Partitioning a set

Partitioning a Set

A Genetic Algorithm for the Set Partitioning

In this paper we present a genetic algorithm-based heuristic for solving the set partitioning problem. The set partitioning problem is an important combinatorial optimisation problem used by many airlines as a mathematical model for ight crew scheduling. We develop a steady-state genetic algorithm in conjunction with a specialised heuristic feasibility operator for solving the set partitioning ...

A Dual Heuristic for Set Partitioning

Dual heuristics have been successfully used to generate bounds in the context of branch and bound algorithms. In the current work, we present a new dual heuristic for the set partitioning problem. Our approach provides a lower bound at each node of the branch and bound tree by calculating approximate solutions to the dual of the linear relaxation of the set partitioning problem. The calculation...

A Set Partitioning Approach to Shunting

The Vehicle Positioning Problem (VPP), also know as the shunting problem, is a classical combinatorial optimization problem in public transport planning. It has been investigated using several models and approaches, which work well for small instances, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation approach for the VPP and f...

Set Partitioning via Inclusion-Exclusion

Given a set N with n elements and a family F of subsets, we show how to partition N into k such subsets in 2nnO(1) time. We also consider variations of this problem where the subsets may overlap or are weighted, and we solve the decision, counting, summation, and optimisation versions of these problems. Our algorithms are based on the principle of inclusion–exclusion and the zeta transform. In ...