Combinatorial applications such as configuration, transportation and resource allocation often operate under highly dynamic and unpredictable environments. In this regard, one of the main challenges is to maintain a consistent solution anytime constraints are (dynamically) added. While many solvers have been developed to tackle these applications, they often work under idealized assumptions of environmental stability. In order to address limitation, we propose a methodology, relying on nature-inspired techniques, for solving constraint problems when constraints are added dynamically. The choice for nature-inspired techniques is motivated by the fact that these are iterative algorithms, capable of maintaining a set of promising solutions, at each iteration. Our methodology takes advantage of these two properties, as follows. We first solve the initial constraint problem and save the final state (and the related population) after obtaining a consistent solution. This saved context will then be used as a resume point for finding, in an incremental manner, new solutions to subsequent variants of the problem, anytime new constraints are added. More precisely, once a solution is found, we resume from the current state to search for a new one (if the old solution is no longer feasible), when new constraints are added. This can be seen as an optimization problem where we look for a new feasible solution satisfying old and new constraints, while minimizing the differences with the solution of the previous problem, in sequence. This latter objective ensures to find the least disruptive solution, as this is very important in many applications including scheduling, planning and timetabling. Following on our proposed methodology, we have developed the dynamic variant of several nature-inspired techniques to tackle dynamic constraint problems. Constraint problems are represented using the well-known constraint satisfaction problem (CSP) paradigm. Dealing with constraint additions in a dynamic environment can then be expressed as a series of static CSPs, each resulting from a change in the previous one by adding new constraints. This sequence of CSPs is called the dynamic CSP (DCSP). To assess the performance of our proposed methodology, we conducted several experiments on randomly generated DCSP instances, following the RB model. The results of the experiments are reported and discussed. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
