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The Multiobjective Average Network Flow Problem: Formulations, Algorithms, Heuristics, And Complexity, Jeremy D. Jordan
The Multiobjective Average Network Flow Problem: Formulations, Algorithms, Heuristics, And Complexity, Jeremy D. Jordan
Theses and Dissertations
Integrating value focused thinking with the shortest path problem results in a unique formulation called the multiobjective average shortest path problem. We prove this is NP-complete for general graphs. For directed acyclic graphs, an efficient algorithm and even faster heuristic are proposed. While the worst case error of the heuristic is proven unbounded, its average performance on random graphs is within 3% of the optimal solution. Additionally, a special case of the more general biobjective average shortest path problem is given, allowing tradeoffs between decreases in arc set cardinality and increases in multiobjective value; the algorithm to solve the average …