# A Multi-Strategy ALNS for the VRP with Flexible Time Windows and Delivery Locations
## 5 Results and Discussion
### Algorithm Analysis
#### 5.2.2 Comparisons with Meta-Heuristic Algorithms  
For the examples that are difficult to solve with exact methods such as Gurobi, further analysis is needed to evaluate the performance of MSALNS. Therefore, a comparative analysis was performed on all instances using the proposed MSALNS and three other metaheuristic algorithms: a standard Adaptive Large Neighborhood Search (ALNS), the Tunicate Swarm Algorithm (TSA, [PERSON] et al. [51]), and the Sand Cat Swarm Optimization (SCSO, Seyyedabbasi and Kiani, [52]). The algorithms selected for comparison include:  
1. **ALNS:** This represents the standard Adaptive Large Neighborhood Search framework, upon which our MSALNS is built. The ALNS does not include the specific improvements introduced in our MSALNS, such as the satisfaction-based operators, dual-weighted local search, or the secondary simulated annealing restart mechanism. 2. **TSA (Tunicate Swarm Algorithm):** TSA is a recent bio-inspired metaheuristic algorithm that mimics the survival behaviors of tunicates in the ocean. It models two key aspects: the jet propulsion used by individual tunicates for movement (including mechanisms to avoid conflicts between individuals and move towards the best neighbor) and the swarm intelligence that updates the positions of search agents relative to the best-found solutions so far. 3. **SCSO (Sand Cat Swarm Optimization):** SCSO is another nature-inspired algorithm based on the survival strategies of sand cats in deserts. The algorithm models two main behaviors derived from the sand cat's hunting techniques: searching for prey (exploration phase), inspired by the cat's ability to detect low-frequency sounds to locate prey, and attacking the prey (exploitation phase), guided by the cat's position relative to the prey. The algorithm uses adaptive parameters to balance these two phases. The effectiveness of the algorithm improvements can be evaluated by comparing MSALNS with the standard ALNS. Additionally, comparisons with two recent swarm intelligence algorithms, TSA and SCSO, provide further insights into the performance of MSALNS relative to other recent metaheuristic algorithms. For the TSA and SCSO algorithms, the number of iterations is set to 500, and the number of populations is set to 100. To verify the performance of MSALNS, the four algorithms are verified on different datasets with 16, 21, 31, and 61 customers, respectively. The performance comparison results of the algorithms are shown in Table 3. For each algorithm, the best solution cost and coefficient of variation in the solution are calculated by the calculation 10 times. The first column represents the different instances used, and the second column represents the best solution cost, coefficient of variation, and solving time (the unit is second) of the solution found in the MSALNS method. The third, fourth, and fifth columns are similar and represent the corresponding parameters of the ALNS, TSA, and SCSO algorithms. The experimental results show that MSALNS has a significant improvement effect on ALNS. MSALNS can find the best solution in 20 instances, and only in 3 instances with fewer customers is the best solution obtained by TSA and SCSO. At the same time, our MSALNS fully expands the search range, and the solution quality can be basically controlled within 10%, showing good stability. At the same time, in all instances, we can see that MSALNS has been effectively improved compared to the basic ALNS. The experimental results show that MSALNS achieves this significant improvement in solution quality (compared to ALNS) with comparable computational effort (see average run times in Table 3). While TSA and SCSO were generally slower, MSALNS demonstrates a strong balance between effectiveness and efficiency for the VRP-CS. In Figure 7, the red line represents the median and the blue line represents the mean. When the number of customers is 15, the performance of MSALNS is not much different from that of other algorithms. When the number of customers increases, MSALNS shows better solving ability.