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Data of the INFORMS Journal on Computing paper: Routing replenishment workers: The prize collecting traveling salesman problem in scattered storage warehouses
<p>In what follows, you will find data of the paper:<br> "Routing replenishment workers: The prize collecting traveling salesman problem in scattered storage warehouses" published in INFORMS Journal on Computing</p> <p>List of files:<br> - Computational_results_BB_NN_RW_CPLEX.xlsx: Excel file that gives all results<br> - instance_gen.cc: Instance generator<br> - instances.zip: compressed file of all instances that are sorted by Sections. It additionally includes the generator<br> - Makefile: Makefile for compiling/debugging, i.e., "make all" or "make debug" do the jobs<br> - MersenneTwister.h: needed by schedule_finder.cc<br> - results_Section_5_1.zip: compressed file of all output files of Section 5.1<br> - results_Section_5_2.zip: compressed file of all output files of Section 5.2<br> - results_Section_5_3.zip: compressed file of all output files of Section 5.3<br> - schedule_finder.cc: Main program containing the B&B, the S-shape, and Nearest Neighbor procedure (see details for customizing the parameters at the top of this file)<br> - valgrind_debug.txt: Only contains the used debug command</p> <p>instances/instance_gen.cc generates a problem instance in file problems.txt<br> The structure of the these problem files is the following:<br> /*<br> NE Total number of experiments given by the currently considered file<br> -2 Separator<br> EXPGRP Index of the current experiment group the current experiment belong to<br> N Number of vacant positions in the warehouse<br> M Number of requests to be stored by the tour<br> P Number of pickers to be scheduled in the warehouse<br> A Number of vertical aisles<br> B Number of horizontal (cross) aisles<br> L_A Length of each vertical aisle<br> L_B Length of each cross aisle<br> UF_VA Up-factor of each vertical aisle (A values)<br> DF_VA Down- factor of each vertical aisle (A values)<br> UF_CA Up-factor of each cross aisle (B values)<br> DF_CA Down- factor of each cross aisle (B values)<br> x_pos_vertical_aisle x-position of vertical aisle (A values)<br> y_pos_cross_aisle y-position of cross aisle (B values)<br> warehouse_graph values For each node of the warehouse graph all entries (15 each) are given (total_number_of_warehouse_graph_nodes*15)<br> FS << warehouse_graph[curr_node].free_position << " " << endl;<br> FS << warehouse_graph[curr_node].depot_node << " " << endl;<br> FS << warehouse_graph[curr_node].vertical_aisle << " " << endl;<br> FS << warehouse_graph[curr_node].cross_aisle << " " << endl;<br> FS << warehouse_graph[curr_node].pred_cross_aisle << " " << endl;<br> FS << warehouse_graph[curr_node].succ_cross_aisle << " " << endl;<br> FS << warehouse_graph[curr_node].pred_vertical_aisle << " " << endl;<br> FS << warehouse_graph[curr_node].succ_vertical_aisle << " " << endl;<br> FS << warehouse_graph[curr_node].pred_cross_aisle_dist << " " << endl;<br> FS << warehouse_graph[curr_node].succ_cross_aisle_dist << " " << endl;<br> FS << warehouse_graph[curr_node].pred_vertical_aisle_dist << " " << endl;<br> FS << warehouse_graph[curr_node].succ_vertical_aisle_dist << " " << endl;<br> FS << warehouse_graph[curr_node].region << " " << endl;<br> FS << warehouse_graph[curr_node].x_position << " " << endl;<br> FS << warehouse_graph[curr_node].y_position << " " << endl;<br> shortest_path_distance For each combination of nodes (i.e., for total_number_of_warehouse_graph_nodes_square combinations) the distance<br> shortest_path_length_including_start_and_end For each combination of nodes (i.e., for total_number_of_warehouse_graph_nodes_square combinations) the number of visited nodes<br> shortest_path_visited_nodes For each combination of nodes (i.e., for total_number_of_warehouse_graph_nodes_square combinations) the detailed path (length is respectively given by shortest_path_length_including_start_and_end)<br> dd_free_position For each free position and the depot (here with index N) the due date is transferred (N+1 values) (only relevant for the extended problem, is ignored here)<br> weight_of_free_position For each free position and the depot (here with index N) the weight is transferred (N+1 values) (only relevant for the extended problem, is ignored here)<br> capacity_of_free_position For each free position the storage