Here is a quick summary of the pros and cons of Hexaly (ex LocalSolver), a global optimization solver combining exact and heuristic techniques. Please note that this summary is written by the Hexaly team, as asked by Kuifje in the comment above.
- You will model your problem using nonlinear and set-based mathematical modeling APIs. Then, your math model will be closer to the real-life problem, more concise, and easier to maintain. For an example of what means "set-based modeling" have a look at the TSP model described here. Hexaly also supports external functions in your model (also known as black-box optimization) and offers multiobjective modeling features.
- Having modeled your problem for Hexaly, you will get solutions faster, and your model will be more scalable than MILP solvers, thanks to innovative heuristics. In addition, Hexaly offers (global) dual bounds.
- You must reformulate your problem by using the appropriate Hexaly modeling constructs and following Hexaly modeling best practices.
- Don't give MILP-like models to Hexaly, especially LP or MPS files, in hopes of getting good results.
State-of-the-art MIP solvers remain better than Hexaly when solving pure linear problems and then nearly linear problems (that is, problems that allow good linear approximations). Because the LP codes (simplex, interior-point) used inside these MIP solvers are still stronger than those inside Hexaly (note that we work hard to decrease this gap each year). This performance gap is noticeable for large-scale, ill-posed linear programs. Now, when problems become more combinatorial (in particular: routing, scheduling, packing, assignment) or more nonlinear/nonconvex/nonsmooth in the continuous space, Hexaly is a tool of choice that deserves to be considered for your optimization project.
Additional non-technical strengths of Hexaly that our users mention: the dedicated and reactive support offered by the R&D team to model and solve at best your problems using Hexaly; an aggressive roadmap with two new releases per year with constant performance improvements and new features; a simple, competitive, flexible licensing & pricing.
For examples of problems modeled using Hexaly, have a look at https://www.hexaly.com/docs/last/exampletour/index.html.
Check out this link for some benchmarks against MIP solvers. You can reproduce the results in these benchmarks by registering and asking for free trial licenses on the Hexaly website.
Note that the technical papers related to Hexaly which you can find on the web are largely outdated. We don't publish anymore about Hexaly for several years (mostly for confidentiality reasons).