0, 0,250,0, 0,750,0, 50,750,0) is readily obtained using the complementary slackness theorem [37,47] that agrees with the reported result found using LP package.…”

confidence: 99%

“…A heuristic approach to find the global optimum of complex nonlinear optimization problems is based on evolutionary and genetic algorithms; several works based on this approach can be found in the review papers [26,40]. Recent algorithmic and methodological developments for linear and non-linear integer programming and mixed problems can be found in [29,52,27,25,31,1,4,3,23,49,5]. Additionally, several commercial solvers for linear and non-linear integer programming problems are available.…”

confidence: 99%

“…It is also difficult to construct an efficient filled function according to this definition. In order to deal with these problems, many researchers had modified it in [22][23][24][25], and extended the new definition for discrete cases in [8] as follows:…”

confidence: 99%