What's the best optimization technique for your problem?

1 Problem structure

The first step is to analyze the structure of your problem, such as the number and type of variables, the objective function, and the constraints. Depending on the structure, you may classify your problem as linear, nonlinear, integer, or mixed-integer. For example, if your variables are continuous and your objective and constraints are linear functions, you have a linear optimization problem. If some or all of your variables are discrete, you have an integer or mixed-integer optimization problem. If your objective or constraints are nonlinear functions, you have a nonlinear optimization problem. Each type of problem requires a different optimization technique, such as linear programming, integer programming, or nonlinear programming.

2 Problem size

The second factor is the size of your problem, which refers to the number of variables and constraints. The size of your problem affects the computational complexity and feasibility of finding the optimal solution. Generally, the larger the problem, the more difficult it is to solve. For example, a linear optimization problem with 10 variables and 20 constraints can be solved in seconds using a simple algorithm, such as the simplex method. However, a mixed-integer optimization problem with 100 variables and 200 constraints may take hours or even days to solve using a more sophisticated algorithm, such as branch-and-bound. Therefore, you may need to simplify or decompose your problem, or use heuristics or metaheuristics, to find a good enough solution in a reasonable time.

3 Problem uncertainty

The third factor is the uncertainty of your problem, which refers to the variability or unpredictability of your data, parameters, or environment. Uncertainty can affect the quality and robustness of your solution, as well as the risk and opportunity of your decision. For example, if your demand, cost, or capacity are uncertain, you may not be able to achieve your optimal solution in reality, or you may miss out on better alternatives. Therefore, you may need to incorporate uncertainty into your optimization model, or use stochastic or robust optimization techniques, to account for different scenarios or ranges of values.

4 Problem preference

The fourth factor is your preference, which refers to your goals, values, and priorities for your problem. Preference can influence the definition and evaluation of your objective function and constraints, as well as the selection and comparison of your solutions. For example, if you have multiple objectives, such as minimizing cost and maximizing quality, you may need to weigh them or rank them according to your preference. Or, if you have multiple solutions that are equally optimal or near-optimal, you may need to choose the one that best suits your preference. Therefore, you may need to use multi-objective optimization techniques, or use sensitivity analysis or decision analysis tools, to express and assess your preference.

5 Problem context

The fifth factor is the context of your problem, which refers to the domain, industry, or application of your problem. Context can provide you with relevant information, knowledge, and experience for your problem, as well as specific requirements, standards, or regulations for your solution. For example, if you are optimizing a manufacturing process, you may need to consider the characteristics, specifications, and constraints of your machines, materials, and products. Or, if you are optimizing a healthcare system, you may need to consider the needs, preferences, and outcomes of your patients, providers, and stakeholders. Therefore, you may need to use domain-specific optimization techniques, or use best practices or benchmarks from your industry or application, to tailor and validate your solution.

6 Problem feedback

The sixth factor is the feedback of your problem, which refers to the results, impacts, and learning from your solution. Feedback can help you measure and improve the performance and effectiveness of your solution, as well as identify and resolve any issues or challenges. For example, if you implement your solution in practice, you may need to monitor and evaluate its outcomes, such as cost, quality, or customer satisfaction. Or, if you encounter any changes or uncertainties in your problem, you may need to update or revise your solution accordingly. Therefore, you may need to use optimization techniques that are adaptive, iterative, or dynamic, or use data analysis or simulation tools, to incorporate and leverage feedback.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?