## 2 A Survey of Bio-Inspired Algorithms for Transportation Problems  
### Algorithms for General Transportation Planning  
The basic transportation problem is to ship at minimum cost a homogeneous good from a set of \(m\) sources (warehouses) to a set of \(n\) targets (markets). Suppose the supply of source \(i\) is \(a_{i}\), the demand of target \(j\) is \(b_{j}\) and the cost for transporting one unit of goods from source \(i\) to target \(j\) is \(c_{ij}\) (\(1\leq i\leq m\), \(1\leq j\leq n\)); then, the problem can be modeled as a special case of the linear program (LP) as follows:  
min \[f=\sum_{i=1}^{m}\sum_{j=1}^{n}c_{ij}x_{ij}\] (1) s.t. \[\sum_{i=1}^{m}x_{ij}\geq b_{j},\quad j=1...n\] (2) \[\sum_{j=1}^{n}x_{ij}\leq a_{i},\quad i=1...m\] (3) \[x_{ij}\geq 0,\quad i=1...m,j=1...n\] (4)  
An early work of [PERSON] and [PERSON] [14] proposed some alternative GAs for solving the linear transportation problem, using different representation structures and genetic operators. However, the work was mainly a feasibility study, and in comparison to linear programming and some specialized algorithms, the GAs perform poorly on such a unimodular problem [15]. Real-world transportation problems typically involve heterogeneous goods, multi-modal transportation and strict time windows, especially in emergency logistics [16]. Thus, they should be modeled as integer programming (IP) or mixed integer programming (MIP) problems, which are much more difficult to solve. [PERSON] _et al_. [17] developed a heuristic emergency relief transportation planning algorithm for an MIP transportation problem. The algorithm groups and sorts demands based on multiple criteria and then plans the demands individually using a shortest traveling-time tree and a minimum cost production tree. Based on the analysis of the practice of emergency management in China, [PERSON] _et al_. [18] presented a distribution model of emergency materials in a three-layer relief transportation network, the aim of which is to minimize the system losses while meeting the constraints of emergency response time and fairness. For the formulated nonlinear IP, they proposed a modified PSO algorithm, where different learning objects are used for different dimensions of the particles. Considering multiple transportation modes in an emergency relief problem, [PERSON] and [PERSON] [19] designed a GA that uses natural number coding, tournament selection and single-point crossover. The problem model uses the ratio of transport quantity to total demand quantity as the weights of transport time, and the algorithm utilizes a penalty function to handle the constraints. In [20], [PERSON] _et al_. formulated a practical transportation problem with multiple vehicle types and many other constraints, which is often encountered by crisis managers in emergency situations. To handle the problem, which is shown to be \(NP\)-hard, they developed a GA in which an individual is represented with genes composed of delivery points and products. The GA initializes a population based on the set enumeration heuristic and uses three fast improvement procedures to evolve each individual in the population, whilst some worst solutions in a new population are replaced by new ones for diversification. Computational experiments show that the method can produce near optimal solutions in relatively short computation times and is fast enough to be used interactively in a decision-support system. Transportation under a disaster environment and emergency situation often involves a variety of uncertainty and randomization. [PERSON] _et al_. [21] studied a disaster relief logistics problem in which demands, supplies, cost of procurement and transportation are considered as uncertain parameters. Therefore, the problem is modeled as an uncertain, nonlinear MIP. They used the robust optimization technique [22] to handle the uncertainty, _i.e._, describing uncertain parameters by the discrete scenarios or a continuous range.