capacity transferred (N values)<br> -2 Separator indicating the end of an instances<br> -3 Separator indicating the end of all experiments (i.e., indicating the end of the file)<br> */</p> <p>output files (results_Section_5_1.zip/results_Section_5_2.zip/results_Section_5_3.zip):<br> results_BB_NXXX_MYYY_A10_B05: Output file of applying B&B<br> results_RW_NXXX_MYYY_A10_B05: Output file of applying s-shape random walk<br> results_NN_NXXX_MYYY_A10_B05: Output file of applying nearest neighbor</p> <p>In these files you find all outputs of schedule_finder.cc. <br> Among others, you will find the generated tour schedules (for Experiment with index I) in the output files by searching the phrase: "Experiment I completed with result="<br> or for the next Experiment " completed with result="</p> <p>Example (results_BB_N030_M150_A10_B05.txt, experiment 0, the tardiness values are to be ignored, see comments in schedule_finder.cc)<br> Pos 0 depot node with index 80 Number of stored items 0 CT 0 No tardiness<br> Pos 1 position 27 Number of stored items 4 Current accumulated number of stored items 4 CT 163 DD 5629 No additional tardiness<br> Pos 2 position 28 Number of stored items 5 Current accumulated number of stored items 9 CT 399 DD 2962 No additional tardiness<br> Pos 3 position 29 Number of stored items 4 Current accumulated number of stored items 13 CT 670 DD 12631 No additional tardiness<br> Pos 4 position 26 Number of stored items 5 Current accumulated number of stored items 18 CT 840 DD 10142 No additional tardiness<br> Pos 5 position 23 Number of stored items 7 Current accumulated number of stored items 25 CT 1134 DD 6000 No additional tardiness<br> Pos 6 position 22 Number of stored items 4 Current accumulated number of stored items 29 CT 1170 DD 6396 No additional tardiness<br> Pos 7 position 16 Number of stored items 5 Current accumulated number of stored items 34 CT 1448 DD 8962 No additional tardiness<br> Pos 8 position 11 Number of stored items 10 Current accumulated number of stored items 44 CT 1674 DD 6336 No additional tardiness<br> Pos 9 position 0 Number of stored items 10 Current accumulated number of stored items 54 CT 2062 DD 1141 Additional tardiness 921<br> Pos 10 position 2 Number of stored items 9 Current accumulated number of stored items 63 CT 2201 DD 7742 No additional tardiness<br> Pos 11 position 4 Number of stored items 5 Current accumulated number of stored items 68 CT 2407 DD 4846 No additional tardiness<br> Pos 12 position 3 Number of stored items 5 Current accumulated number of stored items 73 CT 2717 DD 2316 Additional tardiness 401<br> Pos 13 position 1 Number of stored items 8 Current accumulated number of stored items 81 CT 2876 DD 9917 No additional tardiness<br> Pos 14 position 6 Number of stored items 3 Current accumulated number of stored items 84 CT 3073 DD 7299 No additional tardiness<br> Pos 15 position 5 Number of stored items 8 Current accumulated number of stored items 92 CT 3144 DD 6152 No additional tardiness<br> Pos 16 position 8 Number of stored items 6 Current accumulated number of stored items 98 CT 3337 DD 3705 No additional tardiness<br> Pos 17 position 12 Number of stored items 9 Current accumulated number of stored items 107 CT 3452 DD 7622 No additional tardiness<br> Pos 18 position 13 Number of stored items 4 Current accumulated number of stored items 111 CT 3522 DD 7833 No additional tardiness<br> Pos 19 position 14 Number of stored items 5 Current accumulated number of stored items 116 CT 3647 DD 9877 No additional tardiness<br> Pos 20 position 19 Number of stored items 1 Current accumulated number of stored items 117 CT 3922 DD 2905 Additional tardiness 1017<br> Pos 21 position 20 Number of stored items 5 Current accumulated number of stored items 122 CT 3923 DD 2538 Additional tardiness 1385<br> Pos 22 position 21 Number of stored items 7 Current accumulated number of stored items 129 CT 3976 DD 2769 Additional tardiness 1207<br> Pos 23 position 18 Number of stored items 10 Current accumulated number of stored items 139 CT 4173 DD 3552 Additional tardiness 621<br> Pos 24 position 25 Number of stored items 4 Current accumulated number of stored items 143 CT 4482 DD 11710 No additional tardiness<br> Pos 25 position 24 Number of stored items 7 Current accumulated number of stored items 150 CT 4509 DD 10599 No additional tardiness<br> Pos 26 visiting the node with index 80 Number of stored items 0 CT 4710 DD 