Mathematical Optimization Theory and Operations Research. 19th International Conference, MOTOR 2020, Novosibirsk, Russia, July 6–10, 2020, Revised Selected Papers
In this paper we propose an efficient heuristic for the Vehicle Routing Problem on Trees (TVRP). An initial solution is constructed with a greedy algorithm based on the Depth-First Search (DFS) approach. To optimize initial solutions obtained by our DFS heuristic, Ruin-and-Recreate (RR) method is then applied. For diversification purposes a randomization mechanism is added to the construction of initial solutions and DFS+RR algorithm is executed multiple times until the best found solution stops changing. The results of our approach are compared with the solutions obtained by the exact model of Chandran & Raghavan (2008). The computational experiments show that the suggested heuristic is fast and finds solutions which differ from optimal ones less than by 1% in average.
Recently some specific classes of non-smooth and non-Lipsch-itz convex optimization problems were considered by Yu. Nesterov and H. Lu. We consider convex programming problems with similar smoothness conditions for the objective function and functional constraints. We introduce a new concept of an inexact model and propose some analogues of switching subgradient schemes for convex programming problems for the relatively Lipschitz-continuous objective function and functional constraints. Some class of online convex optimization problems is considered. The proposed methods are optimal in the class of optimization problems with relatively Lipschitz-continuous objective and functional constraints.