Supplementary Material for “Boosting Local Search with Lagrangian Relaxation”

In this report, we present the complete experimental results of ALCMALANS , which is obtained by embedding Lagrangian relaxation Assisted Neighborhood Search (LANS) into the Accelerated Limit Crossing based Multilevel Algorithm (ALCMA). In the original version of ALCMA, interchange is applied as the underlying local search subroutine. To investigate the flexibility of LANS, we replace the local search within ALCMA, from interchange to LANS, and apply the variant over the benchmark instances. The algorithms are implemented in C++, compiled with g++ 4.7 with flag -O3. The experiments are conducted on a Pentium IV 3.2 GHz PC with 4GB memory, running GNU/Linux with kernel 3.10. We employ the Euclidean (FL1400, PCB3038, and RL5934), the RW, and the GAP instances to conduct the experiment. We do not consider the other instances for the following reasons. For the ORLIB instances, applying LANS over random initial solutions could achieve the optimality. Besides, the RL11849 instances are not incorporated due to their scales. For each benchmark instance, we independently execute ALCMALANS for 9 times, which follows the experimental design of the existing work (Hansen and Mladenovic (1997); Resende and Werneck (2004); Ren et al (2012a)). Note that for the GAP instances, since not all the solutions are feasible (Kochetov et al (2005)), we shall repeat the executions of ALCMALANS , until 9 feasible output solutions are obtained. The numerical results are presented in Tables 1–10. These tables are organized as follows. We present the instance-specific information in column 1. Column 2 lists the best known results in the literature, to the best of our knowledge (Resende and Werneck (2004); Pullan (2008); Ren et al (2012a,b, 2013)). Then, in columns 3–6, we give the minimum objective value achieved