10893 No additional tardiness<br> opt_makespan=4710 opt_total_tardiness=5552<br> TSP_procedure returned value 4710<br> Experiment 0 completed with result=3<br> BFS Branch&Bound report: Consumed time: 1</p> <p>Copied from schedule_finder.cc:<br> Note that the procedure used as a solution procedure in the paper is int TSP_procedure(struct bb_node *curr_bb_node, int version)</p> <p>It is called by BB_procedure() as a subroutine for computing a lower bound value of an extended problem<br> (for instance, this extended problem additionally covers due dates. Therefore, due dates are also part of the problem instances, but can be ignored)<br> Specifically, TSP_procedure(struct bb_node *curr_bb_node, int version) is called once by lb_computation()</p>
BRAIN Journal-The Presence and Activity on Facebook of the Informative Travel Organizations in Romania-Figure 1. Selected Romanian counties in order to strengthen the target group of tourism organizations with informative role
<p>In this regard, we analysed the current state of presence and communication on Facebook for<br> 109 informative tourism entities located in 25 Romanian counties, selected on the basis of tourist<br> traffic indicators for the period between 2007 and 2013. The structure of the 109 organizations<br> analysed is: 43 tourist information centers (39.45%), 44 entities with the name of the association for<br> tourism promotion, ecotourism promotion, mountaineering promotion etc. (40.36%), 18 tourism<br> clubs (16.51%) and 4 tourist information points/offices (3.67%)</p>
BRAIN Journal-The Presence and Activity on Facebook of the Informative Travel Organizations in Romania-Figure 4. Facebook adoption rate by age group in Romania
<p>Also, according to Facebrands statistics of 15 October 2015, the Facebook penetration rate in the population is 39.76% and in the total number of Romanian Internet users is 82.97%. The statistics infirm the preconceived ideas of skeptics that the websites of socialization have no relevance for tourism organizations because the contained information in these websites is unstructured, inconsistent in terms of content and irrelevant for tourism, or newer, the ideas of those who believe that the majority of Facebook users are young and very young (under 18). From Figure 4 we can see that the segment of major users (over 18 years) totals 88.3% of the total number of Facebook users and these users may have at any time the quality of tourists.</p>
BRAIN Journal-The Presence and Activity on Facebook of the Informative Travel Organizations in Romania-Figure 3. Integration of Social Media elements on tourism organization's websites
<p>Currently, in Romania there are about 8 million Facebook users (Facebrands.ro). In the recent years there has been a spectacular increase of this phenomenon, which shows how important is the use of social networks for an economic and even for a non-profit entity in order to make the brand known or to promote an activity (DailyBusiness.ro). </p>
BRAIN Journal-The Presence and Activity on Facebook of the Informative Travel Organizations in Romania-Figure 2. Online presence through a website of Romanian tourism entities with informative role Source: authors
<p>According to research results (Figure 2), almost 68% of the entities with tourist information and promotion role own a proper site for the presentation of the work, while 18.35%, most probably do not realize in pragmatic terms the usefulness of such promotional tools. The situation can be cataloged as quite worrying, especially if we consider that today, due to the fulminant development of smartphones, more and more tourists choose to seek information on the Internet, even during their trip to a new destination (Wang el. al. 2012).</p>
BRAIN Journal-The Presence and Activity on Facebook of the Informative Travel Organizations in Romania-Figure 5. The attendance rate and active communication on Facebook of the Romanian tourism organizations with informative role
<p>As we can see in Figure 5, the presence on Facebook of the organizations involved in information and promotion of tourism activities (54.12%) is lower than the rate of online presence through a website (67.89%), which broadly confirms that Social Media visibility is the second step in the strategy of online business promotion of entities that were subject of this research. The fact that 99% of the tourist organizations present on Facebook already have a website that promotes their own work confirms the previous statement</p>
