## KNITRO Solver Engine Version

The KNITRO Solver Engine extends the power of the Premium Solver Platform to handle smooth nonlinear optimisation problems with no fixed limits on the number of variables and constraints. This is a field-installable solver engine that plugs into the Premium Solver Platform, and takes advantage of its new Polymorphic Spreadsheet Interpreter. The solver engine solves global optimisation problems using the 'multistart' or 'clustering' methods. This provides greatly improved performance, especially on problems with integer variables and 'alldifferent' constraints.

**Greater speed and accuracy**

With the KNITRO Solver Engine, you will be able to solve smooth nonlinear optimisation problems that are far larger than the standard Excel Solver since there are no fixed limites on the number of variables and constraints. Solution times can be very impressive with some nonlinear problems with many hundreds of variables and constraints solving in just seconds. To handle such large problems, the KNITRO Solver Engine uses sparse matrix storage methods and advanced methods for maintaining numerical stability. The KNITRO Solver takes maximum advantage of the new Polymorphic Spreadsheet Interpreter in the Premium Solver Platform to obtain either first or second partial derivatives of the problem functions (the Jacobian or Hessian matrix) at each major iteration or trial solution.

**New options and tolerances**

The KNITRO 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 speed up evaluation of the Jacobian or Hessian matrix at each major iteration on smooth nonlinear programming problems with all-linear constraints. If you have encountered problems with trial solutions that included small violations of bounds on variables, you will appreciate the ability to control this behavior with the *Relax Bounds on Variables* option in the Large-Scale GRG Solver. The *Bypass Solver Reports* option allows you to save time on runs when you don't need to produce report information. Other new options and tolerances control the *multistart *methods for global optimisation.

**Comprehensive user guide**

In addition to the user guide that comes with the Premium Solver Platform, you'll receive the Solver Engine User Guide that describes several field-installable Solver engines, including the KNITRO Solver. This guide provides complete information on KNITRO Solver options, the various messages which the KNITRO Solver can return, how to diagnose problems and how to control the KNITRO Solver from VBA in Excel.

## Large-Scale GRG Solver Engine Version

The Large-Scale GRG Solver Engine extends the power of the Premium Solver Platform to handle smooth nonlinear optimisation problems. The Standard Large-Scale GRG Solver Engine solves problems of up to 4,000 variables and 4,000 constraints while the Extended Large-Scale GRG Solver Engine solves problems of up to 12,000 variables and 12,000 constraints. This engine solves global optimisation problems using the 'multistart' or 'clustering' methods and supports integer variables as well as 'alldifferent' constraints.

**Greater speed and capacity**

To handle large problems, the Large-Scale GRG Solver Engine uses sparse matrix storage methods and advanced methods for maintaining numerical stability. The Large-Scale GRG 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.

**New options and tolerances**

The Large-Scale GRG Solver offers several new options and tolerances to improve speed and give you better control of the solution process. The *Recognize Linear Variables* option allows the Large-Scale GRG Solver to take advantage of linearly occurring variables (often found in large problems that are nonlinear), and save time in computing the Jacobian matrix. If you have encountered problems with trial solutions that included small violations of bounds on variables, you will appreciate the ability to control this behavior with the *Relax Bounds on Variables* option in the Large-Scale GRG Solver. The *Bypass Solver Reports* option allows you to save time on runs when you don't need to produce report information. Other new options and tolerances control 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 the Solver Engine User Guide that describes several field-installable Solver engines, including the Large-Scale GRG Solver. This guide provides complete information on Large-Scale GRG Solver options, the various messages which the Large-Scale GRG Solver can return, how to diagnose problems, and how to control the Large-Scale GRG Solver from VBA in Excel.

## Large-Scale LP/QP Solver Engine Version

The Large-Scale LP/QP Solver engine extends the power the Premium Solver Platform to handle much larger linear programming and quadratic programming problems. It is a field-installable solver engine that plugs into the Premium Solver Platform and takes advantage of the new Polymorphic Spreadsheet Interpreter. The Standard Large-Scale LP/QP Solver can handle linear programming (LP) and quadratic programming (QP) problems of up to 32,000 variables and 32,000 constraints, while the Extended Large-Scale LP/QP Solver does not have a fixed limit on variables and constraints.

