Bi-objective orienteering for personal activity scheduling.

We present a rich, bi-objective generalization of the orienteering problem.A modular bi-objective large neighborhood search metaheuristic is proposed.We conduct an extensive computational study on real-life-inspired test instances.Near-optimal Pareto sets are rapidly found on instances solvable to optimality.Solution quality, computation time, and reliability scale well to larger instances. We propose and solve a rich, bi-objective extension of the orienteering problem with time windows (OPTW) to model a combined routing and scheduling problem. Our research is motivated by the problem faced by mobile freelancers who have to integrate irregular appointments and tasks into their daily routines. Those people have a number of tasks which they need to perform at various locations (e.g.meetings with different clients), subject to varying time constraints (e.g.opening hours), and with different levels of importance or urgency (e.g.submitting a deliverable versus cleaning the home office). Furthermore, sets of related tasks may be subject to precedence relations and time dependencies. We explicitly consider the trade-off between planning more tasks and enjoying more free time by means of a bi-objective model. The extension of the OPTW and the bi-objective formulation result in the Personal Planning Problem (PPP). We present a mathematical formulation of the PPP and a metaheuristic based on Large Neighborhood Search (LNS) is developed to generate a set of non-dominated solutions to the problem. Solution quality is analyzed on real-world-inspired test instances. Exact reference sets based on a linear single-commodity flow model are used as benchmarks. Extensive computational experiments show that the proposed metaheuristic generates near-optimal solution sets and scales well to larger instances.