Future paths for integer programming and links to artificial intelligence
Computers and Operations Research - Special issue: Applications of integer programming
Sparsest cuts and bottlenecks in graphs
Discrete Applied Mathematics - Computational combinatiorics
Cyclic transfer algorithms for multivehicle routing and scheduling problems
Operations Research
Ejection chains, reference structures and alternating path methods for traveling salesman problems
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
The node capacitated graph partitioning problem: a computational study
Mathematical Programming: Series A and B - Special issue on computational integer programming
Tabu Search
Packing and partitioning orbitopes
Mathematical Programming: Series A and B
Geometry, flows, and graph-partitioning algorithms
Communications of the ACM
Lower bounds for the partitioning of graphs
IBM Journal of Research and Development
Linear and quadratic programming approaches for the general graph partitioning problem
Journal of Global Optimization
Genetic approaches for graph partitioning: a survey
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Engineering multilevel graph partitioning algorithms
ESA'11 Proceedings of the 19th European conference on Algorithms
Engineering graph partitioning algorithms
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
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We consider the problem of partitioning a region into connected areas assigned to administrative officers. The employee in charge of an area takes care of all the activities which involve the towns of that area. An activity requires the effort of a subset of towns, coordinated by the employee in charge. This implies from the employee a fixed basic workload, plus a variable workload proportional to the number of towns involved. If the subset of towns associated to an activity is divided among several areas, the fixed workload is required from each of the corresponding employees, thus leading to a duplication. The problem requires to minimize duplications while balancing the workload among the employees. The Homogeneous Areas Problem (HAP) models this situation as the search for a suitable balanced partition of a vertex-weighted and subset-weighted undirected graph into connected components. We propose a multi-commodity flow formulation, reduction procedures, a Tabu Search and a Very Large Scale Neighbourhood Search algorithm for the problem. We provide computational results for random instances and for two real-world instances, i. e. the provinces of Milan and Monza.