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A new genetic algorithm based on modified Physarum network model for bandwidth-delay constrained least-cost multicast routing

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Abstract

A mobile ad hoc network is a kind of popular self-configuring network, in which multicast routing under the quality of service constraints, is a significant challenge. Many researchers have proved that such problem can be formulated as a NP-complete problem and proposed some swarm-based intelligent algorithms to solve the optimal solution, such as the genetic algorithm (GA), bees algorithm. However, a lower efficiency of local search ability and weak robustness still limit the computational effectiveness. Aiming to those shortcomings, a new hybrid algorithm inspired by the self-organization of Physarum, is proposed in this paper. In our algorithm, an updating scheme based on Physarum network model (PM) is used for improving the crossover operator of traditional GAs, in which the same parts of parent chromosomes are reserved and the new offspring by the PM is generated. In order to estimate the effectiveness of our proposed optimized scheme, some typical genetic algorithms and their updating algorithms (PMGAs) are compared for solving the multicast routing on four different datasets. The simulation experiments show that PMGAs are more efficient than original GAs. More importantly, the PMGAs are more robustness that is very important for solving the multicast routing problem. Moreover, a series of parameter analyses is used to find a set of better setting for realizing the maximal efficiency of our algorithm.

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Notes

  1. http://www.isi.edu/nsnam/ns/.

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Acknowledgments

Prof. Z.L. Zhang and Dr. Chao Gao are the corresponding authors. This work is supported by the National High Technology Research and Development Program of China (No. 2013AA013801), National Natural Science Foundation of China (Nos. 61402379, 61403315), and Natural Science Foundation of Chongqing (No. cstc2013jcyjA40022), Fundamental Research Funds for the Central Universities (No. XDJK2016A008) and Research Fund for the Doctoral Program of Higher Education (RFDP) (No. 20120182120016).

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Authors and Affiliations

  1. School of Computer and Information Science, Southwest University, Chongqing, 400715, China

    Mingxin Liang, Chao Gao & Zili Zhang

  2. Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun, 130012, China

    Chao Gao

  3. School of Information Technology, Deakin University, Locked Bag 20000, Geelong, VIC, 3220, Australia

    Zili Zhang

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  1. Mingxin Liang
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  2. Chao Gao
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  3. Zili Zhang
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Correspondence to Chao Gao or Zili Zhang.

Appendix

Appendix

D1 = {(number of endpoint, number of endpoint, cost, delay)| (8, 1, 0.682, 0.853) (10, 1, 0.975, 0.547) (15, 1, 0.860, 0.0305) (17, 1, 0.595, 0.173) (7, 2, 0.820, 0.961) (15, 2, 0.367, 0.744) (4, 3, 0.856, 0.505) (13, 3, 0.758, 0.801) (14, 3, 0.413, 0.913) (16, 3, 0.648, 0.042) (20, 3, 0.456, 0.617) (5, 4, 0.923, 0.549) (9, 4, 0.404, 0.403) (10, 4, 0.480, 0.188) (19, 5, 0.308, 0.190) (7, 6, 0.484, 0.868) (8, 6, 0.757, 0.075) (16, 6, 0.878, 0.096) (8, 7, 0.579, 0.239) (19, 7, 0.684, 0.460) (10, 8, 0.467, 0.625) (12, 8, 0.334, 0.111) (11, 9, 0.464, 0.622) (13, 9, 0.874, 0.237) (14, 9, 0.310, 0.136) (20, 9, 0.615, 0.584) (11, 10, 0.950, 0.587) (12, 10, 0.843, 0.408) (13, 10, 0.640, 0.458) (17, 10, 0.655, 0.627) (20, 11, 0.604, 0.906) (13, 12, 0.721, 0.546) (14, 12, 0.797, 0.653) (19, 12, 0.596, 0.376) (14, 13, 0.462, 0.494) (15, 14, 0.800, 0.028) (18, 15, 0.798, 0.698) (19, 18, 0.999, 0.226)}, \({\varDelta _d}=5.\)

D2 = {(number of endpoint, number of endpoint, cost, delay)| (2, 1, 11, 4) (3, 1, 7, 6) (8, 1, 21, 3) (4, 2, 4, 4) (5, 2, 2, 5) (11, 2, 5, 3) (4, 3, 24, 3) (6, 4, 7, 11) (6, 5, 39, 1) (12, 5, 3, 5) (7, 6, 22, 3) (14, 6, 35, 4) (12, 7, 15, 4) (13, 7, 2, 3) (9, 8, 21, 3) (10, 8, 14, 6) (10, 9, 10, 7) (12, 9, 13, 1) (12, 10, 20, 3) (12, 11, 21, 3) (15, 13, 5, 3) (15, 14, 6, 4)}, \({\varDelta _d}=18.\)

