The genetic algorithm with search area adaptation (GSA) has a capacity for adapting to the structure of solution space and controlling the tradeoff balance between global and local searches, even if we do not adjust the parameters of the genetic algorithm (GA), such as crossover and/or mutation rates. But, GSA needs the crossover operator that has ability for characteristic inheritance ratio co...

The Gravitational Search Algorithm (GSA) is a novel optimization method based on the law of gravity and mass interactions. It has good ability to search for the global optimum, but its searching speed is really slow in the last iterations. So the hybridization of Particle Swarm Optimization (PSO) and GSA can resolve the aforementioned problem. In this paper, a modified PSO, which the movement o...

A defensive alliance in a graph G = (V,E) is a set of vertices S ⊆ V where for each v ∈ S, at least half of the vertices in the closed neighborhood of v are in S. A defensive alliance S is called global if every vertex in V (G) \S is adjacent to at least one member of the defensive alliance S. In this paper, we derive an upper bound to the size of the minimum global defensive alliances in star ...

An offensive alliance in a graph Γ = (V,E) is a set of vertices S ⊂ V where for every vertex v in its boundary it holds that the majority of vertices in v’s closed neighborhood are in S. In the case of strong offensive alliance, strict majority is required. An alliance S is called global if it affects every vertex in V \S, that is, S is a dominating set of Γ. The offensive alliance number ao(Γ)...

Let Γ = (V,E) be a simple graph. For a nonempty set X ⊆ V , and a vertex v ∈ V , δX(v) denotes the number of neighbors v has in X. A nonempty set S ⊆ V is a defensive k-alliance in Γ = (V,E) if δS(v) ≥ δS̄(v)+k, ∀v ∈ S. A defensive k-alliance S is called global if it forms a dominating set. The global defensive k-alliance number of Γ, denoted by γ k(Γ), is the minimum cardinality of a defensive ...

Let G be a connected graph with vertex set V (G) and edge set E(G). A (defensive) alliance in G is a subset S of V (G) such that for every vertex v ∈ S, |N [v]∩S| ≥ |N(v)∩(V (G)− S)|. The alliance partition number, ψa(G), was defined (and further studied in [11]) to be the maximum number of sets in a partition of V (G) such that each set is a (defensive) alliance. Similarly, ψg(G) is the maximu...

Thanks to the Global Alliance for Vaccines and Immunization (GAVI), the Vaccine Fund and the Bill & Melinda Gates Foundation, the global health community has made enormous progress in providing already existing vaccines to developing countries. However, there still exists a gap to develop vaccines for which there is no market in the Western world, owing to low economic incentives for the privat...

Let G = (V (G), E(G)) be a graph, and let k ≥ 1 be an integer. A set S ⊆ V (G) is called a global offensive k-alliance if |N(v) ∩ S| ≥ |N(v)−S|+k for every v ∈ V (G)−S, where N(v) is the neighborhood of v. The global offensive k-alliance number γ o (G) is the minimum cardinality of a global offensive k-alliance in G. We present different bounds on γ o (G) in terms of order, maximum degree, inde...

The purpose of model-based experimental design is to maximise the information gathered for quantitative model identification. Instead of the commonly used optimal experimental design, robust experimental design aims to address parametric uncertainties in the design process. In this paper, the Bayesian robust experimental design is investigated, where both a Monte Carlo sampling strategy and loc...