This means that the Solver has found solutions that satisfy the constraints, but it has been unable to further improve the objective, even though the tests for optimality (“Solver found a solution”) and convergence (“Solver converged to the current solution”) have not yet been satisfied. The exact meaning depends on whether you are solving a smooth nonlinear problem with the GRG Solver, a global optimization problem with the Interval Global Solver, or a non-smooth problem with the Evolutionary Solver.
When the GRG Solver is being used, this message occurs very rarely. It means that the model is degenerate and the Solver is probably cycling. One possibility worth checking is that some of your constraints are redundant, and should be removed. For more information, see the discussion of “GRG Solver Stopping Conditions” below.
When the Interval Global Solver is being used, this message is more common. It means that the Solver has not found an “improved global solution” (a feasible solution with an objective value better than the currently best known solution), in the amount of time specified for the Max Time without Improvement option Task Pane Engine tab. The reported solution is the best one found so far, but the search space has not been fully explored. For more information, see the discussion of “Interval Global Solver Stopping Conditions” below. If you receive this message, and you are willing to spend more solution time to have a better chance of “proving” global optimality, increase the value of the Max Time without Improvement option.
When the Evolutionary Solver is being used, this message is much more common. It means that the Solver has been unable to find a new, better member of the population whose “fitness” represents a relative (percentage) improvement over the current best member’s fitness of more than the Tolerance value on the Limit Options dialog tab, in the amount of time specified by the Max Time without Improvement option in the same dialog. Since the Evolutionary Solver has no way of testing for optimality, it will normally stop with either “Solver converged to the current solution” or “Solver cannot improve the current solution” if you let it run for long enough. If you believe that this message is appearing prematurely, you can either make the Tolerance value smaller (or even zero) or increase the amount of time allowed by the Max Time without Improvement option. For more information, see the discussion of “Evolutionary Solver Stopping Conditions” below.