Ordinal optimization through multi-objective reformulation

We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. review different optimality concepts for ordinal discuss their similarities differences. then focus on two prevalent are shown be equivalent. Our main lies investigation a bijective linear transformation transforms associated standard multi-objective binary coefficients. Since this preserves all properties underlying problem, problem-specific solution methods remain applicable. A prominent example is dynamic programming Bellman’s principle optimality, can applied, e.g., shortest path knapsack problems. investigate interrelation between scalarization techniques based hypervolume indicator when applied transformed respectively. Furthermore, we extend our results combine real-valued functions.