LINDO's linear, nonlinear and integer programming solvers have been used by thousands of companies worldwide to maximise profit and minimise cost on decisions involving production planning, transportation, finance, portfolio allocation, capital budgeting, blending, scheduling, inventory, resource allocation and more.

Markowitz Portfolio Selection model

Maximize the total return on assets while limiting risk to a specified level.

LINDO API 8.0

LINDO Systems has begun shipping a new release of LINDO API that includes new features to allow users to incorporate uncertainty into their optimization models. LINDO API 8.0 also includes enhancements to the linear, integer and global solvers.

LINDO API 8.0 Enhancements
 
Improved Speed with Multicore Support

The solvers have been enhanced to take advantage of computers with multicore processors to boost speed on a wide range of problems. Multicore extensions have been added to the Barrier, Global, Integer, Multistart and Stochastic solvers.
 
New Branch-and-Price Solver
A new Branch-and-Price solver with multicore support has been added for improved performance on problems with block structures. Detection of decomposition structures has also been improved in support of the Branch-and-Price solver.
 
Improved MIP Solver
The heuristics for finding good feasible solutions to integer models have been significantly improved. Simple rounding and feasibility pump now use bound propagation to improve the current path to a new feasible MIP solution. A new polishing heuristic has been added to improve the best MIP solution using a pool of previous obtained MIP solutions and the current relaxation. As a result, on many problems the solver is able to find better MIP solutions in a shorter amount of time.
 
Faster Better Multistart Solver
The Multistart solver has been improved significantly achieving performance improvements of up to two times compared to the previous version. The chances of finding the globally optimal solution have improved by 10-15% over a wide range of non-convex models.
 
More Powerful Stochastic Solver
Extensive improvements have been made to the Nested Benders Decomposition to make it up to six times faster. Chance-programming solver is now equipped with a Genetic Algorithm to find high-quality feasible solutions to large-scale instances. Models in this class can now also be solved using the Simple Benders Decomposition method.
 
More Probability Distributions Supported
The Beta-Binomial and Stable Paretian distributions have been added to the list of supported distributions. Stochastic programming models may also specify random variables with these distribution. The Beta-Binomial is useful in Bayesian analysis involving the Binomial distribution, e.g., in designing sampling plans for new drug trials. The Stable Paretian is sometimes used to model the movement of prices in financial markets.

Powerful solvers

LINDO API includes a set of built-in solvers to tackle a wide variety of problems. It offers increased control of the algorithms and solver parameters. This allows the user to customise the solution strategy to individual applications to achieve optimal control and speed.

Linear Solvers

The LINDO API 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. You have the option to choose the best pricing strategy based upon problem characteristics.

  • Barrier Solver

    The optional Barrier solver provides an alternative means of solving linear models. The Barrier option utilises 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. The Barrier licence option is required to utilise the Barrier solver.

  • Integer Solver

    For models with general and binary integer restrictions, LINDO API includes an integer solver that works in conjunction with the linear, nonlinear and quadratic solver. For linear models, you have the ability to tailor the solution strategy and apply different classes of cuts to ensure maximum speed on particular problem structures.

Nonlinear Solvers

LINDO API is the first full-featured callable solver to offer general nonlinear capabilities. LINDO API 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 LINDO API's optional nonlinear solver is based upon a Generalised Reduced Gradient (GRG) algorithm. However, to help get to a good feasible solution quickly, LINDO API also incorporates Successive Linear Programming (SLP). The nonlinear solver takes advantage of sparsity for improved speed and more efficient memory usage. The Nonlinear licence option is required to solve nonlinear models.

  • Global Solver

    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 licence options are required to utilise the global optimisation capabilities.

  • Multistart Solver

    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 initialise a series of local optimisations. 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 utilise the multistart capabilities.

  • Quadratic Solver

    In addition to solving linear and mixed integer models, with the Barrier option LINDO API can automatically detect and solve models in which the objective function and/or some constraints include quadratic terms. By taking advantage of the quadratic structure, LINDO API can solve these models much more quickly than using the general nonlinear solver. LINDO API can even handle quadratic models with binary and general integer restrictions. These quadratic capabilities make LINDO API suitable for applications such as portfolio optimisation problems, constrained regression problems, and certain classes of difficult logistics problems (e.g., layout problems, fixed-charge-network problems with quadratic objectives). The Quadratic solver is included in the Barrier licence option.

  • Conic Solver

    The Barrier option 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.

Preprocessing and User Control

Preprocessing routines are included in all solvers. The Linear and Nonlinear solvers include scaling and model reduction techniques. Scaling procedures can improve speed and robustness on numerically difficult models. Model reduction techniques can often make models solve faster by analysing the original formulation and mathematically condensing it into a smaller problem. The Integer solver includes extensive preprocessing and cut generation routines.

LINDO API is designed, so the user has as much control over the input to the solvers as possible. When the Solve routine is initiated, LINDO API analyses the problem and considers internal parameters set by the user to achieve optimal performance for your particular problem.

Linearisation

LINDO API's linearisation capabilities can dramatically improve performance on models with common nonsmooth functions. The feature can automatically convert many nonsmooth functions and operators (e.g., max and absolute value) to a series of linear, mathematically equivalent expressions. Many nonsmooth models may be entirely linearised. This allows the linear solver to quickly find a global solution to what would have otherwise been and intractable problem.


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