Skip to main content
SpringerLink
Log in

Global optimization based on local searches

  • SI: 4OR Surveys
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

In this paper we deal with the use of local searches within global optimization algorithms. We discuss different issues, such as the generation of new starting points, the strategies to decide whether to start a local search from a given point, and those to decide whether to keep the point or discard it from further consideration. We present how these topics have been faced in the existing literature and express our opinion on the relative merits of different choices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Addis, B., & Leyffer, S. (2006). A trust-region algorithm for global optimization. Computational Optimization and Applications, 35, 287–304.

    Article  Google Scholar 

  • Addis, B., Locatelli, M., & Schoen, F. (2005). Local optima smoothing for global optimization. Optimization Methods and Software, 20, 417–437.

    Article  Google Scholar 

  • Banks, A., Vincent, J., & Anyakoha, C. (2007). A review of particle swarm optimization. Part I: Background and development. Natural Computing, 6(4), 467–484.

    Article  Google Scholar 

  • Banks, A., Vincent, J., & Anyakoha, C. (2008). A review of particle swarm optimization. Part II: Hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications. Natural Computing, 7(1), 109–124.

    Article  Google Scholar 

  • Barhen, J., Protopopescu, V., & Reister, D. (1997). TRUST: A deterministic algorithm for global optimization. Science, 276, 1094–1097.

    Article  Google Scholar 

  • Boyan, J., & Moore, A. (2000). Learning evaluation functions to improve optimization by local search. Journal of Machine Learning Research, 1, 77–112.

    Google Scholar 

  • Cabassi, F., & Locatelli, M. (2015). Computational investigation of simple memetic approaches for continuous global optimization. Submitted.

  • Cassioli, A., Di Lorenzo, D., Locatelli, M., Schoen, F., & Sciandrone, M. (2012). Machine learning for global optimization. Computational Optimization and Applications, 51, 279–303.

    Article  Google Scholar 

  • Cassioli, A., Locatelli, M., & Schoen, F. (2010). Dissimilarity measures for population-based global optimization algorithms. Computational Optimization and Applications, 45(2), 257–281.

    Article  Google Scholar 

  • Cheng, L., Feng, Y., Yang, J., & Yang, J. (2009). Funnel hopping: Searching the cluster potential energy surface over the funnels. The Journal of Chemical Physics, 130(21), 214112.

    Article  Google Scholar 

  • Clerc, M., & Kennedy, J. (2002). The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6(1), 58–73.

    Article  Google Scholar 

  • Conn, A. R., Gould, N., & Toint, P. L. (2000). Trust-region methods. Philadelphia: SIAM.

    Book  Google Scholar 

  • Dekkers, A., & Aarts, E. (1991). Global optimization and simulated annealing. Mathematical Programming, 50, 367–393.

    Article  Google Scholar 

  • Doye, J. P. K., Leary, R. H., Locatelli, M., & Schoen, F. (2004). Global optimization of Morse clusters by potential energy transformations. INFORMS Journal on Computing, 16, 371–379.

    Article  Google Scholar 

  • Georgieva, A., & Jordanov, I. (2009). Global optimization based on novel heuristics, lowdiscrepancy sequences and genetic algorithms. European Journal of Operational Research, 196, 413–422.

    Article  Google Scholar 

  • Gomez, S., & Romero, D. (1993). Two global methods for molecular geometry optimization (Tech. Rep. No. 1953). Rocquencourt: INRIA.

    Google Scholar 

  • Grosso, A., Locatelli, M., & Schoen, F. (2007). A population based approach for hard global optimization problems based on dissimilarity measures. Mathematical Programming, 110(2), 373–404.

    Article  Google Scholar 

  • Hansen, N., & Ostermeier, A. (2001). Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation, 9, 159–195.

    Article  Google Scholar 

  • Hansen, P., Mladenović, N., & Moreno Pérez, J. (2008). Variable neighbourhood search: Methods and applications. 4OR: A Quarterly Journal of Operations Research, 6(4), 319–360.

    Article  Google Scholar 

  • Hart, W. (1994). Adaptive global optimization with local search (Unpublished doctoral dissertation). University of California, San Diego.

  • Hartke, B. (2006). Efficient global geometry optimization of atomic and molecular clusters. In J. D. Pinter (Ed.), Global optimization (Vol. 85, pp. 141–168). USA: Springer.

