PSwarm: a hybrid solver for linearly constrained global derivative-free optimization PSwarm was developed originally for the global optimization of functions without derivatives and where the variables are within upper and lower bounds. The underlying algorithm used is a pattern search method, or more specifically, a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the (optional) search step of coordinate search, the algorithm incorporates a particle swarm scheme for dissemination of points in the feasible region, equipping the overall method with the capability of finding a global minimizer. Our extensive numerical experiments showed that the resulting algorithm is highly competitive with other global optimization methods based only on function values. PSwarm is extended in this paper to handle general linear constraints. The poll step now incorporates positive generators for the tangent cone of the approximated active constraints, including a provision for the degenerate case. The search step has also been adapted accordingly. In particular, the initial population for particle swarm used in the search step is computed by first inscribing an ellipsoid of maximum volume to the feasible set. We have again compared PSwarm with other solvers (including some designed for global optimization) and the results confirm its competitiveness in terms of efficiency and robustness.

References in zbMATH (referenced in 36 articles , 1 standard article )

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  1. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  2. Csercsik, Dávid: Lying generators: manipulability of centralized payoff mechanisms in electrical energy trade (2016)
  3. Fliege, Jörg; Vaz, A.Ismael F.: A method for constrained multiobjective optimization based on SQP techniques (2016)
  4. Paulavičius, Remigijus; Žilinskas, Julius: Advantages of simplicial partitioning for Lipschitz optimization problems with linear constraints (2016)
  5. Price, C.J.; Reale, M.; Robertson, B.L.: Stochastic filter methods for generally constrained global optimization (2016)
  6. Custódio, A.L.; Madeira, J.F.A.: GLODS: global and local optimization using direct search (2015)
  7. Diouane, Y.; Gratton, S.; Vicente, L.N.: Globally convergent evolution strategies for constrained optimization (2015)
  8. Sinha, Pritibhushan: A method for solving some optimization problems with bounds on variables (2015)
  9. Sommer, A.; Farle, O.; Dyczij-Edlinger, R.: Certified dual-corrected radiation patterns of phased antenna arrays by offline-online order reduction of finite-element models (2015)
  10. Sommer, Alexander; Farle, Ortwin; Dyczij-Edlinger, Romanus: A fast certified parametric near-field-to-far-field transformation technique for electrically large antenna arrays (2015)
  11. Ceperic, Vladimir; Gielen, Georges; Baric, Adrijan: Sparse varepsilon $\varepsilon$-tube support vector regression by active learning (2014) ioport
  12. Le Thi, Hoai An; Huynh Van Ngai; Dinh, Tao Pham; Vaz, A.Ismael F.; Vicente, L.N.: Globally convergent DC trust-region methods (2014)
  13. Müller, Juliane; Shoemaker, Christine A.: Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems (2014)
  14. Kaucic, Massimiliano: A multi-start opposition-based particle swarm optimization algorithm with adaptive velocity for bound constrained global optimization (2013)
  15. Ochoa, Gabriela; Villasana, Minaya: Population-based optimization of cytostatic/cytotoxic combination cancer chemotherapy (2013) ioport
  16. Rios, Luis Miguel; Sahinidis, Nikolaos V.: Derivative-free optimization: a review of algorithms and comparison of software implementations (2013)
  17. Rocha, H.; Dias, J.M.; Ferreira, B.C.; Lopes, M.C.: Pattern search methods framework for beam angle optimization in radiotherapy design (2013)
  18. Rocha, H.; Dias, J.M.; Ferreira, B.C.; Lopes, M.C.: Selection of intensity modulated radiation therapy treatment beam directions using radial basis functions within a pattern search methods framework (2013)
  19. Cassioli, A.; Di Lorenzo, D.; Locatelli, M.; Schoen, F.; Sciandrone, M.: Machine learning for global optimization (2012)
  20. Le Thi, H.A.; Vaz, A.I.F.; Vicente, L.N.: Optimizing radial basis functions by d.c. programming and its use in direct search for global derivative-free optimization (2012)

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