What should I use for multi-objective ranking?

It depends on what “ranking” means in your case, but the usual choices for multi-objective ranking are:

Best general-purpose options

1. Pareto ranking / non-dominated sorting

   • Good when you want to preserve tradeoffs without forcing weights.
   • Common in evolutionary optimization (e.g. NSGA-II).
   • Produces “fronts” of equally good tradeoff solutions rather than one total order.

2. Weighted scoring / utility function

   • Good when you have clear preference weights for each objective.
   • Simple and fast.
   • Best if objectives are on comparable scales or can be normalized well.
   • Example: score = 0.5*quality + 0.3*relevance - 0.2*latency

3. Lexicographic ranking

   • Good when one objective is clearly more important than the others.
   • Sort by primary objective first, then break ties with secondary objectives.
   • Useful when priorities are strict.

4. TOPSIS / similar MCDA methods

   • Good when you want a compromise solution closest to an “ideal” point.
   • Useful for decision-making with several objectives.
   • Requires normalization and usually weights.

If you need a single ranked list

• Use weighted sum if you can define weights.
• Use Pareto front + tie-breaker if you want to avoid arbitrary weights.
• Use lexicographic if objectives have priority order.

Rule of thumb

• No clear weights? Use Pareto ranking
• Clear tradeoff weights? Use weighted scoring
• Hard priority order? Use lexicographic ranking

If you want, I can recommend one based on your exact setting, e.g.:

• search/retrieval ranking
• recommender systems
• product/feature selection
• optimization / evolutionary algorithms
  and I can suggest an actual implementation strategy.