    Chapter  Google Scholar 

  • Jones, D. R., Perttunen, C. D., & Stuckman, B. E. (1993). Lipschitzian optimization without the Lipschitz constant. Journal of Optimization Theory and Applications, 79(157), 181.

    Google Scholar 

  • Krasnogor, N., & Smith, J. (2005). A tutorial for competent memetic algorithms: Model, taxonomy and design issues. IEEE Transactions on Evolutionary Computation, 9, 474–488.

    Article  Google Scholar 

  • Leary, R. H. (2000). Global optimization on funneling landscapes. Journal of Global Optimization, 18(367), 383.

    Google Scholar 

  • Lee, J., Lee, I.-H., & Lee, J. (2003). Unbiased global optimization of Lennard-Jones clusters for N \(\le \) 201 by conformational space annealing method. Physical Review Letters, 91(8), 1–4.

    Google Scholar 

  • Levy, A. V., & Montalvo, A. (1985). The tunneling method for global optimization. SIAM Journal of Science and Statistical Computation, 1, 15–29.

    Article  Google Scholar 

  • Liang, Y., Zhang, L., Li, M., & Han, B. (2007). A filled function method for global optimization. Journal of Computational and Applied Mathematics, 205, 16–31.

    Article  Google Scholar 

  • Liberti, L., Lavor, C., Maculan, N., & Marinelli, F. (2009). Double variable neighbourhood search with smoothing for the molecular distance geometry problem. Journal of Global Optimization, 43, 207–218.

    Article  Google Scholar 

  • Liuzzi, G., Lucidi, S., & Piccialli, V. (2010). A DIRECT-based approach exploiting local minimizations for the solution of large-scale global optimization problems. Computational Optimization and Applications, 45, 353–375.

    Article  Google Scholar 

  • Locatelli, M., Maischberger, M., & Schoen, F. (2014). Differential evolution methods based on local searches. Computers and Operations Research, 43, 169–180.

    Article  Google Scholar 

  • Locatelli, M., & Schoen, F. (1996). Simple linkage: Analysis of a threshold-accepting global optimization method. Journal of Global Optimization, 9(95), 111.

    Google Scholar 

  • Locatelli, M., & Schoen, F. (1999). Random linkage: A family of acceptance/rejection algorithms for global optimisation. Mathematical Programming, 85(2), 379–396.

    Article  Google Scholar 

  • Locatelli, M., & Schoen, F. (2013a). Global optimization based on local searches. 4OR, 11, 301–321.

    Article  Google Scholar 

  • Locatelli, M., & Schoen, F. (2013b). Global optimization: Theory, algorithms, and applications. Philadelphia: SIAM.

    Book  Google Scholar 

  • Locatelli, M., & Schoen, F. (2013c). Local search based heuristics for global optimization: Atomic clusters and beyond. European Journal of Operational Research, 222, 1–9.

    Article  Google Scholar 

  • Lucidi, S., & Piccialli, V. (2002). New classes of globally convexized filled functions for global optimization. Journal of Global Optimization, 24, 219–236.

    Article  Google Scholar 

  • Mladenovic, N., Drazic, M., Kovacevic-Vujcic, V., & Cangalovic, M. (2008). General variable neighborhood search for the continuous optimization. European Journal of Operational Research, 191, 753–770.

    Article  Google Scholar 

  • Molina, D., Lozano, M., Sànchez, A., & Herrera, F. (2011). Memetic algorithms based on local search chains for large scale continuous optimisation problems: MA-SSW-Chains. Soft Computing, 15, 2201–2220.

    Article  Google Scholar 

  • Moré, J. J., & Wu, Z. (1997). Global continuation for distance geometry problems. SIAM Journal on Optimization, 7, 814–836.

    Article  Google Scholar 

  • Moré, J. J., & Wu, Z. (1999). Distance geometry optimization for protein structures. Journal of Global Optimization, 15, 219–234.

    Article  Google Scholar 

  • Müller, A., Schneider, J. J., & Schömer, E. (2009). Packing a multidisperse system of hard disks in a circular environment. Physical Review E, 79, 021102.

    Article  Google Scholar 

  • Niederreiter, H. (1992). Random number generation and quasi-monte carlo methods. Philadelphia: SIAM.

    Book  Google Scholar 

  • Noman, N., & Iba, H. (2008). Accelerating differential evolution using an adaptive local search. IEEE Transactions on Evolutionary Computation, 12, 107–125.

