Optimizing global connectivity in spatial networks, either through rewiring or adding edges, can increase the flow of information and increase the resilience of the network to failures. Yet, rewiring is not feasible for systems with fixed edges and optimizing global connectivity may not result in optimal local connectivity in systems where that is wanted. We describe the local network connectivity optimization problem, where costly edges are added to a systems with an established and fixed edge network to increase connectivity to a specific location, such as in transportation and telecommunication systems. Solutions to this problem maximize the number of nodes within a given distance to a focal node in the network while they minimize the number and length of additional connections. We compare several heuristics applied to random networks, including two novel planar random networks that are useful for spatial network simulation research, a real-world transportation case study, and a set of real-world social network data. Across network types, significant variation between nodal characteristics and the optimal connections was observed. The characteristics along with the computational costs of the search for optimal solutions highlights the need of prescribing effective heuristics. We offer a novel formulation of the genetic algorithm, which outperforms existing techniques. We describe how this heuristic can be applied to other combinatorial and dynamic problems.