蚁群算法路径规划时间窗matlab

# ACO-VRPTW ```matlab Procedure ACO Initialization while(termination conditions not meet): ConstructAntSolutions ApplyLocalSearch %optional UpdatePheromone end end ``` ### Initialization Set all parameters ### ConstructAntSolutions Each ant starts with an initially empty solution and the current partial solution will be extended by choosing one feasible solution component with the following rules: 1. Prefer the customer with small waiting time(wait = left time window - arrival time), because we don't want the customer to wait for a long time 2. Prefer the customer with a small width of time window (width = right time window - left time window) 3. If the random value $r$ Is smaller than $r_0$, choose the next point $j$ which has the biggest value of $[\tau_{ij}]^\alpha [\eta_{ij}]^\beta [1/width_j]^\gamma [1/wait_j]^\delta$​​ 4. Otherwise, use roulette wheel selection and the $P_{ij}^k$ to choose next point $j$​​ $$ j = \begin{cases} arg\ max_{j \in N_i^k} \lbrace [\tau_{ij}]^\alpha [\eta_{ij}]^\beta [1/width_j]^\gamma [1/wait_j]^\delta \rbrace & \text{$r\leq r_0$} \\[2ex] P_{ij}^k = \frac {[\tau_{ij}]^\alpha [\eta_{ij}]^\beta [1/width_j]^\gamma [1/wait_j]^\delta} {\sum_{l\in N_i^k}[\tau_{il}]^\alpha [\eta_{il}]^\beta [1/width_l]^\gamma [1/wait_l]^\delta} & \text{$r > r_0$} \end{cases} $$ Parameters $\alpha, \beta, \gamma, \delta$​​ determine the influence of the corresponding component. $\tau$​ , pheromone $\eta$​ , the heuristic information, is equal to the inverse value of distance $r$​ , a random value $r_0$ , a constant ### UpdatePheromone Only update the pheromone on the edge with the best route $$ \tau_{ij}^{new} = \rho * \tau_{ij}^{old} + \Delta \tau_{ij}\\ \Delta \tau_{ij} = \frac {Q}{TD} $$ $Q$​ , a constant $TD$ , the total distance