ILOG CPLEX® 11.2

• A new and more flexible interface for solution polishing
• Multiple MIP starts
• A conflict refiner for infeasible MIP starts
• A larger class of convex quadratic constraints, including rotated cones for SOCP

Recent major versions of ILOG CPLEX: ILOG CPLEX 11.1 ILOG CPLEX 11.0 ILOG CPLEX 10.0 ILOG CPLEX 9.0 ILOG CPLEX 11.1 ILOG CPLEX 11.1 supports more varieties of mixed integer programming (MIP) starts for solution polishing, allowing you to start from a feasible solution to a previous problem, and then immediately switch to solution polishing. ILOG CPLEX 11.1 is compatible with Concert 2.6. ILOG CPLEX 11.0 Mixed Integer Programming (MIP) Performance ILOG CPLEX 11 introduces a new search algorithm—dynamic search. It is innovative in its integration and sequencing of the usual branching, nodes and cuts in branch-and-cut algorithms. ILOG CPLEX 11 retains its conventional branch-and-cut algorithm, but with advances in branching, cuts and heuristics. By selecting the more efficient of the two search strategies, ILOG CPLEX 11 improves the time to optimality by 15 percent on average for models solved in less than one minute; and it solves models in the range of one minute to one hour an average of three times faster. For hard models requiring more than one hour to solve, the speed up is a factor of ten on average. Enhanced Parallel MIP ILOG CPLEX 11 extends the functionality of the parallel MIP optimizer to include two modes of operation. In deterministic mode, a newly implemented search algorithm exploits parallelism in solving nodes of the branch-and-cut tree, but produces a repeatable, invariant solution path. In opportunistic mode, the search algorithm (introduced in a previous release), takes full advantage of parallelism; it performs less synchronization between threads and allows random tie breaking, which may result in different solution paths but potentially faster performance. Multiple MIP Solutions ILOG CPLEX 11 introduces the solution pool feature, which allows users to consider multiple solutions to a MIP model. In practice, a single—even optimal—solution is not always sufficient, because every aspect of a problem cannot always be perfectly captured in a MIP model. The solution pool feature offers a mechanism for exploring the effects of subjective preferences on the solution space without enforcing them as constraints in the model. ILOG CPLEX 11 can collect all (optimal) solutions or solutions that satisfy specific criteria. Solution pool parameters and filters allow users to control the properties of the solutions generated and stored in the solution pool. Performance Tuning ILOG CPLEX 11 introduces a performance tuning utility to help users improve the performance of their optimization applications. It analyzes one model or a group of models to identify parameter settings that yield better performance than default settings. ILOG CPLEX 11 tries different parameter settings based on the outcome of the initial and subsequent model runs. Users can customize the tuning and can apply it to models that are solved to optimality or to earlier stopping criteria. ILOG CPLEX 10.0 Performance ILOG CPLEX 10.0 provides several performance improvements. For a set of difficult LP problems, ILOG CPLEX 10.0 has improved the time to optimality by an average of 20% with both the Primal Simplex algorithm and the Barrier Optimizer. For MILP models, ILOG CPLEX 10.0 has improved the time to optimality, on average, by 35 percent overall, and by 70 percent for particularly difficult models. Infeasibility Analysis Given an infeasible model, the Conflict Refiner can identify contradictory constraints and bounds within the model to help users identify the causes of the infeasibility. The Conflict Refiner can work on any type of problem, even mixed integer programs and those containing quadratic elements. The Conflict Refiner also uses groups and preferences to allow the user to guide the process. Model types, groups and preferences make the Conflict Refiner an extension and generalization of the IIS finder. Solution Polishing Solution Polishing is a new ILOG CPLEX heuristic used to boost performance on certain types of models. Solution Polishing is appropriate for finding the best solutions to complex and difficult MIP models within a specified time. Solution Polishing is used to improve the best solution at the end of the branch-and-cut process if optimality has not been proven. It can also be used instead of the branch-and-cut algorithm if an initial solution can be found in the root node. Indicators Indicators are new constraint types that allow users to express relationships among variables by identifying a binary variable to control whether or not a specified linear constraint is active. Formulations using indicator constraints are more numerically robust and accurate than conventional formulations involving so-called Big M data. In Callable Library applications, ILOG CPLEX supports the direct use of indicator constraints in the model. In Concert Technology applications, ILOG CPLEX 10.0 automatically uses indicator constraints when it encounters expressions that can be linearized, such as "IloIfThen." MIP Starts The advanced restart capabilities of ILOG CPLEX have been improved to utilize initial solutions, partial solutions and partially correct solutions. ILOG CPLEX will accept a complete and valid solution, which can significantly improve the time it takes to find an optimal solution. Users can specify values for a subset of the discrete variables and ILOG CPLEX 10.0 will attempt to fill in the missing values or correct the wrong values in a way that leads to an integer-feasible solution, potentially reducing the time to solve the problem.