D3 = {(number of endpoint, number of endpoint, cost, delay)| (1, 6, 8.197, 0.307) (1, 7, 7.549, 0.367) (1, 11, 4.214, 0.642) (1, 12, 9.743, 0.518) (1, 15, 7.722, 0.655) (2, 5, 5.654, 0.312) (2, 6, 7.986, 0.451) (2, 9, 3.002, 0.3662) (2, 11, 3.935, 0.490) (2, 13, 3.155, 0.583) (3, 4, 9.337, 0.539) (3, 7, 6.643, 0.421) (3, 8, 4.057, 0.360) (3, 10, 5.365, 0.441) (4, 8, 7.970, 0.647) (4, 10, 3.572, 0.413) (4, 14, 8.306, 0.398) (5, 9, 9.688, 0.374) (5, 11, 4.029, 0.610) (5, 13, 8.719, 0.387) (6, 7, 7.679, 0.562) (6, 9, 9.061, 0.490) (6, 11, 6.316, 0.346) (6, 12, 6.882, 0.522) (6, 15, 7.190, 0.502) (6, 16, 3.485, 0.612) (7, 8, 6.436, 0.352) (7, 10, 7.347, 0.631) (7, 12, 7.551, 0.329) (7, 15, 9.843, 0.601) (8, 10, 8.144, 0.291) (8, 12, 6.567, 0.479) (8, 14, 5.807, 0.622) (8, 19, 8.837, 0.631) (8, 22, 8.636, 0.660) (9, 11, 7.803, 0.252) (9, 13, 5.529, 0.315) (9, 15, 5.862, 0.651) (9, 16, 6.463, 0.435) (9, 18, 5.801, 0.461) (9, 20, 6.337, 0.622) (9, 21, 5.509, 0.645) (10, 14, 7.929, 0.336) (10, 17, 9.245, 0.455) (11, 12, 6.445, 0.608) (11, 13, 9.912, 0.531) (11, 15, 4.762, 0.403) (11, 16, 4.007, 0.295) (11, 18, 9.952, 0.503) (11, 21, 5.329, 0.470) (11, 23, 9.146, 0.622) (12, 15, 4.351, 0.295) (12, 19, 9.411, 0.373) (12, 21, 4.566, 0.616) (13, 16, 9.953, 0.572) (13, 18, 6.545, 0.379) (13, 20, 3.090, 0.387) (13, 23, 6.023, 0.638) (14, 17, 9.680, 0.303) (14, 25, 3.959, 0.594) (15, 16, 5.267, 0.371) (15, 19, 9.173, 0.385) (15, 21, 7.194, 0.329) (15, 27, 5.202, 0.584) (15, 29, 7.961, 0.634) (16, 18, 3.80, 0.332) (16, 20, 8.485, 0.606) (16, 21, 4.405, 0.211) (16, 23, 8.201, 0.348) (16, 27, 4.002, 0.470) (16, 30, 7.739, 0.582) (17, 22, 9.816, 0.523) (17, 24, 8.302, 0.398) (17, 25, 6.715, 0.334) (17, 32, 4.940, 0.590) (18, 20, 7.453, 0.274) (18, 21, 8.467, 0.471) (18, 23, 9.232, 0.259) (18, 27, 7.068, 0.589) (18, 28, 8.130, 0.441) (18, 30, 8.697, 0.500) (19, 21, 7.585, 0.531) (19, 22, 7.701, 0.455) (19, 24, 3.276, 0.640) (19, 26, 8.093, 0.360) (19, 27, 3.893, 0.622) (19, 29, 3.688, 0.431) (19, 31, 7.232, 0.494) (20, 23, 4.357, 0.441) (20, 28, 7.091, 0.345) (20, 30, 9.546, 0.596) (21, 23, 3.220, 0.352) (21, 27, 5.448, 0.293) (21, 29, 5.166, 0.515) (21, 30, 6.833, 0.507) (21, 33, 8.709, 0.553) (22, 24, 5.198, 0.185) (22, 25, 7.572, 0.602) (22, 26, 6.844, 0.219) (22, 29, 9.269, 0.629) (22, 31, 6.252, 0.445) (22, 32, 3.272, 0.392) (23, 27, 9.829, 