A study on exponential-size neighborhoods for the bin packing problem with conflicts

We propose an iterated local search based on several classes of local and large neighborhoods for the bin packing problem with conflicts. This problem, which combines the characteristics of both bin packing and vertex coloring, arises in various application contexts such as logistics and transportation, timetabling, and resource allocation for cloud computing. We introduce $O(1)$ evaluation procedures for classical local-search moves, polynomial variants of ejection chains and assignment neighborhoods, an adaptive set covering-based neighborhood, and finally a controlled use of 0-cost moves to further diversify the search. The overall method produces solutions of good quality on the classical benchmark instances and scales very well with an increase of problem size. Extensive computational experiments are conducted to measure the respective contribution of each proposed neighborhood. In particular, the 0-cost moves and the large neighborhood based on set covering contribute very significantly to the search. Several research perspectives are open in relation to possible hybridizations with other state-of-the-art mathematical programming heuristics for this problem.Comment: 26 pages, 8 figure

A Hybrid Heuristic for a Broad Class of Vehicle Routing Problems with Heterogeneous Fleet

We consider a family of Rich Vehicle Routing Problems (RVRP) which have the particularity to combine a heterogeneous fleet with other attributes, such as backhauls, multiple depots, split deliveries, site dependency, open routes, duration limits, and time windows. To efficiently solve these problems, we propose a hybrid metaheuristic which combines an iterated local search with variable neighborhood descent, for solution improvement, and a set partitioning formulation, to exploit the memory of the past search. Moreover, we investigate a class of combined neighborhoods which jointly modify the sequences of visits and perform either heuristic or optimal reassignments of vehicles to routes. To the best of our knowledge, this is the first unified approach for a large class of heterogeneous fleet RVRPs, capable of solving more than 12 problem variants. The efficiency of the algorithm is evaluated on 643 well-known benchmark instances, and 71.70\% of the best known solutions are either retrieved or improved. Moreover, the proposed metaheuristic, which can be considered as a matheuristic, produces high quality solutions with low standard deviation in comparison with previous methods. Finally, we observe that the use of combined neighborhoods does not lead to significant quality gains. Contrary to intuition, the computational effort seems better spent on more intensive route optimization rather than on more intelligent and frequent fleet re-assignments

Algoritmos de Broyden combinados para resolução de sistemas de equações não-lineares

Orientador: Jose Mario MartinezDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientíficaResumo: Não informado.Abstract: Not informed.MestradoMestre em Matemática Aplicad

A Neighborhood Exploration Approach with Multi-start for Extend Generalized Block-modeling

International audienc

An iterated local search heuristic for the heterogeneous fleet vehicle routing problem.

This paper deals with the Heterogeneous Fleet Vehicle Routing Problem (HFVRP). The HFVRP is NP-hard since it is a generalization of the classical Vehicle Routing Problem (VRP), in which clients are served by a heterogeneous fleet of vehicles with distinct capacities and costs. The objective is to design a set of routes in such a way that the sum of the costs is minimized. The proposed algorithm is based on the Iterated Local Search (ILS) metaheuristic which uses a Variable Neighborhood Descent procedure, with a random neighborhood ordering (RVND), in the local search phase. To the best of our knowledge, this is the first ILS approach for the HFVRP. The developed heuristic was tested on well-known benchmark instances involving 20, 50, 75 and 100 customers. These test-problems also include dependent and/or fixed costs according to the vehicle type. The results obtained are quite competitive when compared to other algorithms found in the literature

An ils-based heuristic applied to the car renter salesman problem

The present paper tackles the Car Renter Salesman Problem (CaRS), which is a Traveling Salesman Problem variant. In CaRS, the goal is to travel through a set of cities using rented vehicles at minimum cost. The main aim of the current problem is to establish an optimal route using rented vehicles of different types to each trip. Since CaRS is N P-Hard, we herein present a heuristic approach to tackle it. The approach is based on a Multi-Start Iterated Local Search metaheuristic, where the local search step is based on the Random Variable Neighborhood Descent methodology. An Integer Linear Programming Formulation based on a Quadratic Formulation from literature is also proposed in the current study. Computational results for the proposed heuristic method in euclidean instances outperform current state-of-the-art results. The proposed formulation also has stronger bounds and relaxation when compared to others from literature