    Article  Google Scholar 

  • Petalas, Y. G., Parsopoulos, K. E., & Vrahatis, M. N. (2007). Memetic particle swarm optimization. Annals of Operations Research, 156, 99–127.

    Article  Google Scholar 

  • Poli, R., Kennedy, J., & Blackwell, T. (2007). Particle swarm optimization. Swarm Intelligence, 1(1), 33–57.

    Article  Google Scholar 

  • Price, K., Storn, R., & Lampinen, J. (2005). Differential evolution: A practical approach to global optimization. Berlin: Springer.

    Google Scholar 

  • Renpu, G. (1990). A filled function method for finding a global minimizer of a function of several variables. Mathematical Programming, 46, 191–204.

    Article  Google Scholar 

  • Rinnooy Kan, A. H. G., & Timmer, G. T. (1987a). Stochastic global optimization methods. Part I: Clustering methods. Mathematical Programming, 39, 27–56.

    Article  Google Scholar 

  • Rinnooy Kan, A. H. G., & Timmer, G. T. (1987b). Stochastic global optimization methods. Part II: Multi level methods. Mathematical Programming, 39, 57–78.

    Article  Google Scholar 

  • Roberts, C., Johnston, R. L., & Wilson, N. T. (2000). A genetic algorithm for the structural optimization of Morse clusters. Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), 104(2), 123–130.

    Article  Google Scholar 

  • Schoen, F. (1998). Random and quasi-random linkage methods in global optimization. Journal of Global Optimization, 13, 445–454.

    Article  Google Scholar 

  • Storn, R., & Price, K. (1997). Differential evolution. A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341–359.

    Article  Google Scholar 

  • Sutton, A., Whitley, D., Lunacek, M., & Howe, A. (2006). PSO and multi-funnel landscapes: How cooperation might limit exploration. In GECCO’06 Proceedings of the 8th annual conference on genetic and evolutionary computation (pp. 75-82).

  • Vasile, M., Minisci, E., & Locatelli, M. (2011). An inflationary differential evolution algorithm for space trajectory optimization. IEEE Transactions on Evolutionary Computation, 15(2), 267–281.

    Article  Google Scholar 

  • Voglis, C., Parsopoulos, K., Papageorgiou, D., Lagaris, I., & Vrahatis, M. (2012). MEMPSODE: A global optimization software based on hybridization of population-based algorithms and local searches. Computer Physics Communications, 183, 1139–1154.

    Article  Google Scholar 

  • Wales, D. J., & Doye, J. P. K. (1997). Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. Journal of Physical Chemistry A, 101(28), 5111–5116.

    Article  Google Scholar 

  • Wang, H., Moon, I., Yang, S., & Wang, D. (2012). A memetic particle swarm optimization algorithm for multimodal optimization problems. Information Sciences, 197, 38–52.

    Article  Google Scholar 

  • Wu, Z., Bai, F., Lee, H., & Yang, Y. (2007). A filled function method for constrained global optimization. Journal of Global Optimization, 39, 495–507.

    Article  Google Scholar 

  • Xu, Z., Huang, H.-X., Pardalos, P., & Xu, C.-X. (2001). Filled functions for unconstrained global optimization. Journal of Global Optimization, 20, 49–65.

    Article  Google Scholar 

  • Yao, Y. (1989). Dynamic tunneling algorithm for global optimization. IEEE Transactions on Systems, Man and Cybernetics, 19, 1222–1230.

    Article  Google Scholar 

  • Zhang, L., Ng, C., Li, D., & Tian, W. (2004). A new filled function method for global optimization. Journal of Global Optimization, 28, 17–43.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione, Università di Parma, Via G.P. Usberti, 181/A, 43124, Parma, Italy

    Marco Locatelli

  2. Dipartimento di Ingegneria dell’Informazione, Università di Firenze, Via di Santa Marta, 3, 50139, Florence, Italy

    Fabio Schoen

Authors
  1. Marco Locatelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fabio Schoen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marco Locatelli.

Additional information

This is an updated version of the paper that appeared in 4OR, 11(4), 301–321 (2013).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Locatelli, M., Schoen, F. Global optimization based on local searches. Ann Oper Res 240, 251–270 (2016). https://doi.org/10.1007/s10479-015-2014-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-015-2014-2

Keywords

Search

Navigation