Re-Initialising Solutions in a Random Restart Local Search for the Probabilistic Orienteering Problem

The Probabilistic Orienteering Problem is an optimization problem where a set of customers, each with an associated prize and probability of requiring a service, a time budget and travel times between customers are given. The objective is to select the subset of customers that maximize the expected total prize collected in the given time (taking into account of the total travel time spent visiting them). Random Restart Local Search is a heuristic method widely used to solve combinatorial optimization problems. In particular, it is used in conjunction with local search procedures to escape from local optima. The method works by restarting the optimization search once no further improvement is possible by the embedded local search component. Each restart is associated with a new initial solution for the optimization, and selecting such restart initial solutions play an important role in the success of the overall algorithm. In this work we propose a method to effectively selecting such solutions, and we present an empirical study to validate our ideas.