Do these 3 things before closing this tab:
1Repair Windows errors before they cause bigger problems2Scan for outdated or missing drivers - takes under a minute3Clear out junk files and repair common Windows errorsNo. An optimizer’s reported answer may be one of several solutions with the same best objective value. The answer it prints does not, by itself, prove that the optimum is unique. It is also important to distinguish a truly equal optimum from a feasible answer that is merely close in value.
What does “the only one” mean?
There are three different things to keep apart:
- The optimal solutions: all feasible decisions that attain the best objective value for the model.
- The returned solution: the particular answer the solver reports.
- Near-optimal solutions: feasible answers whose objective values are close to the best value but are not necessarily equal to it.
Gurobi’s objective documentation notes that “Most optimization problems have multiple optimal solutions, plus many solutions whose objectives are within a small gap from the optimal value.” Gurobi, Objectives
In a linear program, two different points can have the same best value; in some cases, every point along the line segment between them is optimal. A solver returning one point does not show that the others do not exist. Gurobi, Instability and the Geometry of Optimization Problems
Why can different answers be equally good?
The solver optimizes the objective and constraints you gave it. If the objective minimizes cost, but the model does not encode fairness, robustness, or convenience, the solver has no stated reason to favor one equally low-cost answer on those grounds.
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For example, a staffing model’s objective might depend on how many people are scheduled without distinguishing between interchangeable workers. Different assignments of workers can then have the same objective value. Whether one assignment is preferable in practice depends on criteria that the model may not include. Gurobi, Instability and the Geometry of Optimization Problems
Does “good” mean proven optimal?
Not always. A solver’s result must be interpreted in light of its stopping conditions and numerical tolerances. Some solves may stop when an accepted optimality gap is met rather than establishing exact mathematical equality. Floating-point arithmetic also affects how solvers assess feasibility and optimality. OR-Tools’ LP guidance discusses both numerical tolerances and the possibility of non-unique solutions. Google for Developers, Advanced LP Solving
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Displayed objective values can mislead in either direction: two values that look identical after rounding may differ beyond the displayed digits, while answers accepted within a tolerance are not necessarily mathematically equal. Check the solver’s status, objective and bound information, and configured tolerances before describing an answer as proven optimal or unique.
How can you look for alternatives?
The right method depends on the model class and on what “alternative” means for your use case.
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One solution from a standard solve
A standard solve may return just one optimum. Gurobi says it returns a single optimal solution for continuous models; a single reported answer is not a uniqueness test. Gurobi, Objectives
Solution pools for mixed-integer models
For a mixed-integer model, a configured solution pool can seek or retain additional discrete solutions. Pool settings affect whether the goal is variety or the best-ranked alternatives, and a systematic search mode can seek the requested number of best solutions if the search completes. A default pool or an incidental set of solutions from a normal run should not be treated as an exhaustive catalogue. Gurobi, Solution Pool
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This is not a universal “show every optimum” switch. Gurobi’s help guidance specifically says its MIP solution pool does not provide multiple optimal LP solutions. Gurobi Help Center, How do I find additional solutions to a model?
Analysis of alternative optima in a linear program
If you need to know whether a continuous linear program has other points on its optimal face, use an LP-appropriate analysis rather than assuming a mixed-integer solution pool applies. The shape of the feasible region and objective can allow multiple optimal points even when the solver reports only one. Gurobi, Instability and the Geometry of Optimization Problems
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How should you choose among tied answers?
If several answers satisfy the primary objective equally well, define the additional preference that matters to the decision. A secondary objective can express goals such as fairness or robustness, while a hierarchical or lexicographic objective can prioritize the original goal and then optimize a lower-priority one.
When using hierarchical objectives, be explicit about how much degradation in a higher-priority objective is permitted while optimizing lower-priority objectives. The objective hierarchy and its tolerances determine what “preserve the primary goal” means in the model. Gurobi, Multiple Objectives
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