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A filter-based artificial fish swarm algorithm for constrained global optimization: theoretical and practical issues. (English) Zbl 1312.90066
Summary: This paper presents a filter-based artificial fish swarm algorithm for solving nonconvex constrained global optimization problems. Convergence to an \(\varepsilon\)-global minimizer is guaranteed. At each iteration \(k\), the algorithm requires a \((\rho^{(k)},\varepsilon^{(k)})\)-global minimizer of a bound constrained bi-objective subproblem, where as \(k\to\infty\), \(\rho^{(k)}\to 0\) gives the constraint violation tolerance and \(\varepsilon^{(k)}\to\varepsilon\) is the error bound defining the accuracy required for the solution. The subproblems are solved by a population-based heuristic known as artificial fish swarm algorithm. Each subproblem relies on the approximate solution of the previous one, randomly generated new points to explore the search space for a global solution, and the filter methodology to accept non-dominated trial points. Convergence to a \((\rho ^{(k)},\varepsilon^{(k)})\)-global minimizer with probability one is guaranteed by probability theory. Preliminary numerical experiments show that the algorithm is very competitive when compared with known deterministic and stochastic methods.

90C26 Nonconvex programming, global optimization
90C59 Approximation methods and heuristics in mathematical programming
ipfilter; Ipopt
Full Text: DOI
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