Skip to main content
Log in

Global optimization based on local searches

  • Invited Survey
  • Published:
4OR 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

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Addis B, Leyffer S (2006) A trust-region algorithm for global optimization. Comput Optim Appl 35:287–304

    Article  Google Scholar 

  • Addis B, Locatelli M, Schoen F (2005) Local optima smoothing for global optimization. Optim Methods Softw 20:417–437

    Article  Google Scholar 

  • Banks A, Vincent J, Anyakoha C (2007) A review of particle swarm optimization. Part I: background and development. Nat Comput 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. Nat Comput 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. J Mach Learn Res 1:77–112

    Google Scholar 

  • Cassioli A, Di Lorenzo D, Locatelli M, Schoen F, Sciandrone M (2012) Machine learning for global optimization. Comput Optim Appl 51:279–303

    Article  Google Scholar 

  • Cassioli A, Locatelli M, Schoen F (2010) Dissimilarity measures for population-based global optimization algorithms. Comput Optim Appl 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. J Chem Phys 130(21):214112

    Article  Google Scholar 

  • Clerc M, Kennedy J (2002) The particle swarm—explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73

    Article  Google Scholar 

  • Conn AR, Gould N, Toint PL (2000) Trust-region methods. SIAM, Philadelphia

  • Dekkers A, Aarts E (1991) Global optimization and simulated annealing. Math Program 50:367–393

    Article  Google Scholar 

  • Doye JPK, Leary RH, Locatelli M, Schoen F (2004) Global optimization of Morse clusters by potential energy transformations. Inf J Comput 16:371–379

    Article  Google Scholar 

  • Georgieva A, Jordanov I (2009) Global optimization based on novel heuristics, lowdiscrepancy sequences and genetic algorithms. Eur J Oper Res 196:413–422

    Article  Google Scholar 

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

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

    Article  Google Scholar 

  • Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9:159–195

    Article  Google Scholar 

  • Hansen P, Mladenović N (2008) Variable neighbourhood search: methods and applications. 4OR: Q J Oper Res 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: Pinter JD (ed) Global optimization, vol 85. Springer US, pp 141–168

  • Jones DR, Perttunen CD, Stuckman BE (1993) Lipschitzian optimization without the lipschitz constant. J Optim Theory Appl 79:157–181

    Article  Google Scholar 

  • Krasnogor N, Smith J (2005) A tutorial for competent memetic algorithms: model, taxonomy and design issues. IEEE Trans Evol Comput 9:474–488

    Article  Google Scholar 

  • Leary RH (2000) Global optimization on funneling landscapes. J Global Optim 18:367–383

    Article  Google Scholar 

  • Lee J, Lee I-H, Lee J (2003) Unbiased global optimization of Lennard-Jones clusters for N. 201 by conformational space annealing method. Phys Rev Lett 91(8):1–4

    Google Scholar 

  • Levy AV, Montalvo A (1985) The tunneling method for global optimization. SIAM J Sci Stat Comput 1:15–29

    Google Scholar 

  • Liang Y, Zhang L, Li M, Han B (2007) A filled function method for global optimization. J Comput Appl Math 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. J Global Optim 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. Comput Optim Appl 45:353–375

    Article  Google Scholar 

  • Locatelli M, Maischberger M, Schoen F (2014) Differential evolution methods based on local searches. Comput Oper Res 43:169–180

    Article  Google Scholar 

  • Locatelli M, Schoen F (1996) Simple linkage: analysis of a threshold-accepting global optimization method. J Global Optim 9:95–111

    Article  Google Scholar 

  • Locatelli M, Schoen F (1999) Random linkage: a family of acceptance/rejection algorithms for global optimisation. Math Program 85(2):379–396

    Article  Google Scholar 

  • Locatelli M, Schoen F (2013a) Global optimization: theory, algorithms, and applications. SIAM, Philadelphia

    Book  Google Scholar 

  • Locatelli M, Schoen F (2013b) Local search based heuristics for global optimization: atomic clusters and beyond. Eur J Oper Res 222:1–9

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Mladenovic N, Drazic M, Kovacevic-Vujcic V, Cangalovic M (2008) General variable neighborhood search for the continuous optimization. Eur J Oper Res 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 Comput 15:2201–2220

    Article  Google Scholar 

  • Moré JJ, Wu Z (1997) Global continuation for distance geometry problems. SIAM J Optim 7:814–836

    Article  Google Scholar 

  • Moré JJ, Wu Z (1999) Distance geometry optimization for protein structures. J Global Optim 15:219–234

    Article  Google Scholar 

  • Müller A, Schneider JJ, Schömer E (2009) Packing a multidisperse system of hard disks in a circular environment. Phys Rev E 79:021102

    Article  Google Scholar 

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

  • Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evol Comput 12:107–125

    Article  Google Scholar 

  • Petalas YG, Parsopoulos KE, Vrahatis MN (2007) Memetic particle swarm optimization. Ann Oper Res 156:99–127

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • Renpu G (1990) A filled function method for finding a global minimizer of a function of several variables. Math Program 46:191–204

    Article  Google Scholar 

  • Rinnooy Kan AHG, Timmer GT (1987a) Stochastic global optimization methods. Part I: clustering methods. Math Program 39:27–56

    Article  Google Scholar 

  • Rinnooy Kan AHG, Timmer GT (1987b) Stochastic global optimization methods. Part II: multi level methods. Math Program 39:57–78

    Article  Google Scholar 

  • Roberts C, Johnston RL, Wilson NT (2000) A genetic algorithm for the structural optimization of Morse clusters. Theor Chem Acc 104(2):123–130

    Article  Google Scholar 

  • Schoen F (1998) Random and quasi-random linkage methods in global optimization. J Global Optim 13:445–454

    Article  Google Scholar 

  • Storn R, Price K (1997) Differential evolution. A simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 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 Trans Evol Comput 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. Comput Phys Commun 183:1139–1154

    Article  Google Scholar 

  • Wales DJ, Doye JPK (1997) Global optimization by Basin-Hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J Phys Chem 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. Inf Sci 197:38–52

    Article  Google Scholar 

  • Wu Z, Bai F, Lee H, Yang Y (2007) A filled function method for constrained global optimization. J Global Optim 39:495–507

    Article  Google Scholar 

  • Xu Z, Huang H-X, Pardalos P, Xu C-X (2001) Filled functions for unconstrained global optimization. J Global Optim 20:49–65

    Article  Google Scholar 

  • Yao Y (1989) Dynamic tunneling algorithm for global optimization. IEEE Trans Syst Man Cybern 19:1222–1230

    Article  Google Scholar 

  • Zhang L, Ng C, Li D, Tian W (2004) A new filled function method for global optimization. J Global Optim 28:17–43

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marco Locatelli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Locatelli, M., Schoen, F. Global optimization based on local searches. 4OR-Q J Oper Res 11, 301–321 (2013). https://doi.org/10.1007/s10288-013-0251-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10288-013-0251-2

Keywords

Mathematics Subject Classification

Navigation