Abstract
This paper considers a variant of the Vehicle Routing Problem with Time Windows, with site dependencies, multiple depots and outsourcing costs. This problem is the basis for many technician routing problems. Having both site-dependency and time window constraints lresults in difficulties in finding feasible solutions and induces highly constrained instances. Matheuristics based on Mixed Integer Linear Programming compact formulations are firstly designed. Column Generation matheuristics are then described by using previous matheuristics and machine learning techniques to stabilize and speed up the convergence of the Column Generation algorithm. The computational experiments are analyzed on public instances with graduated difficulties in order to analyze the accuracy of algorithms for ensuring feasibility and the quality of solutions for weakly to highly constrained instances. The results emphasize the interest of the multiple types of hybridization between mathematical programming, machine learning and heuristics inside the Column Generation framework. This work offers perspectives for many extensions of technician routing problems.
Highlights
If mathematical programming and especially Mixed Integer Linear Programming (MILP) are powerful frameworks for modeling a vast diversity of N P-hard combinatorial optimization problems, including complex real-world optimization problems, the resolution with exact methods such as the Branch and Bound (B&B) algorithm is limited in practice for large instances of real-world applications [1]
By choosing the MILP formulations and the cuts to add for the integer resolution, these results on the dual bounds shall be compared with the computation time
The LP relaxation of the DW extended formulation efficiently guides us toward primal solutions of an excellent quality.Matheuristics based on the compact ILP formulation may be inefficient even with combinations of large neighborhoods in a Variable Neighborhood Descent (VND) local search, contrary to [4], or with parallelization using a portfolio of matheuristics, contrary to [5]
Summary
If mathematical programming and especially Mixed Integer Linear Programming (MILP) are powerful frameworks for modeling a vast diversity of N P-hard combinatorial optimization problems, including complex real-world optimization problems, the resolution with exact methods such as the Branch and Bound (B&B) algorithm is limited in practice for large instances of real-world applications [1]. Solving the exact neighborhoods allows studying the quality of implied local minimums; such intermediate results are of interest for selecting which types of neighborhoods have to be carefully implemented in a local search heuristic [4]. Having other complementary advantages and drawbacks, machine learning (ML) techniques are recently considered in such hybridization schemes [6,7]. Note that such hybridization can provide dual bounds for large instances of optimization problems, using aggregation or decomposition techniques to compute dual bounds for heuristically reduced or decomposed problems with a proof that a dual bound of the original problem is computed despite the heuristic reduction [8,9]. ML techniques are useful in this context for selecting the promising dual bound among many alternatives [9]
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