ILOG CPLEX 9.0

• Performance improvements
  ILOG CPLEX 9.0 contains major enhancements that improve performance for mixed-integer and linear programs. The ILOG CPLEX MIP Optimizer is 50% faster, on average, for a set of difficult customer models. ILOG CPLEX Simplex Optimizers have also improved. The dual simplex algorithm is 40% faster and the primal simplex is 20% faster, on average. (Performance improvements are measured using the default setting of current and previous ILOG CPLEX versions.)
  
  
• Concert Technology for .NET Users
  ILOG Concert Technology for .Net Users is a new application programming interface (API). This API gives developers the ability to write mathematical programming applications using any .NET-supported languages. ILOG CPLEX includes examples in C# and Visual Basic .NET. Programming objects make it easy to define variables, define constraints and interact with models. Users can create models, modify models or customize ILOG CPLEX algorithms, all without leaving their favorite .NET programming language.
  
  
• Quadratically constrained programs
  Quadratically constrained programs (QCPs) can be solved using ILOG CPLEX. In QCPs, quadratic terms may appear in one or more of the problem’s constraints. Such a problem’s objective function may or may not contain quadratic terms as well. The ILOG CPLEX Mixed Integer Optimizer has been extended to handle QCPs with integrality constraints. The full complement of MIP features -- including presolve, probing, cuts, heuristics, and callbacks -- is available for solving MIQCP problems. A MIQCP problem may contain any combination of continuous, binary, general integer, semi-continuous or special ordered set variables.
  
  
• Infeasibility analysis tool
  ILOG CPLEX provides an automatic approach to find the best feasible alternative to an infeasible model. This approach is called FeasOpt (for feasible optimization). FeasOpt accepts an infeasible model and selectively relaxes the bounds and constraints, minimizing a weighted penalty function that you define. In essence, FeasOpt tries to suggest the smallest change that would achieve feasibility. FeasOpt does not actually modify your model. Instead, it returns a suggested set of bounds and constraint ranges, along with the solution that would result from these relaxations. Optionally, FeasOpt can provide an optimal solution to the original objective function with the new relaxed model.
  
  
• XML
  ILOG Concert Technology for C++ Users provides an API that allows you to serialize models and solutions in XML. An XML schema specifies the format of optimization models in XML. Users can serialize custom model objects, in addition to using ready-made ILOG objects. Models and solutions can be read into Concert.

Previous versions of ILOG CPLEX: ILOG CPLEX 8.0 ILOG CPLEX 7.5 ILOG CPLEX 7.1 ILOG CPLEX 7.0

• MIP performance
  ILOG CPLEX contains major enhancements that will typically find feasible solutions to MIP models faster. On the path to the optimal solution the MIP algorithm will uncover more feasible solutions than it did previously. This gives users an increased flexibility to determine when to end the MIP solution algorithm. This feature has helped the ILOG CPLEX MIP Optimizer achieve an average 40% speed increase to optimality, with a 70% increase on difficult problems.
  
  
• MIQP
  Mixed integer quadratic programming (MIQP) problems now can be handled by ILOG CPLEX. MIQP models are ones having quadratic objective functions, integer variables, and linear constraints. The ILOG CPLEX Mixed Integer Optimizer has been extended to handle this quadratic case, and thus the full complement of MIP features, such as Presolve, Probing, Cuts, Heuristics, and Callbacks, is available to aid in the solving of MIQP problems.
  
  
• MIP search strategy
  Users can customize and control the MIP search strategy with goals. Goals are a control mechanism that allows users to specify the branching strategy, node selection strategy and other MIP control features all from the same user created route. Goals make it easier for the developer to specify constraints during the search. Goals also give you the flexibility to easily treat subtrees in the branch-and-cut tree differently.
  
  
• Sifting algorithm
  A new algorithm is added that can significantly reduce the solution time for LPs with a very large number of decision variables and few constraints. On tests where the number of variables was 100 times (or more) greater than the number of constraints, the average solution time was cut in half. Developers who use column generation techniques will be particularly interested in trying this new algorithm.
  
