Multiple objectives

To consider multiple objectives in an AMPL model, either natively supported by the solver, or emulated, use solver option obj:multi. Otherwise, only the 1st objective is considered (or any objective specified by obj:no.)

See the Multi-objective AMPL Colab notebooks for examples.

minimize total_cost {s in STORE}:
   sum {j in FOOD} cost[s,j] * Buy[j];

minimize total_number:  sum {j in FOOD} Buy[j];

Blended objectives

By default, all objectives are blended together (summed up with the corresponding signs.) Suffixes .objweight can be used to change the individual weights and objective senses, according to the option obj:multi:weight.

Lexicographical objectives

To apply hierarchical optimization, use suffix .objpriority, as described in the obj:multi option description.

maximize ReverseSeniority {e in 1..2, i in I: E[i]==e}:
  sum {t in V[i]: Pr[i, t]==0}
    S[i] * x[i, t]
  suffix objpriority (2-e)*S_range + 1 + S[i] - min {j in I} S[j];

Suffixes .objabstol and .objreltol allow for objective degradation. However their exact meaning can vary for a solver’s native multi-objective mode (obj:multi=1), in particular for LPs. Consult the solver documentation.