Objectives and evaluated candidates

Evaluation turns a candidate into an objective vector. HeuristicLib stores the candidate and vector together as an evaluated candidate. Selection, analysis and reporting can then reuse the evaluation.

Single objective

A single objective problem still returns an objective vector with one value. Its objective defines whether smaller or larger values are better.

objective: SingleObjective.Minimize

Use the problem's comparer when selecting the best result. It already understands the objective direction:

var best = state.Population.EvaluatedCandidates
    .MinBy(
        candidate => candidate.ObjectiveVector,
        problem.Objective.TotalOrderComparer)!;

Avoid comparing raw values with < or > in generic code because that silently assumes minimization.

Multiple objectives

A multiobjective vector might contain cost, duration and emissions. One candidate can be better on cost while another is better on emissions, so there may be no single best answer.

A candidate dominates another when it is no worse on every objective and better on at least one. Candidates that are not dominated form a Pareto front. Algorithms such as NSGA-II approximate that front and preserve a diverse set of tradeoffs.

Do not invent a total ordering unless your domain supplies a real preference, such as a weighted utility function. A display order is not automatically an optimization objective.

MultiObjective.Create builds directions for several objectives, and multiobjective directions carry no total order comparer, so TotalOrderComparer is unavailable by design. Use ParetoFront.ExtractFrom to reduce a population to its nondominated members. Multiobjective optimization works through a complete NSGA-II run and shows how to read and use the resulting front.

Evaluated candidates

An evaluated candidate contains:

• the original candidate
• its objective vector

Treat the pair as one result. If a candidate changes, it must be evaluated again. Mutation and crossover should produce a new candidate rather than modifying a candidate already paired with objective values.

Reporting results

For a single objective run, report at least the best candidate, objective value, seed and algorithm configuration. For a multiobjective run, report the nondominated set and keep every objective label and unit visible.

Repeated experiments should summarize distributions across runs. A median and spread are more informative than the best value from one lucky seed.