King Fahd University of Petroleum and Minerals.

Mail Box 492.

Dhahran, 31261, KSA

slimb at kfupm.edu.sa

+966 13 860 1054

Office 201-2, Building 5.



You can download our XGame-Solver Software for free on the following links:

Version 1.0

Version 2.0

Other Interseting Links:





Copyright (C) 2010-2016.

Slim Belhaiza.

 د.سليم بالحائزة

إجازة وسند في القرآن الكريم

روايتي قالون عن نافع

و حفص عن الإمــام عاصـــم
من طريق طيبة النشــر
( القصر المطلق )


   I am expert in Mathematics of Operations Research. My research interests include the development of algorithms for Game theory and Vehicle Routing. I have published my research in many high impact journals like Journal of Optimization Theory and Applications, Automatica, Computers & Operations Research, IEEE Transaction on Smart Grid and IEEE Systems Journal. I also serve as a reviewer for many top journals like Automatica, Artificial Intelligence and Journal of the Operations Research Society. I am also a reviewer for the American Mathematical Society.

I obtained a Ph.D. degree in mathematics for engineers from the École Polytechnique de Montréal, and worked for an optimization company in Montréal. I have also obtained a M.Sc. degree in Operations Research from HEC Montréal.

* This current Semester 162 (Winter 2017)

Math 102-Calculus II-Sections 9 & 36.

* Previous Semesters Teaching

Undergraduate Courses

Math 101-Calculus I , Math 102-Calculus II,, Math 201-Calculus III.

Math 202-Elements of Differential Equations, Math 260-Differential Equations & Linear Algebra.

Stat 361-Operations Research I

Math 480-Linear and Non-Linear Programming.

Graduate Courses

Math 592-Special Topics in Math: Game Theory & Applications.


Software Documentation

New Architecture for the XGame-Solver Software: AUTOMATIC REFINEMENT OF EQUILIBRIA IN GAME THEORY. JF10002. King Fahd University of Petroleum & Minerals. Dhahran, KSA.

The XGame Solver Software: Equilibria Enumeration and Refinement in Game Theory, GERAD-Group for Research in Decision Analysis, Montreal, 2010, pp. 1-21. G2010-35-Manual/Handbook.

Published & Working Papers

    10. A Game Theoretic Approach for the Real-Life Vehicle Routing Problem with Multiple Time Windows. IEEE Systems Journal, 2017, To Appear..

    9. A Pareto Non-Dominated Solution Approach for the Vehicle Routing Problems with Multiple Time Windows, with M’Hallah R., Proceedings of the IEEE World Congress on Computational Intelligence, 2016.

    8. A Game Theoretic Model for Smart Grids Demand Management, with O. Baroudi.Published in IEEE Transactions on Smart Grid, 6,3, 1386-1393, 2015. PDF

    7. On Perfect Nash Equilibria of Polymatrix Games. Published in Game Theory, 11 pages, 2014. PDF

    6. A Note on Bimatrix Game Maximal Selten Subsets, with Charles AUDET and Pierre HANSEN. Published in Arabian Journal of Mathematics, Springer-Berlin-Heidelberg, Volume 3-Issue 3, p 299-311, 2014. PDF

    5. A Hybrid Variable Neighborhood Tabu Search Heuristic for the Vehicle Routing Problem with Multiple Time Windows, with  Pierre Hansen and Gilbert Laporte. Published in Computers and Operations Research, Volume 52-Part B, p 269-281, 2014.  PDF

-> VRPMTW NEW INSTANCES                   -> Some Best Solutions Files             

    4. On Proper Refinement of Nash Equilibrium for Bimatrix Games, with Charles AUDET and Pierre  HANSEN. Automatica, Vol.48, Issue 2, pp 297-303, February, 2012. PDF

     3. A New Sequence form approach for the enumeration of all extreme Nash equilibria for Extensive form Games, with Charles AUDET and Pierre HANSEN.International Game Theory Review, vol. 11, no. 4, Dec. 2009.  PDF 

    2. Enumeration of all extreme Nash equilibria in Game theory: Bimatrix and Polymatrix Games, with Charles AUDET and Pierre Hansen. Journal of Optimization Theory and Applications Vol.129 No.3, 349-372, June 2006. PDF

    1. Variable neighborhood search for extremal graphs XI. Bounds on algebraic connectivity, with Nair Maria Maia de ABREU,  Pierre HANSEN and Carla Silva OLIVEIRA.Graph Theory and Combinatorial Optimization, edited by David Avis, Alain Hertz and Odile Marcotte, Springer US, 2005. PDF


Last Update 18-12-2016