Would the initial solution affect the "path" the evolutionary/ non-linear algorithm takes, such that an initial solution can potentially be too good?
one would think that the initial solution impacts the local solutions the algorithm still faces, or must still confront. hence, a better initial solution can reduce this count, and from that perspective it can be said that the optimization problem is simplified.
at the same time, it may cause the optimization problem not to look in certain regions, and depending on the non-linearity of the solution space - how "close" local or optimal solutions are to each other - overlook and miss certain optimal solutions.
The answer depends on many other factors, such as:
the type of evolutionary algorithm;
the restart triggers and methods;
the way in which the EA initialises step-lengths and how those step-lengths change during the run;
whether the EA uses elitism (where the best solution is kept in the population);
and many, many more.
A heuristic would quite probably move away if you are close, but I did tell you to not only look at heuristics.
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