An Improvement Heuristic Based on Variable Neighborhood Search for Dynamic Orienteering Problems with Changing Node Values and Changing Budgets

Abstract

AbstractWe study the Dynamic Orienteering Problem (DOP) with changing node values and changing budgets. It is a complex combinatorial optimization problem with many applications, e.g., in tour planning. To solve the DOP, an improvement heuristic based on Variable Neighborhood Search $$\mathrm {VNS}_{\mathrm {DOP}}$$ VNS DOP is proposed. In addition, three methods for handling solutions that became invalid by budget changes are presented. Heuristic $$\mathrm {VNS}_{\mathrm {DOP}}$$ VNS DOP is experimentally compared with two improvement heuristics based on state-of-the-art algorithms for the static Orienteering Problem. In addition, the influence of the three invalid solution handling methods on the algorithms’ optimization behavior is evaluated experimentally. For the experiments, benchmark instances as well as instances generated from existing road networks are used. As a quality measure for the algorithms, their performance over time is used. The results show that both types of dynamic changes, i.e., changes in the node values and changes in the budget, lead to higher volatility in the results for all compared algorithms. However, the latter type has a more negative effect on the performance. Out of the compared algorithms, the proposed heuristic $$\mathrm {VNS}_{\mathrm {DOP}}$$ VNS DOP obtains the best results in most cases on a variety of problem instances with dynamic node values and dynamic budgets, showing that it has a high performance over time in dynamic environments and is able to deal with different levels of dynamic changes. For DOPs with changing budgets, the invalid solution handling method that repairs solutions by fixing the violation of the budget constraint as fast as possible performs best for the considered algorithms.