**Greater speed and capacity**

Solve linear and quadratic programming problems that are a thousand times larger than the what standard Excel Solver can handle. The Large-Scale LP/QP Solver also supports integer variables and *alldifferent *constraints. To handle such large problems, this engine uses sparse matrix storage methods and advanced methods for matrix factorisation. Solution times are often hundreds of times faster than the standard Excel Solver, and many times faster than the Premium Solver.

**Fast problem setup**

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 LP/QP Solver Engine can provide speedups as much as 100 times faster. However, as the Large-Scale LP/QP 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.

**New options and tolerances**

The Large-Scale LP/QP Solver Engine lets you adjust the most critical tolerances in the Simplex method – the Primal Tolerance and Dual Tolerance, while other tolerances are determined automatically. You can also select a variety of Cut Generation options, set limits on the number of subproblems and feasible solutions in mixed-integer linear programming models.

**Comprehensive user guide**

In addition to the user guide that comes with the Premium Solver Platform, you will also receive the Solver Engine User Guide that describes several field-installable solver engines. This guide provides complete information on Large-Scale LP/QP Solver options, the various messages that this solver engine can return, diagnosing problems, and controlling the Large-Scale LP/QP Solver from VBA in Excel. You will also obtain access to protected support pages on the developer's website.

## Large-Scale SQP Solver Engine Version

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.

## MOSEK Solver Engine Version

The MOSEK Solver Engine extends the power of the Premium Solver Platform to solve linear (LP), quadratic (QP), quadratically constrained (QCP) and second order cone programming (SOCP) problems. The Extended MOSEK Solver Engine provides the additional capability to solve smooth convex nonlinear optimisation (NLP) problems. The Standard MOSEK Solver can solve problems of up to 32,000 variables and 32,000 constraints, while the version does not have any fixed limits on variables and constraints. These solver engines also supports integer variables and 'alldifferent' constraints.

**Solve Linear, Quadratic and New Conic Optimisation problems with lightning speed**

With the Standard MOSEK Solver, you will be able to solve LP, QP, QCP, SOCP and NLP* problems hundreds to thousands of times larger than what the standard Excel Solver can handle. The MOSEK Solver typically matches the Large-Scale LP/QP Solver and other world-class LP Solvers for linear and mixed-integer linear programming problems (LP/MIP), and it is widely regarded as the world's best solver for QCP and SOCP problems. This solver takes maximum advantage of the new Polymorphic Spreadsheet Interpreter in the Premium Solver Platform to obtain second partial derivatives of the problem functions (the Hessian matrix) at each major iteration or trial solution. For QP and SOCP problems, whereby the Hessian matrices are constant, the MOSEK Solver is as fast as it is on LP problems.

**New options and tolerances**

The MOSEK Solver offers nearly 40 options and tolerances that you can set to fine-tune the solution for LP, QP, QCP and NLP* problems. These include the primal and dual feasibility tolerance, complementarity gap tolerance, relative step size to the constraint boundary and central path tolerance.

## OptQuest Solver Engine Version

The OptQuest Solver Engine employs metaheuristics such as tabu search and scatter search to solve nonsmooth optimisation problems of up to 5,000 variables and 1,000 constraints. It is a new field-installable engine that plugs into the Premium Solver Platform and takes advantage of its Polymorphic Spreadsheet Interpreter. The engine handles models with any Excel formulas and functions, yet finds remarkably good solutions with unprecedented speed. Furthermore, it supports integer variables and 'alldifferent' constraints.

## XPRESS Solver Engine Version

The XPRESS Solver Engine extends the power of the Premium Solver Platform to handle linear programming problems with up to millions of variables and constraints, with no fixed limits on problem size. It solves mixed-integer linear (LP/MIP) problems with great speed and supports the 'alldifferent' constraint in the Premium Solver Platform.