GAMBIT: A Parameterless Model-Based Evolutionary Algorithm for Mixed-Integer Problems

Learning and exploiting problem structure is one of the key challenges in optimization. This is especially important for black-box optimization (BBO) where prior structural knowledge of a problem is not available. Existing model-based Evolutionary Algorithms (EAs) are very efficient at learning structure in both the discrete, and in the continuous domain. In this article, discrete and continuous model-building mechanisms are integrated for the Mixed-Integer (MI) domain, comprising discrete and continuous variables. We revisit a recently introduced model-based evolutionary algorithm for the MI domain, the Genetic Algorithm for Model-Based mixed-Integer opTimization (GAMBIT). We extend GAMBIT with a parameterless scheme that allows for practical use of the algorithm without the need to explicitly specify any parameters. We furthermore contrast GAMBIT with other model-based alternatives. The ultimate goal of processing mixed dependences explicitly in GAMBIT is also addressed by introducing a new mechanism for the explicit exploitation of mixed dependences. We find that processing mixed dependences with this novel mechanism allows for more efficient optimization. We further contrast the parameterless GAMBIT with Mixed-Integer Evolution Strategies (MIES) and other state-of-the-art MI optimization algorithms from the General Algebraic Modeling System (GAMS) commercial algorithm suite on problems with and without constraints, and show that GAMBIT is capable of solving problems where variable dependences prevent many algorithms from successfully optimizing them.

[1]  Dirk Thierens,et al.  Optimal mixing evolutionary algorithms , 2011, GECCO '11.

[2]  Jorge Nocedal,et al.  Knitro: An Integrated Package for Nonlinear Optimization , 2006 .

[3]  Dirk Thierens,et al.  A Clustering-Based Model-Building EA for Optimization Problems with Binary and Real-Valued Variables , 2015, GECCO.

[4]  Peter A. N. Bosman,et al.  Exploiting Linkage Information and Problem-Specific Knowledge in Evolutionary Distribution Network Expansion Planning , 2018, Evolutionary Computation.

[5]  Peter A. N. Bosman,et al.  A novel population-based multi-objective CMA-ES and the impact of different constraint handling techniques , 2014, GECCO.

[6]  Michael T. M. Emmerich,et al.  Mixed-integer Bayesian Optimization Utilizing A-priori Knowledge on Parameter Dependences , 2008 .

[7]  N. Hansen A CMA-ES for Mixed-Integer Nonlinear Optimization , 2011 .

[8]  Thierry Benoist,et al.  LocalSolver 1.x: a black-box local-search solver for 0-1 programming , 2011, 4OR.

[9]  Fernando G. Lobo,et al.  A parameter-less genetic algorithm , 1999, GECCO.

[10]  Dirk Thierens,et al.  Linkage neighbors, optimal mixing and forced improvements in genetic algorithms , 2012, GECCO '12.

[11]  Dirk Thierens,et al.  On the usefulness of linkage processing for solving MAX-SAT , 2013, GECCO '13.

[12]  Xin Yao,et al.  Constrained Evolutionary Optimization , 2003 .

[13]  Michael R. Bussieck,et al.  General Algebraic Modeling System (GAMS) , 2004 .

[14]  Linus Schrage,et al.  The global solver in the LINDO API , 2009, Optim. Methods Softw..

[15]  Dirk Thierens,et al.  The Linkage Tree Genetic Algorithm , 2010, PPSN.

[16]  Dirk Thierens,et al.  AMaLGaM IDEAs in noiseless black-box optimization benchmarking , 2009, GECCO '09.

[17]  Dirk Thierens,et al.  Combining Model-Based EAs for Mixed-Integer Problems , 2014, PPSN.

[18]  Thomas Bäck,et al.  Mixed Integer Evolution Strategies for Parameter Optimization , 2013, Evolutionary Computation.

[19]  Michael R. Bussieck,et al.  Mixed-Integer Nonlinear Programming , 2003 .

[20]  Tobias Achterberg,et al.  SCIP: solving constraint integer programs , 2009, Math. Program. Comput..

[21]  Dirk Thierens,et al.  Enhancing the Performance of Maximum-Likelihood Gaussian EDAs Using Anticipated Mean Shift , 2008, PPSN.