Heuristics for Routing Heterogeneous Unmanned Vehicles with Fuel Constraints

Algorithm 1

Steps of the basic VNS by Hansen and Mladenovic.

Initialization: Select a set of neighborhood structures denoted by 𝑁_𝜅 (𝜅=1,…,𝜅_max) that will be used in

the search; find an initial solution 𝑥; choose a stopping condition.

Repeat the following until the stopping condition is met:

 (1) Set 𝜅←1.

 (2) Repeat the following steps until 𝜅=𝜅_max:

  (a)   Shaking: Generate a feasible solution 𝑥^′ at random from the 𝜅th neighborhood of 𝑥 (𝑥^′∈𝑁_𝜅(𝑥));

  (b)   Local search: Apply a local search method with 𝑥^′ as initial solution; denote the so obtained

       local optimum as 𝑥^′′;

  (c)   Move or not: If 𝑥^′′ is better than incumbent 𝑥, set 𝑥←𝑥^′′ and continue the search with 𝑁₁ (𝜅←1);

       otherwise set 𝜅←𝜅+1;