========== [Paper] ========== Tsung-Che Chiang and Wei-Huai Hsu, A knowledge-based evolutionary algorithm for the multiobjective vehicle routing problem with time windows, Computers & Operations Research, vol. 45, 2014. http://dx.doi.org/10.1016/j.cor.2013.11.014 ========== [Benchmark instances] ============= Gehring and Homberger's VRPTW instances (6 categories, 60 200-customer instances) http://www.sintef.no/project/TOP/VRPTW/Homberger/200/Homberger_200_customer_instances.zip ========== [Benchmark algorithms] ============= Benchmark algorithms and notations: [N] Y. Nagata, O. Bräysy, and W. Dullaert, "A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows," Computers & Operations Research, vol. 37, no. 4, pp. 724–737, 2010. [V] T. Vidal, T. G. Crainic, M. Gendreau, and C. Prins, "A hybrid genetic algorithm with adaptive diversity management for a large class of vehicle routing problems with time-windows," Computers & Operations Research, vol. 40, no. 1, pp. 475–489, 2013. [K] is our paper ========== [Net set of non-dominated solutions] ========== Each row represents the number of vehicles, the total distance, and the papers that found the solution. r1_2_1------------------ Totally 3 Pareto optimal solutions: 20 4784.11 [N][V] 21 4765.27 [K] 22 4755.63 [K] r1_2_2------------------ Totally 2 Pareto optimal solutions: 18 4040.6 [V] 19 4017.08 [K] r1_2_3------------------ Totally 1 Pareto optimal solutions: 18 3381.96 [N][V] r1_2_4------------------ Totally 1 Pareto optimal solutions: 18 3057.81 [N][V] r1_2_5------------------ Totally 1 Pareto optimal solutions: 18 4107.86 [N][V] r1_2_6------------------ Totally 1 Pareto optimal solutions: 18 3583.14 [V] r1_2_7------------------ Totally 1 Pareto optimal solutions: 18 3150.11 [N][V] r1_2_8------------------ Totally 1 Pareto optimal solutions: 18 2951.99 [N][V] r1_2_9------------------ Totally 1 Pareto optimal solutions: 18 3760.58 [V] r1_2_10------------------ Totally 1 Pareto optimal solutions: 18 3301.18 [N][V] r2_2_1------------------ Totally 6 Pareto optimal solutions: 4 4483.16 [N][V] 5 4085.11 [K] 6 3850.93 [K] 7 3765.72 [K] 8 3713.2 [K] 9 3681.37 [K] r2_2_2------------------ Totally 4 Pareto optimal solutions: 4 3621.2 [N][V] 5 3439.6 [K] 6 3328.95 [K] 7 3250.73 [K] r2_2_3------------------ Totally 3 Pareto optimal solutions: 4 2880.62 [N][V] 5 2812.79 [K] 6 2720.7 [K] r2_2_4------------------ Totally 2 Pareto optimal solutions: 4 1981.3 [N][V] 5 1980.08 [K] r2_2_5------------------ Totally 3 Pareto optimal solutions: 4 3366.79 [N][V] 5 3311.86 [K] 6 3260.93 [K] r2_2_6------------------ Totally 2 Pareto optimal solutions: 4 2913.03 [N][V] 5 2843.82 [K] r2_2_7------------------ Totally 3 Pareto optimal solutions: 4 2451.14 [N][V] 5 2437.8 [K] 6 2411.22 [K] r2_2_8------------------ Totally 1 Pareto optimal solutions: 4 1849.87 [N][V] r2_2_9------------------ Totally 3 Pareto optimal solutions: 4 3092.04 [N][V] 5 3026.73 [K] 6 2958.67 [K] r2_2_10------------------ Totally 1 Pareto optimal solutions: 4 2654.97 [N][V] rc1_2_1------------------ Totally 3 Pareto optimal solutions: 18 3602.8 [V] 19 3574.79 [K] 20 3571.03 [K] rc1_2_2------------------ Totally 1 Pareto optimal solutions: 18 3249.05 [V] rc1_2_3------------------ Totally 1 Pareto optimal solutions: 18 3008.33 [N][V] rc1_2_4------------------ Totally 1 Pareto