Greedy randomized adaptive search procedure with exterior path relinking for differential dispersion minimization

Less is more: Basic variable neighborhood search for minimum differential dispersion problem

“…The objective function may represent either efficiency-based measure, considering some dispersion quantity for 4 the entire selection S, or an equity-based measure, guaranteeing equitable dispersion among the selected elements. Widely stud-5 ied problems that use efficiency-based objective functions are: the Maximum diversity problem (MDP), where the goal is to find 6 a subset S maximizing the sum of the distances between the selected elements, and the Max-Min diversity problem (MMDP), 7 whose goal is to maximize the minimal distance between the selected elements. The problems considering equity-based mea-8 sures, introduced by Prokopyev et al [21], are: Maximum mean dispersion problem (Max-Mean DP), Minimum differential dis- 9 persion problem (Min-Diff DP), and Maximum min-sum dispersion problem (Max-Min-sum DP).…”

“…(4) 35 t ≥ r − s (5) 36 i∈N x i = m; (6) 37 x ∈ {0, 1} n (7) Constraints (3)/(4) ensure that the value of variable r/s is greater/less than the maximum (minimum) sum of distances of an 38 element i ∈ S from the remaining elements in the selected set S. Constraint (5) together with the objective function require that 39 the difference between r and s is minimal (for details see [21]). Constraint (6) assures that the cardinality of the set S equals to m. 40 Min-Diff DP is a NP-hard problem [21].…”

“…Constraint (6) assures that the cardinality of the set S equals to m. 40 Min-Diff DP is a NP-hard problem [21]. For solving it, several approaches are proposed in the literature.…”

“…For solving larger instances, they proposed 43 generic GRASP heuristic (for solving dispersion problems using equity-based measure). More recently, Duarte et al [6] pro-44 posed a specialized GRASP heuristic, and a hybrid approach that combines GRASP, variable neighborhood search, and ex- 45 terior path relinking. The last mentioned hybrid heuristic may be considered as a state-of-the-art heuristic for solving 46 Min-Diff DP.…”

Efficient Greedy Randomized Adaptive Search Procedure for the Generalized Regenerator Location Problem

“…Finally, the algorithm stores the best solution found during the exploration. This metaheuristic has been successfully applied in several recent NP-hard problems 15,16 .…”