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Using ILOG Cplex

Using ILOG Cplex. Mathematical Programming Problem. Seeks to optimize an objective function subject to constraints. Types of mathematical programming problems Linear Programming Mixed Integer Programming Non-linear Programming. ILOG CPLEX. Efficient Fast Industry standard

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Using ILOG Cplex

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  1. Using ILOG Cplex

  2. Mathematical Programming Problem • Seeks to optimize an objective function subject to constraints. • Types of mathematical programming problems • Linear Programming • Mixed Integer Programming • Non-linear Programming

  3. ILOG CPLEX • Efficient • Fast • Industry standard • offers C, C++, Java, and C#.NET libraries that solve linear programming (LP) and related problems.

  4. Characteristics of Linear Programming • Objective function (min or max) is a linear function. • Constraint types are ,=, or . • If f is a linear function and if b is a real number, then the equation • f(x1,x2,…,xn) = b is called a linear equation, and the inequalities • f(x1,x2,…,xn) ≤b, and • f(x1,x2,…,xn) ≥b are called linear inequalities. • Linear equations and linear inequalities are both referred to as linear constraints.

  5. Feasible and Optimal Solutions • Variables x1,x2,…,xnthat satisfy all the constraints of an LP problem are said to constitute a feasible solution. • A feasible solution that maximizes ( or minimizes) the objective function is called an optimal solution, the corresponding value of the objective function is called the optimal value. • Optimal solution may not be unique.

  6. Additional Types of Variables • All integer • All variables are restricted to have integer values • Mixed integer • some variables are restricted to have integer values • Binary • variables are restricted to have integer values of either 0 or 1

  7. ILOG CPLEX Optimizer • The data provided as input to the solver are: • Objective function coefficients  c1, c2, ... , cn • Constraint coefficients,  a11, a21, ... , an1,... am1, am2, ..., amn • Right-hand sides constants, b1, b2, ... , bm • Upper and lower bounds u1, u2, ... , unand l1, l2, ... , ln • The optimal solution that ILOG CPLEX computes and returns is: • Value of the variables x1, x2, ... , xn • Objective value

  8. Using Cplex • ILOG CPLEX comes in three forms: • The ILOG CPLEX Interactive Optimizer • can read a problem interactively or from files in certain standard formats, • solve the problem, and deliver the solution interactively or into text files. • ILOG Concert • a set of libraries to allow a programmer to embed ILOG CPLEX optimizers in C++, Java, or C#.NET applications. • The ILOG CPLEX Callable Library • a C library that allows the programmer to embed ILOG CPLEX optimizers in applications written in C, Visual Basic, Fortran or any other language that can call C functions.

  9. Example 3 • Let us consider the following LP problem • Maximize  x1 + 2x2 + 3x3 • subject to  • -x1 + x2 + x3 ≤ 20  • x1 - 3x2 + x3 ≤ 30   • with these bounds  • 0 ≤ x1 ≤ 40  • 0 ≤ x2 ≤ +   • 0 ≤ x3 ≤ +   • Let us consider the following LP problem • Maximize  x1 + 2x2 + 3x3 • subject to  • -x1 + x2 + x3 ≤ 20  • x1 - 3x2 + x3 ≤ 30   • with these bounds  • 0 ≤ x1 ≤ 40  • 0 ≤ x2 ≤ +   • 0 ≤ x3 ≤ +  

  10. Before Running CPLEX • Login to cplex.cs.uwindsor.ca • Make sure you add the following lines to the bottom of .profile file in your home directory if [ -d /opt/ibm/ILOG/CPLEX_Studio124/cplex/bin/x86-64_sles10_4.1 ]; then PATH=${PATH}:/opt/ibm/ILOG/CPLEX_Studio124/cplex/bin/x86-64_sles10_4.1 fi • May need to set the ‘view hidden files’ option, if you are using SSH

  11. Starting ILOG CPLEX Interactive Optimizer • Steps • Set up your path(s) and log in to cplex.cs.uwindsor.ca server • Open a shell • At the command prompt, type and enter cplex • And you are there • yourname@cplex:~$ cplex • CPLEX>

  12. ILOG CPLEX Interactive Optimizer • > cplex • CPLEX> enter Enter name for problem: myProblem Enter new problem ['end' on a separate line terminates]: maximize x1 + 2x2 + 3 x3 subject to -x1 + x2 + x3 <= 20 x1 - 3x2 + x3 <=30 bounds 0 <= x1 <= 40 0 <= x2 0 <= x3 end Example 3 • Let us consider the following LP problem • Maximize  x1 + 2x2 + 3x3 • subject to  • -x1 + x2 + x3 ≤ 20  • x1 - 3x2 + x3 ≤ 30   • with these bounds  • 0 ≤ x1 ≤ 40  • 0 ≤ x2 ≤ +   • 0 ≤ x3 ≤ +  

  13. Interactive Optimizer • CPLEX> • CPLEX> opt Tried aggregator 1 time. No LP presolve or aggregator reductions. Presolve time = 0.00 sec. Iteration log . . . Iteration: 1 Dual infeasibility = 0.000000 Iteration: 2 Dual objective = 202.500000 Dual simplex - Optimal: Objective = 2.0250000000e+02 Solution time = 0.00 sec. Iterations = 2 (1) • CPLEX> dis sol var - Variable Name Solution Value x1 40.000000 x2 17.500000 x3 42.500000 • CPLEX> quit • grid-2:~> • Reporting the solution: • the objective function value • the problem solution time in seconds • the total iteration count • the Phase I iteration count (in parentheses) • Interrupting the Optimization Process • control –c

  14. Some ILOG CPLEX Commands • Cplex: start the ILOG CPLEX Interactive Optimizer • Enter: enter a new problem • Read: read problem or basis information from a file • Optimize: solve the problem • Display: display problem, solution, or parameter settings • Solution • Variable • - (for all nonzero variables) • Ex. CPLEX> display solution variables -

  15. Interactive – Reading lp file • Let us consider the following LP problem • Maximize  x1 + 2x2 + 3x3 • subject to  • -x1 + x2 + x3 ≤ 20  • x1 - 3x2 + x3 ≤ 30   • with these bounds  • 0 ≤ x1 ≤ 40  • 0 ≤ x2 ≤ +   • 0 ≤ x3 ≤ +   • CPLEX> read Name of file to read: 567ex3.lp Problem 'myProblem.lp' read. Read time = 0.01 sec. • CPLEX> opt Tried aggregator 1 time. No LP presolve or aggregator reductions. Presolve time = 0.00 sec. Iteration log . . . Iteration: 1 Dual infeasibility = 0.000000 Iteration: 2 Dual objective = 202.500000 Dual simplex - Optimal: Objective = 2.0250000000e+02 Solution time = 0.00 sec. Iterations = 2 (1) • CPLEX> dis sol var - Variable Name Solution Value x1 40.000000 x2 17.500000 x3 42.500000 • CPLEX> quit Text file content maximize obj: x1 + 2x2 + 3x3 subject to c1: -x1 + x2 + x3 <= 20 c2: x1 - 3 x2 + x3 <=30 Bounds 0 <= x1 <= 40 0 <= x2 0 <= x3 End

  16. Some additional Commands • Help: provide information on CPLEX commands • Set: set parameters • Write: write problem or solution information to a file • Add: add constraints to problem • Change: change the problem • Mipopt: solve a mixed integer program • Type either the full command name, or any shortened version that uniquely identifies that name. • ILOG CPLEX does not distinguish between upper- and lower-case letters.

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