A Memetic Algorithm for Resource Allocation Problem Based on Node-Weighted Graphs [Application Notes]

Resource allocation problems usually seek to find an optimal allocation of a limited amount of resources to a number of activities. The allocation solutions of different problems usually optimize different objectives under constraints [1, 2]. If the activities and constraints among them are presented as nodes and edges respectively, the resource allocation problem can be modeled as a k-coloring problem with additional optimization objectives [3, 4]. Since the amount of resources is limited, it is common that some of the activities (nodes) cannot obtain a resource (color). Because the importance of the nodes is usually different, let the weight of a node denote the cost if it cannot obtain a resource, then the resource allocation problem can be described by a node-weighted graph G(E,V), where E and V are the edge and node set, respectively. Some of the nodes that cannot obtain a resource will incur cost to the allocation solution. The optimization objective of the resource allocation problem formulated in this paper is to minimize the total cost of all the nodes that do not obtain a resource. If the total cost is zero, the obtained solution is a k-coloring of the graph; otherwise, the obtained solution is a k -coloring of the graph after removing the nodes that do not obtain a resource. So the resource allocation problem is a generalization of the k-coloring problem.