A simple and effective algorithm for the maximum happy vertices problem

In a recent paper, a solution approach to the Maximum Happy Vertices Problem has been proposed. The approach is based on a constructive heuristic improved by a matheuristic local search phase. We propose a new procedure able to outperform the previous solution algorithm both in terms of solution quality and computational time. Our approach is based on simple ingredients implying as starting solution gen- erator an approximation algorithm and as an improving phase a new matheuristic local search. The procedure is then extended to a multi-start configuration, able to further improve the solution quality at the cost of an acceptable increase in compu- tational time

Order Scheduling with Tardiness Objective: Improved Approximate Solutions

The problem addressed in this paper belongs to the topic of order scheduling, in which customer orders --composed of different individual jobs-- are scheduled so the objective sought refers to the completion times of the complete orders. Despite the practical and theoretical relevance of this problem, the literature on order scheduling is not very abundant as compared to job scheduling. However, there are several contributions with the objectives of minimising the weighted sum of completion times of the orders, the number of late orders, or the total tardiness of the orders. In this paper, we focus in the last objective, which is known to be NP-hard and for which some constructive heuristics have been proposed. We intend to improve this state-of-the-art regarding approximate solutions by proposing two different methods: Whenever extremely fast (negligible time) solutions are required, we propose a new constructive heuristic that incorporates a look-ahead mechanism to estimate the objective function at the time that the solution is being built. For the scenarios where longer decision intervals are allowed, we propose a novel matheuristic strategy to provide extremely good solutions. The extensive computational experience carried out shows that the two proposals are the most efficient for the indicated scenarios

A single machine scheduling problem with two-dimensional vector packing constraints

International audienceIn this paper we consider a scheduling problem where jobs consume a perishable resource stored in vials. It leads to a new scheduling problem, with two-dimensional jobs, one dimension for the duration and one dimension for the consumption. Jobs have to be finished before a given due date, and the objective is to schedule the jobs on a single machine so that the maximum lateness does not exceed a given treshhold and the number of vials required for processing all the jobs is minimized. We propose a two-step approach embedding a Recovering Beam Search algorithm to get a good-quality initial solution reachable in short time and a more time consuming matheuristic algorithm. Computational experiments are performed on the benchmark instances available for the two-constraint bin packing problem integrated with additional due dates to take into account the maximum lateness constraints. The computational results show very good performances of the proposed approach that remains effective also on the original two-constraint bin packing instances without due dates where 7 new bounds are obtained