Some Remarks on Trade-off Analysis in Multi-objective Programming

In multi-objective programming, the trade-off analysis is very important because it reflects decision makers’ value judgment. In many practical applications, people usually take a scalarization of linearly weighted sum of vector-valued objective function without paying much attention to the trade-off analysis. However, the linearly weighted sum causes several difficulties in the trade-off analysis, eg. "duality gap" for nonconvex problems, and that the weight can not necessarily reflect decision makers’ value faithfully.