  
• Concurrent optimization
  Users on multi-CPU systems do not need to determine which is the best algorithm for all problems they would like to solve. The new concurrent optimization feature solves your LP (or the LP relaxation of your MIP) using two or three different LP algorithms and automatically stops all algorithms when the first one finishes.

• Mathematical programming for Java
  ILOG CPLEX 7.5 brings ILOG CPLEX power to the Java programming language. Combining a Java interface with the fastest mathematical programming engine available, ILOG CPLEX 7.5 lets users write mathematical programming applications in Java without sacrificing ILOG CPLEX's robust performance.
  
  
• Java interface
  ILOG CPLEX 7.5 supports a complete Java interface, based on a Java version of ILOG Concert Technology. ILOG CPLEX 7.5 includes a set of lightweight Java modeling objects for representing optimization problems. Provided Java objects include variables, constraints and models. Users can create their models in rows or columns.
  
  
• The power of ILOG CPLEX
  ILOG CPLEX 7.5 harnesses the problem-solving power that thousands of ILOG CPLEX users have come to expect - the internal engine is unchanged. In addition to ILOG CPLEX 7.0's algorithms and features, ILOG CPLEX 7.5 also offers control over the branch-and-cut algorithm, as well as piecewise linear modeling capability.
  
  
• Cooperative solving
  ILOG Concert Technology provides a way for users to take advantage of the power of mathematical programming and constraint programming. ILOG JSolver and ILOG CPLEX 7.5 can be combined to create hybrid solution approaches, extending each engine's usefulness.

• Pentium IV speed
  Pentium IV users can solve problems faster than ever before when employing the barrier algorithm. Taking advantage of Intel's NetBurst microarchitecture, ILOG CPLEX 7.1 utilizes the SSE2 instruction set. Tuning the barrier algorithm to Pentium IV processors delivers significant speed improvements.
  
  
• Solve larger problems
  The ILOG CPLEX barrier algorithm can now solve even larger linear programs. ILOG CPLEX 7.1 writes the matrix factorization to disk, allowing 32-bit architectures to exceed the 2-gigabyte limitation when using the barrier algorithm.
  
  
• Model compression
  ILOG CPLEX 7.1 makes more memory available for algorithm computations by compressing the original model while ILOG CPLEX works with the presolved model.
  
  
• Quadratic presolve
  Presolve features have been extended to include models with quadratic objectives, offering a significant advantage for some mathematical models. All APIs in the ILOG CPLEX component library support this feature.

• ILOG Concert Technology
  In addition to ILOG CPLEX Interactive Optimizer and ILOG CPLEX Callable Library , ILOG CPLEX 7.0 also includes ILOG Concert Technology. This technology provides a C++ modeling layer for linear and mixed integer programs, and a C++ interface for solving these problems. With ILOG Concert Technology, users can build and modify a model, solve it and examine its solution, all in terms of the modeling entities. For example, it's no longer necessary to translate from a modeling entity to a constraint or variable index.
  
  
• Optimizer performance and control
  The three optimizers for linear programs (LPs) - dual simplex, primal simplex and barrier - all offer improved performance:
  • The ILOG CPLEX Primal Simplex method is, on average, 30% faster than ILOG CPLEX 6.5 on a large collection of hard linear programs
  • The ILOG CPLEX Dual Simplex method is, on average, 10% faster than ILOG CPLEX 6.5 on a large collection of hard linear programs
  • ILOG CPLEX Barrier Optimizer is, on average, 60% faster than ILOG CPLEX 6.5 on a large collection of hard linear programs
  • ILOG CPLEX Mixed Integer Optimizer is, on average, 60% faster than ILOG CPLEX 6.5 on a large collection of hard mixed integer programs
    
    
Improvements in the barrier method enable it to effectively solve a wider variety of numerically difficult problems. LP optimizers can now be selected using a parameter rather than by calling different functions.


• Improved MIP performance and new feasible solution feature
  The ILOG CPLEX Mixed Integer optimizer contains a number of features that allow solution of previously unsolvable mixed integer programs (MIPs), including mixed integer rounding cuts, disjunctive cuts, flow path cuts and improved probing. Gomory cuts, which were introduced in ILOG CPLEX 6.6, are now available by default, and there are several parameters to fine-tune their use. These and other enhancements result in improved performance.
  
  
A new parameter is available to direct the MIP optimizer to emphasize finding feasible solutions over proving optimality. This is useful when good feasible solutions must be found quickly, such as when a solution must be found within a certain time limit. On a large collection of mixed integer programs, a first feasible solution is found twice as fast when emphasizing feasibility as compared to when emphasizing optimality.