BRAIN Journal-An Efficient Combined Meta-Heuristic Algorithm for Solving the Traveling Salesman Problem-Figure 7. Execution plot, for instance Eil51 (left figure) and KroB100 (right figure)
<p>The evolution of the best solution found by the proposed algorithm is plotted in Figure 7 during a typical execution when solving instance Eil51 and KroB100. In this figure, the horizontal and vertical axes show the number of iterations and gained values of the proposed algorithm respectively. Besides, there is a fast convergence toward the BKS at the beginning of the execution while in the rest of the search the evolution of the BKS is not that fast. </p>
BRAIN Journal-An Efficient Combined Meta-Heuristic Algorithm for Solving the Traveling Salesman Problem-Figure 5. The process of MICALK for solving the TSP
<p>Moreover, in order to prevent the ICA from getting trapped in stagnation, we used a local searching algorithm when the algorithm attained a better solution compared to previous iterations. In fact, the probability of finding better solutions near a good solution is relatively high. There exist many algorithms for the local search and they have of course their pros and cons. Since LinKernighan algorithm is simple and it is one of the most successful methods for generating optimal or near optimal solutions for the TSP, we have used it in this study. The main steps of MICALK are summarized in the pseudo-code given in Figure 5. </p>
BRAIN Journal-An Efficient Combined Meta-Heuristic Algorithm for Solving the Traveling Salesman Problem-Figure 6. Some best routes found by the proposed algorithm
<p>Figure 6 shows some of the best solutions searched by the proposed method. In this figure, the horizontal axis represents the x-axis with increasing positive values to the right and the vertical axis represents the y-axis with increasing positive values upward. </p>
BRAIN Journal-An Efficient Combined Meta-Heuristic Algorithm for Solving the Traveling Salesman Problem-Figure 3. Flowchart of the ICA
<p>At last, the most powerful empire will take the possession of other empires and will win the competition. In other words, imperialistic competition hopefully converges to a state in which there exists only one empire and its colonies are in the same position and have the same cost as the imperialist. Figure 3 shows the flowchart of the basic ICA.</p>
BRAIN Journal-An Efficient Combined Meta-Heuristic Algorithm for Solving the Traveling Salesman Problem-Figure 1. The Initial Empires
<p>The ICA is a novel global search strategy which uses imperialism and imperialistic competition process as a source of inspiration. This algorithm is based on the fact that in a real world, countries try to extend their power over other countries in order to use their resources and bolster their own government. The first step in ICA is to generate an initial population like other evolutionary algorithms. The population set includes a number of feasible solutions called a ‘country’, which corresponds to the term ‘chromosome’ in the GA method. These countries are of two types: colonies and imperialists that altogether form some empires. As it is shown in Figure 1 (Atashpaz Gargari & Lucas, 2007), bigger and stronger empires have more colonies than smaller and weaker ones.</p>
BRAIN Journal-An Efficient Combined Meta-Heuristic Algorithm for Solving the Traveling Salesman Problem-Figure 2. Eliminate the weakest colony of the weakest empire
<p>After initial empires are formed, their colonies start moving toward their relevant imperialist country. This movement is a simple model of assimilation policy which was pursued by some of the imperialist states. If one of the colonies possesses more power than its relevant imperialist after this movement, they will exchange their positions. To begin the competition between empires, the total objective function of each empire should be calculated. It depends on the objective function of both an imperialist and its colonies. Imperialistic competition among these empires forms the basis of the proposed evolutionary algorithm. During this competition, weak empires collapse and powerful ones take the possession of their colonies - Figure 2 (Atashpaz Gargari & Lucas, 2007). The empire, which has lost all its colonies, will collapse. </p>
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