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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.

##### MSC:
 90C26 Nonconvex programming, global optimization 90C59 Approximation methods and heuristics in mathematical programming
ipfilter; Ipopt
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##### References:
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