A Multi-start Algorithm with Intelligent Neighborhood Selection for solving multi-objective humanitarian vehicle routing problems

Higher order convergence for a class of set differential equations with initial conditions

“…Taking account of the fact that N (t, V, W ; Y, X) is nonincreasing in X and Lemma 2.9, we can conclude that there exists a solution W n+1 of (19) such that V n ≤ W n+1 ≤ W n by applying (29) and (30). From (6), (13) and the condition (…”

“…With this method we can prove that the monotone sequences are convergent uniformly. This fruitful method has been extended to set differential equations in a general setup which includes various known results, and the reader is referred to the papers of Devi and Vatsala [9], Devi [10], Dhaigudel and Naidu [13], McRae, Devi and Drici [26] for details. In [10], the authors introduced a partial ordering in the metric space (K c (R n ), D) and developed a monotone iterative method for set differential equations when the forcing function is the sum of a convex and a concave function.…”

“…Proof. In view of assumption D H 2k U F ≥ θ and D H 2k U G ≤ θ, we obtain the inequalities (6), (7), (12) and (13). Consider the following coupled IVPs:…”

“…are the solutions respectively of IVPs (18) and (19) such that V = V n , W = W n . Applying (6), (13) and (26) imply…”

“…Proof. We associate with the inequalities (6), (7), (12) and (13), and consider the following coupled IVPs:…”