Search Results (2)

Machine scheduling is a hard combinatorial problem having many manifestations in real life. Due to the schedule followed, the possibility of installations of machines operating sub-optimally is high. In this work, we examine the problem of a single machine with time-dependent capacity that performs jobs of deterministic durations, while for each job, its due time is known in advance. The objective is to minimize the aggregated tardiness in all tasks. The problem was motivated by the need to schedule charging times of electric vehicles effectively. We formulate an integer programming model that clearly describes the problem and a constraint programming model capable of effectively solving it. Due to the usage of interval variables, global constraints, a powerful constraint programming solver, and a heuristic we have identified, which we call the “due times rule”, the constraint programming model can reach excellent solutions. Furthermore, we employ a hybrid approach that exploits three local search improvement procedures in a schema where the constraint programming part of the solver plays a central role. These improvement procedures exhaustively enumerate portions of the search space by exchanging consecutive jobs with a single job of the same duration, moving cost-incurring jobs to earlier times in a consecutive sequence of jobs or even exploiting periods where capacity is not fully utilized to rearrange jobs. On the other hand, subproblems are given to the exact constraint programming solver, allowing freedom of movement only to certain parts of the schedule, either in vertical ribbons of the time axis or in groups of consecutive sequences of jobs. Experiments on publicly available data show that our approach is highly competitive and achieves the new best results in many problem instances. Full article

This paper addresses the problem of scheduling a set of jobs on a machine with time-varying capacity, with the goal of minimizing the total tardiness objective function. This problem arose in the context scheduling the charging times of a fleet of electric vehicles and it is NP-hard. Recent work proposed an efficient memetic algorithm for solving the problem, combining a genetic algorithm and a local search method. The local search procedure is based on swapping consecutive jobs on a C-path, defined as a sequence of consecutive jobs in a schedule. Building on it, this paper develops new memetic algorithms that stem from new local search procedures also proposed in this paper. The local search methods integrate several mechanisms to make them more effective, including a new condition for swapping pairs of jobs, a hill climbing approach, a procedure that operates on several C-paths and a method that interchanges jobs between different C-paths. As a result, the new local search methods enable the memetic algorithms to reach higher-quality solutions. Experimental results show significant improvements over existing approaches. Full article