Optimizing Alloy for Multi-objective Software Product Line Configuration

  • Ed Zulkoski
  • Chris Kleynhans
  • Ming-Ho Yee
  • Derek Rayside
  • Krzysztof Czarnecki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8477)


Software product line (SPL) engineering involves the modeling, analysis, and configuration of variability-rich systems. We improve the performance of the multi-objective optimization of SPLs in Alloy by several orders of magnitude with two techniques.

First, we rewrite the model to remove binary relations that map to integers, which enables removing most of the integer atoms from the universe. SPL models often require using large bitwidths, hence the number of integer atoms in the universe can be orders of magnitude more than the other atoms. In our approach, the tuples for these integer-valued relations are computed outside the sat solver before returning the solution to the user. Second, we add a checkpointing facility to Kodkod, which allows the multi-objective optimization algorithm to reuse previously computed internal sat solver state, after backtracking.

Together these result in orders of magnitude improvement in using Alloy as a multi-objective optimization tool for software product lines.


Product Lines Multi-objective Optimization Kodkod Alloy 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bąk, K., Czarnecki, K., Wąsowski, A.: Feature and Meta-Models in Clafer: Mixed, Specialized, and Coupled. In: Malloy, B., Staab, S., van den Brand, M. (eds.) SLE 2010. LNCS, vol. 6563, pp. 102–122. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Brummayer, R.: Efficient SMT solving for bit vectors and the extensional theory of arrays. Ph.D. thesis, JKU Linz (2010)Google Scholar
  3. 3.
    Clements, P.C., Northrop, L.: Software Product Lines: Practices and Patterns. Addison-Wesley (2001)Google Scholar
  4. 4.
    Esfahani, N., Malek, S.: Guided Exploration of the Architectural Solution Space in the Face of Uncertainty. Tech. rep., George Mason U., Dept. of C.S. (March 2011)Google Scholar
  5. 5.
    Franzen, A.: Efficient solving of the satisfiability modulo bit-vectors problem and some extensions to SMT. Ph.D. thesis, Univ. of Trento (2010)Google Scholar
  6. 6.
    Ganesh, V., Dill, D.L.: A Decision Procedure for Bit-Vectors and Arrays. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 519–531. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Kang, K.C., Cohen, S.G., Hess, J.A., Novak, W.E., Peterson, A.S.: Feature-Oriented Domain Analysis (FODA) feasibility study. Tech. rep., SEI-CMU (1990)Google Scholar
  8. 8.
    Knuth, D.E., Bendix, P.B.: Simple word problems in universal algebra. In: Proc. Conf. on Computational Problems in Abstract Algebra. Pergamon Press (1970)Google Scholar
  9. 9.
    Merz, F., Falke, S., Sinz, C.: LLBMC: Bounded Model Checking of C and C++ Programs Using a Compiler IR. In: Joshi, R., Müller, P., Podelski, A. (eds.) VSTTE 2012. LNCS, vol. 7152, pp. 146–161. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    Montaghami, V., Rayside, D.: Extending Alloy with partial instances. In: Derrick, J., Fitzgerald, J., Gnesi, S., Khurshid, S., Leuschel, M., Reeves, S., Riccobene, E. (eds.) ABZ 2012. LNCS, vol. 7316, pp. 122–135. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  11. 11.
    Olaechea, R., Stewart, S., Czarnecki, K., Rayside, D.: Modelling and Optimization of Quality Attributes in Variability-Rich Software. In: NFPinDSML Workshop at MODELS Conference (2012)Google Scholar
  12. 12.
    Pohl, K., Böckle, G., van der Linden, F.J.: Software Product Line Engineering: Foundations, Principles and Techniques. Springer (2005)Google Scholar
  13. 13.
    Rayside, D., Estler, H.-C., Jackson, D.: A Guided Improvement Algorithm for Exact, General Purpose, Many-Objective Combinatorial Optimization. Tech. Rep. MIT-CSAIL-TR-2009-033, MIT CSAIL (2009)Google Scholar
  14. 14.
    Siegmund, N., Kolesnikov, S., Kastner, C., Appel, S., Batory, D., Rosenmuller, M., Saake, G.: Predicting performance via automated feature-interaction detection. In: Murphy, G., Pezze, M. (eds.) Proc. 34th ICSE, Zurich, Switzerland (2012)Google Scholar
  15. 15.
    Siegmund, N., Rosenmuller, M., Kastner, C., Giarrusso, P.G., Apel, S., Kolesnikov, S.S.: Scalable prediction of non-functional properties in software product lines. In: Schaefer, I., John, I., Schmid, K. (eds.) SPLC Workshops. ACM (2011)Google Scholar
  16. 16.
    Siegmund, N., Rosenmuller, M., Kuhlemann, M., Kastner, C., Apel, S., Saake, G.: SPL Conqueror: Toward optimization of non-functional properties in software product lines. Software Quality Journal 1(3), 1–31 (2011)Google Scholar
  17. 17.
    Wintersteiger, C., Hamadi, Y., de Moura, L.: Efficiently solving quantified bit-vector formulas. Formal Methods in System Design 42(1), 3–23 (2013)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ed Zulkoski
    • 1
  • Chris Kleynhans
    • 1
  • Ming-Ho Yee
    • 1
  • Derek Rayside
    • 1
  • Krzysztof Czarnecki
    • 1
  1. 1.University of WaterlooWaterlooCanada

Personalised recommendations