In the field of global optimization, many efforts have been devoted to globally solving bound constrained optimization problems without using derivatives. In this paper we consider global optimization problems where both bound and general nonlinear constraints are present. To solve this problem we propose the combined use of a DIRECT-type algorithm with a derivative-free local minimization of a nonsmooth exact penalty function. In particular, we define a new DIRECT-type strategy to explore the search space by explicitly taking into account the two-fold nature of the optimization problems, i.e. the global optimization of both the objective function and of a feasibility measure. We report an extensive experimentation on hard test problems to show viability of the approach.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Birgin, E.G., Floudas, C.A., Martinez, J.M.: Global minimization using an augmented lagrangian method with variable lower-level constraints. Math. Program. (Ser. A) 125(1), 139–162 (2010)
Campana, E.F., Liuzzi, G., Lucidi, S., Peri, D., Pinto, A., Piccialli, V.: New global optimization methods for ship design problems. Optim. Eng. 10(4), 533–555 (2009)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Di Pillo, G., Lucidi, S., Rinaldi, F.: An approach to constrained global optimization based on exact penalty functions. J. Glob. Optim. 54(2), 251–260 (2012)
Di Pillo, G., Lucidi, S., Rinaldi, F.: A derivative-free algorithm for constrained global optimization based on exact penalty functions. J. Optim. Theory Appl. (2013)
Fasano, G., Liuzzi, G., Lucidi, S., Rinaldi, F.: A linesearch-based derivative-free approach for nonsmooth constrained optimization. SIAM J. Optim. (2014)
Gablonsky, J.M.: DIRECT Version 2.0, User Guide
Hansen, N., Müller, S.D., Koumoutsakos, P.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput. 11(1), 1–18 (2003)
Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9(2), 159–195 (2001)
Jones, D.R.: The direct global optimization algorithm. In: Floudas, C., Pardalos, P. (eds.) Encyclopedia of Optimization, pp. 431–440. Kluwer Academic Publishers, Dordrecht (2001)
Jones, D.R., Perttunen, C.D., Stuckman, B.E.: Lipschitzian optimization without the lipschitz constant. J. Optim. Theory Appl. 79(1), 157–181 (1993)
Liuzzi, G., Lucidi, S., Piccialli, V.: A direct-based approach exploiting local minimizations for the solution of large-scale global optimization problems. Comput. Optim. Appl. 45(2), 353–375 (2010)
Liuzzi, G., Lucidi, S., Piccialli, V.: A partition-based global optimization algorithm. J. Glob. Optim. 48, 113–128 (2010)
Liuzzi, G., Lucidi, S., Piccialli, V.: Partitioning techniques for global optimization. In De Simone, V., Di Serafino, D., Toraldo, G. (eds.) Recent Advances in Nonlinear Optimization and Equilibrium Problems: A Tribute to Marco D’Apuzzo, volume 27 of Quaderni di Matematica, Dipartimento di Matematica, Seconda Università di Napoli, pp. 253–272. Aracne Editrice S.r.l. (2012)
Liuzzi, G., Lucidi, S., Piccialli, V.: Exploiting derivative-free local searches in direct-type algorithms for global optimization. Comput. Optim. Appl., 1–27 (2015)
Liuzzi, G., Lucidi, S., Piccialli, V., Sotgiu, A.: A magnetic resonance device designed via global optimization techniques. Math. Program. 101(2), 339–364 (2004)
Sergeyev, Y.D.: On convergence of divide the best global optimization algorithms. Optimization 44, 303–325 (1998)
Shcherbina, O., Neumaier, A., Sam-Haroud, D., Vu, X.H., Nguyen, T.V.: Benchmarking global optimization and constraint satisfaction codes. In: Bliek, Ch., Jermann, Ch., Neumaier, A. (eds.) Global Optimization and Constraint Satisfaction, pp. 211–222. Springer, Berlin (2003)
Tawarmalani, M., Sahinidis, N.V.: Convexification and global optimization in continuous and mixed-integer nonlinear programming. In: Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Dordrecht (2002)
Wang, C.Y., Li, D.: Unified theory of augmented lagrangian methods for constrained global optimization. J. Glob. Optim. 44, 433–458 (2009)
This work has been partially funded by the UE (ENIAC Joint Undertaking) in the MODERN project (ENIAC-120003).
About this article
Cite this article
Di Pillo, G., Liuzzi, G., Lucidi, S. et al. A DIRECT-type approach for derivative-free constrained global optimization. Comput Optim Appl 65, 361–397 (2016). https://doi.org/10.1007/s10589-016-9876-3
- Global optimization
- Derivative-free optimization
- Nonlinear optimization
- DIRECT-type algorithm