optimal solutions: 18 2851.68 [N][V] rc1_2_5------------------ Totally 1 Pareto optimal solutions: 18 3371 [V] rc1_2_6------------------ Totally 1 Pareto optimal solutions: 18 3324.8 [V] rc1_2_7------------------ Totally 1 Pareto optimal solutions: 18 3189.32 [N][V] rc1_2_8------------------ Totally 1 Pareto optimal solutions: 18 3083.93 [N][V] rc1_2_9------------------ Totally 1 Pareto optimal solutions: 18 3081.13 [N][V] rc1_2_10------------------ Totally 1 Pareto optimal solutions: 18 3000.3 [V] rc2_2_1------------------ Totally 4 Pareto optimal solutions: 6 3099.53 [N][V] 7 2950.99 [K] 8 2877.59 [K] 9 2861.54 [K] rc2_2_2------------------ Totally 3 Pareto optimal solutions: 5 2825.24 [N][V] 6 2641.21 [K] 7 2543.62 [K] rc2_2_3------------------ Totally 4 Pareto optimal solutions: 4 2601.87 [N] 5 2448.11 [K] 6 2397.26 [K] 7 2366.26 [K] rc2_2_4------------------ Totally 3 Pareto optimal solutions: 4 2038.56 [N][V] 5 1961.38 [K] 6 1899.99 [K] rc2_2_5------------------ Totally 4 Pareto optimal solutions: 4 2911.46 [N][V] 5 2713.78 [K] 6 2584.7 [K] 7 2538.72 [K] rc2_2_6------------------ Totally 4 Pareto optimal solutions: 4 2873.12 [N][V] 5 2703.64 [K] 6 2586.54 [K] 7 2577.23 [K] rc2_2_7------------------ Totally 3 Pareto optimal solutions: 4 2525.83 [N][V] 5 2397.95 [K] 6 2355.6 [K] rc2_2_8------------------ Totally 4 Pareto optimal solutions: 4 2292.53 [V] 5 2237.01 [K] 6 2225.06 [K] 7 2220.88 [K] rc2_2_9------------------ Totally 2 Pareto optimal solutions: 4 2175.04 [N][V] 5 2167.63 [K] rc2_2_10------------------ Totally 1 Pareto optimal solutions: 4 2015.61 [N][V] c1_2_1------------------ Totally 1 Pareto optimal solutions: 20 2704.57 [N][V][K] c1_2_2------------------ Totally 3 Pareto optimal solutions: 18 2917.89 [N][V] 19 2796.73 [K] 20 2700.65 [K] c1_2_3------------------ Totally 3 Pareto optimal solutions: 18 2707.35 [N][V] 19 2700.82 [K] 20 2682.18 [K] c1_2_4------------------ Totally 2 Pareto optimal solutions: 18 2643.31 [N][V] 19 2631.77 [K] c1_2_5------------------ Totally 1 Pareto optimal solutions: 20 2702.05 [N][V][K] c1_2_6------------------ Totally 1 Pareto optimal solutions: 20 2701.04 [N][V][K] c1_2_7------------------ Totally 1 Pareto optimal solutions: 20 2701.04 [N][V][K] c1_2_8------------------ Totally 2 Pareto optimal solutions: 19 2775.48 [N][V] 20 2690.27 [K] c1_2_9------------------ Totally 2 Pareto optimal solutions: 18 2687.83 [N][V] 19 2645.47 [K] c1_2_10------------------ Totally 2 Pareto optimal solutions: 18 2643.55 [N][V] 19 2640.45 [K] c2_2_1------------------ Totally 2 Pareto optimal solutions: 6 1931.44 [N][V][K] 7 1931.3 [K] c2_2_2------------------ Totally 1 Pareto optimal solutions: 6 1863.16 [N][V][K] c2_2_3------------------ Totally 1 Pareto optimal solutions: 6 1775.08 [N][V][K] c2_2_4------------------ Totally 1 Pareto optimal solutions: 6 1703.43 [N][V] c2_2_5------------------ Totally 1 Pareto optimal solutions: 6 1878.85 [V] c2_2_6------------------ Totally 1 Pareto optimal solutions: 6 1857.35 [N][V][K] c2_2_7------------------ Totally 1 Pareto optimal solutions: 6 1849.46 [N][V][K] c2_2_8------------------ Totally 1 Pareto optimal solutions: 6 1820.53 [N][V] c2_2_9------------------ Totally 1 Pareto optimal solutions: 6 1830.05 [N][V] c2_2_10------------------ Totally 2 Pareto optimal solutions: 6 1806.58 [N][V] 7 1803.04 [K]