When it comes to speed, What’sBest! outperforms stand alone solvers, much less any competing spreadsheet solver. Its commercial quality Linear Programming solver combines with superior Integer Programming technology to set a new standard in optimization speed.
While competing spreadsheet solvers boast of “industrial strength” versions handling LP models of up to 2,000 variables, the largest version of What’sBest! has no capacity limit. What’sBest! users routinely solve models of well over 100,000 variables.
Day in and day out, thousands of companies around the world rely on What’sBest! to provide critical solutions to their toughest optimization problems. What’sBest! is able to solve complex and numerically difficult problems that competing products simply cannot.
What’sBest! is available with three state of the art solvers for linear models.
Primal and Dual Simplex Solvers
The base version includes the Primal and Dual Simplex solvers, which incorporate numerous enhancements for maximum speed and robustness. Pricing options, for instance, include partial pricing and Devex. The solver dynamically chooses the best pricing option based upon problem characteristics.
The optional Barrier solver provides an alternative means of solving linear models. The Barrier option utilizes a barrier or interior point method to solve linear models. Unlike the Simplex solvers that move along the exterior of the feasible region, the Barrier solver moves through the interior space to find the optimum. Depending upon the size and structure of a particular model, the Barrier solver may be significantly faster than the Simplex solvers and can provide exceptional speed on large linear models — particularly on sparse models with more than 5,000 constraints or highly degenerate models.
For models with general and binary integer restrictions, What’sBest! includes an integer solver that works in conjunction with the linear and nonlinear solvers. For linear models, the integer solver does extensive preprocessing and adds constraint “cuts” of several different varieties to greatly improve solution times on large classes of integer models.
What’sBest! includes a number of ways to find locally or globally optimal solutions to nonlinear models.
General Nonlinear Solver
For nonlinear programming models, the primary underlying technique used by What’sBest’s optional nonlinear solver is based upon a Generalized Reduction Gradient (GRG) algorithm. However, to help get a good feasible solution quickly, What’sBest! also incorporates Successive Linear Programming (SLP). The nonlinear solver takes advantage of sparsity for improved speed and more efficient memory usage. The Nonlinear license option is required to solve nonlinear models.
Local search solvers are generally designed to search only until they have identified a local optimum. If the model is non-convex, other local optima may exist that yield significantly better solutions. Rather than stopping after the first local optimum is found, the global solver will search until the global optimum is confirmed. The global solver converts the original non-convex, nonlinear problem into several convex, linear subproblems. Then, it uses the branch-and-bound technique to exhaustively search over these subproblems for the global solution. The nonlinear and global license options are required to utilize the global optmization capabilities.
When limited time makes searching for the global optimum prohibitive, the multistart solver can be a powerful tool for finding good solutions more quickly. This intelligently generates a set of candidate starting points in the solution space. Then, the general nonlinear solver intelligently selects a subset of these to initialize a series of local optimizations. For non-convex nonlinear models, the quality of the solution returned by the multistart solver will be superior to that of the general nonlinear solver. The nonlinear and global license options are required to utilize the multistart capabilities.
In addition to solving linear models, the barrier option in What’sBest! can automatically detect and solve models in which the objective function includes quadratic terms. By taking advantage of the quadratic structure, What’sBest! can solve these models much more quickly than using the general nonlinear solver. What’sBest! can even handle quadratic models with binary and general integer restrictions. These quadratic capabilities make What’sBest! suitable for applications such as portfolio optimization problems, constrained regression problems, and certain classes of difficult logistics problems (e.g., layout problems, fixed-charge-network problems with quadratic objective). The quadratic solver is included in the Barrier license option.
The Conic option for What’sBest! includes a Conic solver to efficiently solve Second Order Cone Problems (SOCP). By expressing certain nonlinear models as SOCPs, the Conic solver can be used to solve the model substantially faster than the general nonlinear solver. The Barrier and Conic options are required to utilize the Conic solver.
Stochastic Programming Solver
Incorporate risk into multi-stage optimization models, maximize expected profit, and summarize results in histograms showing the distribution of possible profit, etc. This new option allows modeling and optimization for models with uncertain elements via multistage stochastic linear, nonlinear and integer stochastic programming (SP). Benders decomposition is used for solving large linear SP models. Deterministic equivalent method is used for solving nonlinear and integer SP models. Support is available for over 20 distribution types (discrete or continuous). The Stochastic Programming solver is included in the Stochastic Programming option.
Preprocessing routines are included in all solvers. The linear and nonlinear solver include scaling and model reduction techniques. Scaling procedures can improve speed and robustness on numerically difficult models. Model reduction techniques cn often make models solve faster by analyzing the original formulation and mathematically condensing it into a smaller problem. The integer solver includes extensive preprocessing and cut generatin routines.
What’sBest! is designed, so the process of solving the model requires as little input from the user as possible. When the Solve command is initiated, What’sBest! analyzes the problem and, when possible, reduces the problem and even substitutes out variables. Based upon the models structure, What’sBest! automatically selects the appropriate solver and intelligently adjusts internal parameters.
What’sBest! linearization capabilities can dramatically improve performance on certain nonlinear models. The feature can automatically convert many nonsmooth Excel functions (e.g., IF, MAX, MIN and ABS) as well as the product of a continuous and binary variable into a series of linear, mathematically equivalent expressions. Many nonsmooth models may be entirely linearized. This allows the linear solver to quickly find a global solution to what would have otherwise been an intractable problem.
What’sBest! handles the details of the solution process, so you can focus on modeling. When the Solve command is initiated, What’sBest! analyzes the problem and, when possible, reduces the problem and even substitutes out variables. With What’sBest!, you never have to specify whether to use the linear or nonlinear solver. Based upon the model’s structure, What’sBest! automatically selects the appropriate solver and intelligently adjusts internal parameters.