Mesh network topologies are becoming increasingly popular in battery-powered wireless sensor networks, primarily because of the extension of network range. However, multihop mesh networks suffer from higher energy costs, and the routing strategy employed directly affects the lifetime of nodes with limited energy resources. Hence when planning routes there are trade-offs to be considered between individual and system-wide battery lifetimes. We present a multiobjective routing optimisation approach using hybrid evolutionary algorithms to approximate the optimal trade-off between the minimum lifetime and the average lifetime of nodes in the network. In order to accomplish this combinatorial optimisation rapidly, our approach prunes the search space using k -shortest path pruning and a graph reduction method that finds candidate routes promoting long minimum lifetimes. When arbitrarily many routes from a node to the base station are permitted, optimal routes may be found as the solution to a well-known linear program. We present an evolutionary algorithm that finds good routes when each node is allowed only a small number of paths to the base station. On a real network deployed in the Victoria & Albert Museum, London, these solutions, using only three paths per node, are able to achieve minimum lifetimes of over 99% of the optimum linear program solution’s time to first sensor battery failure.

Multi-objective optimisation yields an estimated Pareto front of mutually non- dominating solutions, but with more than three objectives, understanding the relationships between solutions is challenging. Natural solutions to use as landmarks are those lying near to the edges of the mutually non-dominating set. We propose four definitions of edge points for many-objective mutually non-dominating sets and examine the relations between them. The first defines edge points to be those that extend the range of the attainment surface. This is shown to be equivalent to finding points which are not dominated on projection onto subsets of the objectives. If the objectives are to be minimised, a further definition considers points which are not dominated under maximisation when projected onto objective subsets. A final definition looks for edges via alternative projections of the set. We examine the relations between these definitions and their efficacy in many dimensions for synthetic concave- and convex-shaped sets, and on solutions to a prototypical many-objective optimisation problem, showing how they can reveal information about the structure of the estimated Pareto front. We show that the “controlling dominance area of solutions” modification of the dominance relation can be effectively used to locate edges and interior points of high-dimensional mutually non-dominating sets.