What is the best way to select a solver for your OR model?

Em termos de solvers, há diversos específicos para programa??o linear (LP), programa??o inteira (IP), programa??o n?o linear (PNL), programa??o inteira mista (MIP), etc. Uma decis?o é um solver comercial x open source. Além de conhecer limita??es de licen?a de cada, também há diferen?as que podem ser significativas em performance, justificando eventuais custos.

Selecting a solver for your Operations Research (OR) model depends on the specific characteristics of your problem. Linear Programming (LP) problems are well-suited for simplex or interior-point methods, while Mixed-Integer Programming (MIP) problems may benefit from branch-and-bound or branch-and-cut methods. For large-scale problems, heuristic or metaheuristic solvers like genetic algorithms or simulated annealing can be effective. Constraint Programming (CP) solvers are suitable for problems with complex logical constraints. Consider the size, structure, and nature of your OR model, and choose a solver that aligns with these factors. Experimentation and benchmarking different solvers can help identify the most efficient one.

A year ago, a student approached me because she wanted to compare different solvers for the thesis. I asked her a very simple question: How can she level the playing field and compare the solvers and not the respective models? See, a MIP model looks very different from a SAT model or a CP model or an InsideOpt Seeker model. Just as a MIP model is writtten to give the solver traction by allowing it to derive meaningfully accurate bounds on the objective, a model for a primal solver like Seeker needs to provide local gradients that lead to improving solutions. I have no good answer for this, but the issue of solver-specific modeling should not be ignored by assuming that the entire OR world consisted only of MIP solvers

Evaluate the efficacy of the solver by analyzing its performance on benchmark problems or those closely mirroring your specific scenario. Explore published performance benchmarks or case studies, considering key factors such as the precision of solutions, convergence speed, and overall reliability.

A good start are the famous, but sadly discontinued, Mittelman benchmarks. One can also try out several solvers oneself. Many solvers are free. The commercial ones offer free licenses too (albeit with limitations to model size) or free evaluation licenses (these are only valid for a specified short time). If one has some connection with academia (e.g. being a student or faculty member), it is also possible to obtain an academic license for the commericial solvers. It cannot be used for commercial purposes though,

To select the best solver for your OR model, consider the following: Benchmarking: Test different solvers on your specific problem, varying sizes and complexities. Compare their solution times, optimality gaps, and feasibility checking capabilities. Problem-specific Metrics: Identify metrics relevant to your problem, such as solution quality, running time, and memory usage. Evaluate how well each solver performs against these metrics. Solver Documentation: Examine documentation for each solver to understand its strengths, limitations, and recommended use cases. Some solvers may be more efficient for specific types of problems.

The choice of solver for OR problems depends on the characteristics of the problem, e.g., the number of variables, constraints, and whether it's an LP or NLP. Each solver has its own advantages and disadvantages. We can even use MS Excel effectively utilizing its Solver Add-in to solve linear, nonlinear, and even non-smooth problems. For professionals and students having no programming knowledge or coding skills, I recommend to use Excel solver, LINGO solver, etc. for which no programming or coding knowledge required; and they are affordable and easily accessible. Others can go for Gurobi, CPLEX (they’re not free), Pyomo (requires knowledge of python), etc. The choice ultimately hinges on specific needs, expertise, and budget constraints.

Certainly, taking into account the features of a solver is a pivotal consideration in the process of choosing the most suitable one for an Operations Research (OR) model. These encompass the distinctive attributes of your problem, the nature of the optimization or simulation model utilized, the magnitude of your problem, and the software and computational resources at your disposal. Beyond these considerations, the features provided by the solver assume a critical role in ensuring a well-informed decision.

The choice of the best solver is usually made according to the benchmark on different volumes of variables. It is important to understand which algorithms are used, which settings and solver parameters are selected to launch a solution search. The effectiveness of the search for a solution may depend on the parameters of the strategy, the presolve, the methods of branching, relaxation. Therefore, it is important to try different modes and settings of solvers to compile a complete table of bermark. By the way, you can also solve an optimization problem to find the best parameters, as well as to select a solver.

Choosing the optimal solver for an Operations Research (OR) model involves considering several factors, such as the nature of your particular problem, the type of optimization or simulation model in use, the dimensions of your problem, and the software and computational resources at your disposal. Key aspects to factor in when selecting a suitable solver include its scalability, integration capabilities, and overall performance.