Abstract Many security companies offer patrolling services, such that guards inspect facilities or streets on a regular basis. Patrolling routes should be cost efficient, but the inspection patterns should not be predictable for offenders. We introduce this setting as a multi‐objective periodic mixed capacitated general routing problem with objectives being cost minimization and route inconsistency maximization. The problem is transformed into an asymmetric capacitated vehicle routing problem, on both a simple‐graph and a multi‐graph; and three multi‐objective frameworks using adaptive large neighborhood search are implemented to solve it. As tests with both artificial and real‐world instances show that some frameworks perform better for some indicators, a hybrid search procedure, combining two of them, is developed and benchmarked against the individual solution methods. Generally, results indicate that considering more than one shortest path between nodes, can significantly increase solution quality for smaller instances, but is quickly becoming a detriment for larger instances.

中文翻译：

---

简单图和多图的节点、边和弧上的安全高效路由

摘要 许多保安公司提供巡逻服务，例如保安定期检查设施或街道。巡逻路线应该具有成本效益，但检查模式对于违法者来说不应该是可预测的。我们将此设置引入为多目标周期性混合容量一般路由问题，其目标是成本最小化和路由不一致性最大化。该问题转化为简单图和多重图上的非对称容量车辆路径问题；并实现了三个使用自适应大邻域搜索的多目标框架来解决这个问题。由于对人工和现实世界实例的测试表明，某些框架对于某些指标表现更好，因此开发了将两者结合起来的混合搜索程序，并针对各个解决方案方法进行了基准测试。一般来说，结果表明，考虑节点之间的多个最短路径可以显着提高较小实例的解决方案质量，但很快就会对较大实例产生损害。