An improved multi-directional local search algorithm for the multi-objective consistent vehicle routing problem

Multi-directional local search for sustainable supply chain network design

“…It has been later applied to intermodal train loading planning (Heggen et al, 2018) and several variants of the travelling salesman problem 60 (Defryn and Sörensen, 2018) and vehicle routing problems (Kovacs et al, 2015;Molenbruch et al, 2017;Lehuédé et al, 2019). A variant of the original MDLS, called Improved Multi-Directional Local Search (IMDLS) was proposed by Lian et al (2016). IMDLS limits the size of the non-dominated set.…”

“…A new idea introduced by Lian et al (2016) is to limit the size of the non-dominated set to a predefined number, hereby denoted by P max . In order to select the P max active solutions, they measure crowding distance of each solution of the non-dominated set.…”

“…We evaluate our MDLS implementation through a comparison with the results obtained framework proposed by Lian et al (2016). All algorithms were coded in C++ and run on a computer with four Intel 3.0 GHz CPUs and 8 GB of RAM.…”

“…As stated earlier, the number of non-dominated solutions is slightly decreased by the post-optimization step, since calculating optimal product flows enables merging some neighboring non-dominated solutions. Regarding computing times, One main difference between MDLS proposed in this study and in Lian et al (2016) 350 with the original one in Tricoire (2012) is to provide a non-dominated set with a small set of solutions. Providing a reasonable number of representative solutions to decision makers might be more desirable (Govindan et al, 2015).…”

“…propose a bi-objective extension of the model proposed inEskandarpour et al (2017), with environmental assessment and technology levels (Section 2) (ii) to solve this problem with an 70 MDLS approach limiting the number of trade-off solutions as proposed byLian et al (2016) (Section 3) (iii) to compare the results of the MDLS algorithm with an ε-constraint method (Section 4) and (iv) to propose managerial insights based on the analysis of solutions to our model (Section 5).…”