Biobjective combinatorial optimization (BOCO) deals with mathematical programming models where two competing objectives have to be minimised subject to constraints. A number of real world applications may be cast in this setting, where the objective and constraint functions are linear and the variables are binary. In a BOCO problem usually there is no solution that simultaneously minimise both objectives, so it is necessary to describe a set of Pareto optimal solutions, or solutions such that it is not possible to improve one objective without worsening the other. In this work we review the exact, heuristic and approximated methods developed to date for the construction of the Pareto optimal set in BOCO problems. Emphasis is given to exact and to approximate methods where a subset of the exact set of Pareto optimal solutions is given. We apply all the analysed methods to a hard BOCO problem: the Traveling Salesman Problem with Profits (TSPP). Specific approaches for the TSPP on g16raphs with special metrics and/or with time windows are also discussed. Finally, the approaches studied are suggested as a methodology to face a case study connecting Medicine and Computer Science.
Biobjective combinatorial optimization and the TSP with profits
ZANGHIRATI, Gaetano;
2012
Abstract
Biobjective combinatorial optimization (BOCO) deals with mathematical programming models where two competing objectives have to be minimised subject to constraints. A number of real world applications may be cast in this setting, where the objective and constraint functions are linear and the variables are binary. In a BOCO problem usually there is no solution that simultaneously minimise both objectives, so it is necessary to describe a set of Pareto optimal solutions, or solutions such that it is not possible to improve one objective without worsening the other. In this work we review the exact, heuristic and approximated methods developed to date for the construction of the Pareto optimal set in BOCO problems. Emphasis is given to exact and to approximate methods where a subset of the exact set of Pareto optimal solutions is given. We apply all the analysed methods to a hard BOCO problem: the Traveling Salesman Problem with Profits (TSPP). Specific approaches for the TSPP on g16raphs with special metrics and/or with time windows are also discussed. Finally, the approaches studied are suggested as a methodology to face a case study connecting Medicine and Computer Science.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
