The Large-Scale SQP Solver Engine solves linear, integer, quadratic, conic, smooth nonlinear, and even non-smooth optimisation problems that are far larger than what the Premium Solver Platform can handle as there are no fixed limits on problem size. It plugs into the Premium Solver Platform and takes special advantage of its new Polymorphic Spreadsheet Interpreter. Version 8.0 solves non-smooth problems using an integrated hybrid Evolutionary Solver and solves global optimisation problems using either the Evolutionary Solver or the 'multistart' methods. Furthermore, it supports integer variables and 'alldifferent' constraints.
Huge capacity and outstanding speed
The Large-Scale SQP Solver Engine is the most versatile of all the engines. The solution times obtained can be impressive, whereby some problems with thousands of variables and constraints will solve in just seconds. The Large-Scale SQP Solver can also solve very large smooth nonlinear programming (NLP) problems far faster than the Premium Solver Platform's GRG Solver, or even the Large-Scale GRG Solver Engine. It uses a world-class implementation of the Sequential Quadratic Programming (SQP) method to solve smooth NLP problems.The Large-Scale SQP Solver has no fixed limits on problem size. However, the degrees of freedom (the number of variables minus the number of constraints that are binding at the solution) should not exceed about 20,000 (ten times the capacity of earlier versions). For nonlinear problems, the Large-Scale SQP Solver can exploit the new Polymorphic Spreadsheet Interpreter in the Premium Solver Platform to obtain partial derivatives of the problem functions (the Jacobian matrix) at each major iteration or trial solution. This yields significant benefits in speed and accuracy that are up to ten times faster or more than without the Polymorphic Spreadsheet Interpreter.
Fast problem setup for linear models
Large linear programming models normally require a significant amount of time in problem setup, and then reach a solution quickly. With some work in redesigning the model to use functions such as SUM and SUMPRODUCT, the Large-Scale SQP Solver Engine can provide speedup as much as 100 times faster. However, as the Large-Scale SQP Solver can now use the new Polymorphic Spreadsheet Interpreter to extract the LP coefficients of the model, you may get most of this speed benefit without redesigning your model at all. Furthermore, the coefficients are up to twice as accurate as they were without the Polymorphic Spreadsheet Interpreter.
Mixed linear / nonlinear models: Breakthrough performance
Often, large nonlinear optimisation models include many linear or partially linear constraints, or variables that occur linearly in the objective or in some of the constraints. The Large-Scale SQP Solver is designed for outstanding performance on such models. Using the information on how the objective function and constraints depend on each variable, the engine can automatically break down the model into linear and nonlinear parts. It will then solve each part using the best algorithms from both linear programming and nonlinear optimisation. The result is breakthrough performance, far beyond the level of earlier spreadsheet solvers.
Handling of mixed linear / nonlinear / nonsmooth models
Users often build large Excel models that have some non-smooth functions such as IF, CHOOSE, LOOKUP, or database functions that depend on the decision variables. Only some non-smooth functions such as IF, MIN and MAX can be automatically transformed by the Polymorphic Spreadsheet Interpreter in the Premium Solver Platform. The Large-Scale SQP Solver includes an integrated hybrid Evolutionary Solver that uses genetic algorithms to optimise non-smooth problems. Using information from the Interpreter, the Large-Scale SQP Solver uses genetic algorithm methods to deal with non-smooth or discontinuous variable occurrences and the SQP method for smooth nonlinear, quadratic and linear variable occurrences. This potent combination allows you to get results for large, complex models that might seem impossible before.
New options and tolerances
The Large-Scale SQP Solver offers several new options and tolerances to improve speed and give you better control of the solution process. The Treat Constraints as Linear and Treat Objective as Linear options allow you to bypass evaluation of the Jacobian matrix at each major iteration and achieve speeds typical of linear programming problems. The Large-Scale SQP Solver includes a world-class implementation of sparse matrix active-set methods with modern matrix factorisation that provides extremely fast solutions. The Bypass Solver Reports option allows you to save time on runs when you do not need to produce report information. Other new options and tolerances control the Evolutionary Solver and the multistart methods for global optimisation.
Comprehensive user guide
In addition to the user guide that comes with the Premium Solver Platform, you will receive theSolver Engine User Guide that describes several field-installable Solver engines, including the Large-Scale SQP Solver. This guide provides complete information on Large-Scale SQP Solver options, the various messages which the Large-Scale SQP Solver can return, how to diagnose problems, and how to control the Large-Scale SQP Solver from VBA in Excel.