0.352) (23, 28, 6.379, 0.385) (23, 30, 5.975, 0.259) (23, 33, 6.377, 0.500) (23, 35, 7.838, 0.663) (23, 36, 7.603, 0.600) (23, 37, 9.731, 0.613) (24, 25, 3.208, 0.417) (24, 26, 6.701, 0.376) (24, 31, 7.755, 0.564) (24, 32, 9.647, 0.274) (24, 38, 8.590, 0.638) (25, 32, 5.922, 0.428) (25, 34, 7.025, 0.442) (26, 29, 7.727, 0.413) (26, 31, 5.885, 0.241) (26, 32, 3.088, 0.473) (26, 40, 9.290, 0.615) (27, 28, 6.010, 0.661) (27, 29, 9.107, 0.370) (27, 30, 3.222, 0.324) (27, 31, 4.900, 0.651) (27, 33, 9.154, 0.261) (27, 36, 3.054, 0.496) (27, 37, 8.970, 0.656) (27, 39, 5.462, 0.615) (28, 30, 9.940, 0.363) (28, 35, 5.724, 0.349) (28, 36, 6.793, 0.601) (28, 37, 7.897, 0.445) (28, 41, 8.896, 0.631) (29, 31, 3.070, 0.281) (29, 33, 8.962, 0.434) (29, 36, 8.669, 0.692) (29, 39, 6.361, 0.491) (29, 40, 6.408, 0.590) (30, 33, 3.811, 0.313) (30, 35, 3.595, 0.498) (30, 36, 9.168, 0.343) (30, 37, 6.422, 0.376) (30, 41, 8.374, 0.637) (30, 42, 5.428, 0.648) (30, 44, 4.848, 0.694) (31, 32, 8.768, 0.551) (31, 33, 5.957, 0.667) (31, 38, 6.297, 0.617) (31, 39, 3.348, 0.537) (31, 40, 6.643, 0.410) (32, 34, 7.376, 0.464) (32, 38, 6.803, 0.374) (32, 40, 4.431, 0.637) (32, 43, 5.908, 0.668) (33, 36, 5.626, 0.266) (33, 37, 7.402, 0.491) (33, 39, 7.982, 0.417) (33, 42, 8.390, 0.450) (33, 44, 8.534, 0.627) (34, 38, 3.360, 0.499) (34, 43, 4.324, 0.456) (35, 36, 5.521, 0.510) (35, 37, 4.452, 0.251) (35, 41, 9.006, 0.305) (35, 44, 9.669, 0.579) (35, 46, 8.093, 0.655) (36, 37, 7.797, 0.263) (36, 39, 5.230, 0.500) (36, 41, 7.476, 0.458) (36, 42, 3.0563, 0.313) (36, 44, 8.227, 0.379) (36, 49, 4.107, 0.668) (37, 41, 7.264, 0.260) (37, 42, 3.519, 0.507) (37, 44, 6.914, 0.391) (37, 46, 3.308, 0.631) (38, 40, 6.990, 0.435) (38, 43, 5.081, 0.386) (38, 47, 6.347, 0.561) (38, 48, 7.744, 0.681) (39, 40, 4.309, 0.419) (39, 42, 5.630, 0.355) (39, 44, 3.077, 0.654) (39, 45, 7.530, 0.497) (39, 50, 8.132, 0.601) (40, 45, 9.557, 0.526) (40, 47, 9.185, 0.574) (41, 42, 6.132, 0.572) (41, 44, 3.230, 0.319) (41, 46, 6.869, 0.378) (41, 49, 4.788, 0.511) (42, 44, 5.267, 0.300) (42, 45, 6.418, 0.575) (42, 49, 4.340, 0.493) (42, 50, 9.512, 0.429) (43, 47, 3.246, 0.528) (43, 48, 8.404, 0.316) (44, 46, 7.936, 0.438) (44, 49, 8.298, 0.294) (44, 50, 6.236, 0.513) (45, 47, 3.476, 0.530) (45, 50, 4.900, 0.372) (46, 49, 7.593, 0.364) (47, 48, 7.700, 0.553) (49, 50, 8.928, 0.423)}, \({\varDelta _d}=5.\)

