What is optimization?
Optimization is a math-based technology that allocates resources with the goal of maximizing operational efficiency.
How does ILOG CPLEX work?
Optimization is a process that can be applied to a specific problem. The logical first step is a clear description of the problem to be solved. The subsequent steps are as follows:
Construct a model for your problem
Add data to the model
Analyze the model using a mathematical optimization engine to find the best possible solution
When the optimization model is embedded in the actual application, planners and operations managers can analyze and compare various scenarios.
The chart below illustrates some of the types of information that optimization needs to process, and the results of the optimization process.
Application field of mathematical optimization in management
1. Optimize the application in finance
2. Portfolio optimization
3. Loan portfolio optimization
Optimize applications in operations management
1. Production plan (production plan, equipment allocation, process arrangement, etc.)
2, staff scheduling
3, facility layout
Optimize the application of logistics management
1. Logistics network planning (regional, national, global)
2, distribution line optimization (express, retail distribution, e-commerce delivery)
3, location / location optimization (warehouse, freight yard, container yard)
4, inventory optimization (single / multi-level / network, single cycle / multi-cycle)
Classification of optimization algorithms
1, Mathematical Programming method
An optimization method that can prove the final solution to the global optimal solution, such as linear programming, mixed integer programming
2, Constraint Programming method
A search method for solving a finite solution space and failing to prove that the result is a global optimal solution
3, Heuristic Programing method
Can solve the problem of infinite solution space, can not prove that the result is a global optimal search method
Meta-Heuristic method (taboo algorithm, annealing algorithm, genetic algorithm, neural network, ant colony algorithm)
Heuristic method based on mathematical programming (eg Lagrangian relaxation)
Other Heuristic methods (search methods based on experience for specific problems)
Why can't you just rely on the MP method?
Some problems cannot find an algorithm that can be proved to get the optimal solution.
Some problems can get the optimal solution even through the MP method. However, as the number of variables increases, the number of constraints increases exponentially, and the calculation time increases geometrically. For example, the traveling business problem.
What is a good optimization model?
Readability vs. model size
The meaning of variables should be simpler or more complicated
Time complexity vs. space complexity
Whether the increase in the variable increase can be exchanged for the decrease in the number of calculations
Number of variables vs. number of constraints
Whether constraints and variables can be converted, how will the calculation speed change?
Hierarchical structure vs. single layer structure
The division of the main problem and the sub-question may not get the optimal solution, but it can simplify the problem.
Comparison of optimization algorithms
Different algorithms have different operating efficiencies and different operational results for a particular model. There are usually two comparisons between the advantages and disadvantages of the algorithm:
Comparison of the quality of solutions under the same operation time
A comparison of the time taken to get the final solution (or a satisfactory solution above a certain level).
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