To achieve good and fast approximations to these two solutions, we design heuristic algorithms, including mixed integer programming heuristics, construction heuristics and local search procedures.
The matheuristic is composed of four main algorithmic components: a construction heuristic, an improvement heuristic, a reinsertion heuristic, and a perturbation heuristic.
In this work, we cover more heuristics, and divide 22 construction heuristics into 3 new categories, namely (1) space-partitioning-based heuristics, (2) node-based heuristics and (3) edge-based heuristics.
While the majority of scheduling heuristics investigated in the literature are construction heuristics [23], i.e. step-by-step construct the schedule, some have also investigated improvement heuristics that iteratively refine the schedule [74, 88, 110, 136].
We also develop efficient construction heuristics and transshipment heuristics that are incorporated into the heuristic procedures for the solution of subproblems.
where τ0, the initial amount of pheromone, is calculated as τ0 = (nC i )−1, n is the number of nodes, C i is the cost of the initial tour produced by a construction heuristic such as the nearest neighbor heuristic, SW, etc., and ρ is a parameter called evaporation rate in the range [0, 1] regulating the reduction of pheromone on the edges.
These methods use a combination of heuristics and constructions to achieve an ultimate shape.
The method relies on a greedy construction heuristic for finding feasible allocations and local search for improving initially constructed allocations.
We have also compared the results with the state-of-the-art meta-heuristic GVNS and observed that the proposed construction heuristics improves the results for some of the input instances.
