## 3 Test of Bio-Inspired Algorithms on a Transportation Planning Problem
### Comparative Experiments  
To test the performance of our BBO algorithm and other typical meta-heuristics on the proposed transportation planning problem, we have implemented the following three bio-inspired algorithms:  
* A GA method from [64], which uses a two-part chromosome representation: the first part is a permutation of targets, and the second part gives the number of cities assigned to each source. Accordingly, a two-part chromosome crossover operator is employed in the GA.
* A combinatorial PSO method inspired by [65], where a particle is a (\(m\times n\))-dimensional vector, and each component \(x_{ij}\in\{0,1\}\) denotes whether target \(j\) is assigned to source \(i\). * An improved ACO method from [66], which adds to the problem a virtual central depot as the \"nest\", takes the actual sources as the \"entries\" of the nest, and takes targets as the \"food\". We generate a set of 10 test problems, which are generated based on data from disaster relief operations of the 2010 Yushu earthquake, the 2011 Yingjiang earthquake and the 2012 Ninglang earthquake. For a fair comparison, on every problem, a maximum running time limit, \(T^{\max}\) (in seconds), is set for all the algorithms. The experiments are conducted on a computer with an Intel Core i5-2520M processor and 8 GB memory. Empirically, for our BBO algorithm, we set \(I=E=1\), \(p=0.02\) and \(|P|=50\). The control parameters of other algorithms are set as suggested in the literature. We respectively run each algorithm 30 times with different random seeds on each test problem. Table 1 presents the experimental results, where the problem size is given in terms of \(m\times n\), _best_ denotes the best objective value obtained by the algorithm among the 30 runs, _mean_ denotes the average best objective value over the 30 runs and _std_ denotes the corresponding standard deviation. All the objective values are scaled to the range of [0,100] for the convenience of comparison. We also perform the paired \(t\)-test between the average pests of BBO and each comparative algorithm on the test problems and mark \({}^{\dagger}\) in Columns 5, 8 and 11 of the table if BBO has statistically significant improvement over the algorithm (at the 95% confidence level). As we can see from the results, on the simplest Problem 1, all the algorithms achieve the same optimal value; on Problem 2, PSO, ACO and BBO always achieve the same optimal value, but GA fails to do so. On the remaining problems, the mean pests obtained by ACO and BBO are always better than GA and PSO. In general, the performance of GA is the worst among the four bio-inspired algorithms. PSO exhibits a relatively fast convergency speed, but it is more easily trapped by local optima than ACO and BBO. The statistical tests also show that BBO has significant performance advantage over GA and PSO on nine and eight test problems, respectively. In comparison, the search mechanisms of ACO and BBO make them have more ability to jump out of local optima without sacrificing their performance. Therefore, we can conclude that ACO and BBO are more suitable for solving the proposed transportation planning problem. By comparing ACO and BBO, we find that the performance of the two algorithms are similar or have no significant differences on small-sized or moderate-sized problems (1-6). However, on large-sized problems (7-10), BBO has more performance advantage over ACO, and the advantage becomes more obvious with the increase of the problem size. In summary, our BBO algorithm exhibits the best