# Exploiting sets of independent moves in VRP

- 149 Downloads

## Abstract

Most heuristic methods for VRP and its variants are based on the partial exploration of large neighborhoods, typically by means of single, simple moves applied to the current solution. In this paper we define an extended concept of independent moves and show how even a very standard heuristic method can significantly improve when considering the simultaneous application of carefully chosen sets of moves. We show in particular that, when choosing a set such that the total cost variation is equal to the sum of the variations induced by each single move, the quality of solutions obtained is in general very high. When compared with numerical results obtained by some of the best available heuristics on challenging, large scale, problems, our simple algorithm equipped with the application of optimally chosen independent moves displayed very good quality.

## Keywords

VRP Tabu search Matheuristic Independent moves## Notes

### Acknowledgements

We are grateful to both reviewers and the associate editor for their stimulating comments on the first version of this paper: answering those comments helped us to significantly improve the quality of this paper.

## References

- Boschetti M, Maniezzo V (2015) A set covering based matheuristic for a real-world city logistics problem. Int Trans Oper Res 22:169–196CrossRefGoogle Scholar
- Bosco A, Laganà D, Musmanno R, Vocaturo F (2014) A matheuristic algorithm for the mixed capacitated general routing problem. Networks 64(4):262–281CrossRefGoogle Scholar
- Bräysy O, Gendreau M (2005) Vehicle routing problem with time windows, part i: route construction and local search algorithms. Trans Sci 39(1):104–118CrossRefGoogle Scholar
- Congram RK, Potts CN, van de Velde SL (2002) An iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem. INFORMS J Comput 14(1):52–67CrossRefGoogle Scholar
- Corman F, Voß S, Negenborn RR (eds) (2015) An ant colony-based matheuristic approach for solving a class of vehicle routing problems. Springer International Publishing, ChamGoogle Scholar
- Dayarian I, Crainic TG, Gendreau M, Rei W (2016) An adaptive large neighborhood search heuristic for a multi-period vehicle routing problem. Transp Res Part E: Logist Transp Rev 95:95–123CrossRefGoogle Scholar
- De Franceschi R, Fischetti M, Toth P (2006) A new ILP-based refinement heuristic for vehicle routing problems. Math Program 105(2–3):471–499CrossRefGoogle Scholar
- Ergun Ö, Orlin JB, Steele-Feldman A (2006) Creating very large scale neighborhoods out of smaller ones by compounding moves. J Heuristics 12(1):115–140CrossRefGoogle Scholar
- Foster BA, Ryan DM (1976) An integer programming approach to the vehicle scheduling problem. J Oper Res Soc 27(2):367–384CrossRefGoogle Scholar
- Gurobi Optimization Inc (2016) Gurobi optimizer reference manual. http://www.gurobi.com. Accessed 24 Mar 2017
- Kelly JP, Xu J (1999) A set-partitioning-based heuristic for the vehicle routing problem. INFORMS J Comput 11(2):161–172CrossRefGoogle Scholar
- Koç Ç, Bektaş T, Jabali O, Laporte G (2015) A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows. Comput Oper Res 64:11–27CrossRefGoogle Scholar
- Mancini S (2016) A real-life multi depot multi period vehicle routing problem with a heterogeneous fleet: Formulation and adaptive large neighborhood search based matheuristic. Transportation Research Part C: Emerging Technologies, pp. 100–112Google Scholar
- Nemhauser GL, Wolsey LA (1988) Integer programming and combinatorial optimization. Wiley, New YorkGoogle Scholar
- Pillac V, Guéret C, Medaglia AL (2013) A parallel matheuristic for the technician routing and scheduling problem. Optim Lett 7(7):1525–1535CrossRefGoogle Scholar
- Potts CN, van de Velde SL (1995) Dynasearch-Iterative local improvement by dynamic programming. Part I. The traveling salesman problem. Tech. rep., University of TwenteGoogle Scholar
- Riise A, Burke EK (2014) On parallel local search for permutations. J Oper Res Soc 66(5):822–831CrossRefGoogle Scholar
- Rochat Y, Taillard ÉD (1995) Probabilistic diversification and intensification in local search for vehicle routing. J Heuristics 1(1):147–167CrossRefGoogle Scholar
- Rousseau LM, Gendreau M, Pesant G (2002) Using constraint-based operators to solve the vehicle routing problem with time windows. J Heuristics 8(1):43–58CrossRefGoogle Scholar
- Schmid V, Doerner KF, Hartl RF, Savelsbergh MW, Stoecher W (2009) A hybrid solution approach for ready-mixed concrete delivery. Transp Sci 43(1):70–85CrossRefGoogle Scholar
- Subramanian A, Uchoa E, Ochi LS (2013) A hybrid algorithm for a class of vehicle routing problems. Comput Oper Res 40(10):2519–2531CrossRefGoogle Scholar
- Toth P, Vigo D (2014) Vehicle routing: problems, methods, and applications, second, edition edn. SIAM/MOS, PhiladelphiaCrossRefGoogle Scholar
- Uchoa E, Pecin D, Pessoa A, Poggi M, Vidal T, Subramanian A (2017) New benchmark instances for the capacitated vehicle routing problem. Eur J Oper Res 257(3):845–858CrossRefGoogle Scholar
- Vidal T, Crainic TG, Gendreau M, Prins C (2014) A unified solution framework for multi-attribute vehicle routing problems. Eur J Oper Res 234(3):658–673CrossRefGoogle Scholar