Modern heuristic techniques for combinatorial problems

TLDR: In this paper, the Lagrangian relaxation and dual ascent tree search were used to solve the graph bisection problem and the graph partition problem, and the traveling salesman problem scheduling problems.

Abstract: Part 1 Introduction: combinatorial problems local and global optima heuristics. Part 2 Simulated annealing: the basic method enhancements and modifications applications conclusions. Part 3 Tabu search: the tabu framework broader aspects of intensification and diversification tabu search applications connections and conclusions. Part 4 Genetic algorithms: basic concepts a simple example extensions and modifications applications conclusions. Part 5 Artificial neural networks: neural networks combinatorial optimization problems the graph bisection problem the graph partition problem the travelling salesman problem scheduling problems deformable templates inequality constraints, the Knapsack problem summary. Part 6 Lagrangian relaxation: overview basic methodology Lagrangian heuristics and problem reduction determination of Lagrange multipliers dual ascent tree search applications conclusions. Part 7 Evaluation of heuristic performance: analytical methods empirical testing statistical inference conclusions.