D4 = {(number of endpoint, number of endpoint, cost, delay, jitter, bandwidth)| (1, 2, 229.2, 123.27, 1.751, 797.457) (1, 5, 277.884, 123.312, 1.7516, 797.403) (1, 16, 153.24, 123.205, 1.75, 797.539) (1, 17, 132.163, 123.187, 1.7497, 797.562) (1, 18, 53.8145, 123.12, 1.7487, 797.648) (1, 19, 168.808, 123.219, 1.7502, 797.522) (2, 3, 215.969, 123.259, 1.7508, 797.471) (2, 4, 267.247, 123.303, 1.7515, 797.415) (2, 5, 63.7104, 123.129, 1.7488, 797.637) (2, 6, 176.894, 123.226, 1.7503, 797.513) (2, 8, 152.6, 123.205, 1.75, 797.54) (2, 9, 239.438, 123.279, 1.7511, 797.446) (2, 11, 202.107, 123.247, 1.7506, 797.486) (2, 12, 266.533, 123.302, 1.7515, 797.416) (2, 16, 126.895, 123.183, 1.7496, 797.568) (2, 18, 197.297, 123.243, 1.7506, 797.491) (3, 5, 260.038, 123.297, 1.7514, 797.423) (3, 6, 63.0259, 123.128, 1.7488, 797.638) (3, 8, 248.496, 123.287, 1.7513, 797.435) (3, 9, 80, 123.143, 1.749, 797.62) (4, 5, 221.549, 123.264, 1.7509, 797.465) (4, 8, 294.157, 123.326, 1.7519, 797.386) (4, 11, 244.492, 123.283, 1.7512, 797.44) (4, 12, 82.8908, 123.145, 1.7491, 797.616) (4, 13, 52.5624, 123.119, 1.7487, 797.65) (4, 16, 224.185, 123.266, 1.7509, 797.462) (5, 6, 210.481, 123.254, 1.7508, 797.477) (5, 8, 116.669, 123.174, 1.7495, 797.579) (5, 9, 266.66, 123.302, 1.7515, 797.416) (5, 11, 144.867, 123.198, 1.7499, 797.549) (5, 12, 208.471, 123.253, 1.7507, 797.479) (5, 13, 255.831, 123.293, 1.7514, 797.427) (5, 16, 147.683, 123.2, 1.7499, 797.545) (5, 18, 238.255, 123.278, 1.7511, 797.447) (6, 8, 186.141, 123.233, 1.7504, 797.504) (6, 9, 64.9019, 123.13, 1.7488, 797.636) (6, 11, 272.403, 123.307, 1.7516, 797.409) (6, 16, 294.214, 123.326, 1.7519, 797.386) (7, 8, 239.9, 123.279, 1.7511, 797.445) (7, 10, 84.9586, 123.147, 1.7491, 797.614) (7, 11, 221.828, 123.264, 1.7509, 797.464) (8, 9, 219.14, 123.262, 1.7509, 797.468) (8, 10, 280.165, 123.314, 1.7517, 797.401) (8, 11, 86.539, 123.148, 1.7491, 797.612) (8, 12, 248.458, 123.287, 1.7513, 797.435) (8, 16, 263.536, 123.3, 1.7515, 797.419) (10, 11, 235.5, 123.276, 1.7511, 797.449) (11, 12, 182.129, 123.23, 1.7504, 797.508) (11, 13, 250.027, 123.288, 1.7513, 797.434) (11, 16, 284.1, 123.317, 1.7517, 797.397) (12, 13, 68.656, 123.133, 1.7489, 797.632) (12, 16, 262.887, 123.299, 1.7515, 797.419) (13, 14, 264.3, 123.3, 1.7515, 797.418) (13, 16, 275.18, 123.31, 1.7516, 797.406) (14, 15, 199, 123.244, 1.7506, 797.489) (16, 17, 235.9, 123.276, 1.7511, 797.449) (16, 18, 102.801, 123.162, 1.7493, 797.595) (16, 19, 297.402, 123.329, 1.7519, 797.382) (17, 18, 146.756, 123.2, 1.7499, 797.547) (17, 19, 71.1157, 123.135, 1.7489, 797.629) (17, 20, 261.873, 123.298, 1.7514, 797.421) (18, 19, 200, 123.245, 1.7506, 797.489) (19, 20, 200, 123.245, 1.7506, 797.489)}, \({\varDelta _d}=1200, {\varDelta _b}=797.4, {\varDelta _j}=17.\)

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Liang, M., Gao, C. & Zhang, Z. A new genetic algorithm based on modified Physarum network model for bandwidth-delay constrained least-cost multicast routing. Nat Comput 16, 85–98 (2017). https://doi.org/10.1007/s11047-016-9545-6

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