Abstract
Retraining of staff is a compulsory managerial function in many organisations and often requires planning for a large number of employees. The large scale of this problem and various restrictions on the resultant assignment to classes make this planning challenging. The paper presents a complexity analysis of this problem together with linear and nonlinear mathematical programming formulations. Three different column generation based optimisation procedures and a large neighbourhood search procedure, incorporating column generation, are compared by means of computational experiments. The experiments used data typical to large electricity distributors.
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Blte A, Thonemann UW (1996) Optimizing simulated annealing schedules with genetic programming. Eur J Oper Res 92(2):402–416. https://doi.org/10.1016/0377-2217(94)00350-5. http://www.sciencedirect.com/science/article/pii/0377221794003505
Caprara A, Pisinger D, Toth P (1999) Exact solution of the quadratic knapsack problem. INFORMS J Comput 11(2):125–137
Chen Y, Hao JK (2015) Iterated responsive threshold search for the quadratic multiple knapsack problem. Ann Oper Res 226:101–131
Chen Y, Hao JK, Glover F (2016) An evolutionary path relinking approach for the quadratic multiple knapsack problem. Knowl Based Syst 92:23–34
Chopra S, Rao MR (1993) The partition problem. Math Program 59(1–3):87–115
Cornuéjols G, Nemhauser GL, Wolsey LA (1983) The uncapacitated facility location problem. Carnegie-mellon univ pittsburgh pa management sciences research group, Tech. rep
Desrosiers J, Lübbecke ME (2005) A primer in column generation. Springer, Berlin
Drezner Z (2003) A new genetic algorithm for the quadratic assignment problem. INFORMS J Comput 15(3):320–330. https://doi.org/10.1287/ijoc.15.3.320.16076.
García-Martínez C, Rodriguez F, Lozano M (2014) Tabu-enhanced iterated greedy algorithm: a case study in the quadratic multiple knapsack problem. Eur J Oper Res 232:454–463
Garey MR, Johnson DS (1979) Computers and intractability: a guide to np-completeness. Freeman, San Francisco
Gintner V, Kliewer N, Suhl L (2005) Solving large multiple-depot multiple-vehicle-type bus scheduling problems in practice. OR Spectr. 27(4):507–523
Goldschmidt O, Hochbaum DS, Levin A, Olinick EV (2003) The sonet edge-partition problem. Networks 41(1):13–23
Hiley A, Julstrom BA (2006) The quadratic multiple knapsack problem and three heuristic approaches to it. In: Proceedings of the 8th annual conference on genetic and evolutionary computation. ACM, pp 547–552
Johnson EL, Mehrotra A, Nemhauser GL (1993) Min-cut clustering. Math program 62(1–3):133–151
Julstrom BA (2005) Greedy, genetic, and greedy genetic algorithms for the quadratic knapsack problem. In: Proceedings of the 7th annual conference on genetic and evolutionary computation. ACM, pp 607–614
Pisinger D, Ropke S (2010) Large neighborhood search. In: Potvin J-Y, Gendreau M (eds) Handbook of metaheuristics. Springer, Boston, pp 399–419
Pochet Y, Wolsey LA (2006) Production planning by mixed integer programming. Springer, Berlin
Shaw P (1998) Using constraint programming and local search methods to solve vehicle routing problems. In: International conference on principles and practice of constraint programming. Springer, pp 417–431
Taşkın ZC, Smith JC, Ahmed S, Schaefer AJ (2009) Cutting plane algorithms for solving a stochastic edge-partition problem. Discrete Optim 6(4):420–435
Wang H, Kochenberger G, Glover F (2012) A computational study on the quadratic knapsack problem with multiple constraints. Comput Oper Res 39(1):3–11
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Czibula, O.G., Gu, H. & Zinder, Y. Planning personnel retraining: column generation heuristics. J Comb Optim 36, 896–915 (2018). https://doi.org/10.1007/s10878-018-0253-2
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DOI: https://doi.org/10.1007/s10878-018-0253-2