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What are the best methods for incorporating domain knowledge into optimization models?

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Optimization models are mathematical tools that help decision makers find the best solutions to complex problems involving trade-offs, constraints, and uncertainties. However, optimization models are not always accurate or realistic representations of the real world. Domain knowledge, or the expertise and insights of the people who understand the problem context, can improve the quality and relevance of optimization models. In this article, you will learn about some of the best methods for incorporating domain knowledge into optimization models, and how they can enhance your decision making.

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1 Problem formulation

The first step in incorporating domain knowledge into optimization models is to formulate the problem correctly. This means defining the objective function, the decision variables, the constraints, and the parameters of the model. Domain knowledge can help you identify the most important aspects of the problem, the relevant data sources, the assumptions and simplifications, and the potential pitfalls and challenges. You can use domain knowledge to guide your literature review, data collection, model validation, and sensitivity analysis.

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Jayant Swamy

CTO | Machine Learning | Deep Learning | Artificial Intelligence | Data Engineering | Technologist | Strategy | ex-Accenture
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First things first. Who owns the problem. Please ensure the data scientist is not the owner of the problem. He/ She can own the model formulation- but the problem formulation should be the domain leaders, as should be the data completeness. This will ensure the accountability will be in right place and there is sponsorship for getting the problem solved and validated.

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Joachim H.
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Since you say that you have a model already, it is probably a good idea to understand if that model has been able to generate any outcomes that has resulted in a verifiable fact. Problem ownership is important especially when working with facts (ML assisting in finding that). It can have immense wide spread societal and economic impacts (global even) as we have seen in several cases. So accountability for quality in terms of problem formulation is the I in O for sure. That is where the thinktank pre project should focus its efforts and weed out and prioritize the best questions. Ownership perhaps best assigned after a qualitative list is available in that tank.

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2 Model selection

The second step in incorporating domain knowledge into optimization models is to select the most appropriate model type and method for solving the problem. There are many types of optimization models, such as linear, nonlinear, integer, stochastic, dynamic, and multi-objective. Each type has its own advantages and disadvantages, and requires different techniques and algorithms to solve. Domain knowledge can help you choose the model type that best captures the features and complexities of the problem, and the method that best suits the available data, time, and resources.

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Jayant Swamy

CTO | Machine Learning | Deep Learning | Artificial Intelligence | Data Engineering | Technologist | Strategy | ex-Accenture
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This maybe an iterative process, rarely does it happen in linear fashion. But best to ensure domain expert and data scientist are collaborating well. This will ensure outcomes are more reliable.

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3 Parameter estimation

The third step in incorporating domain knowledge into optimization models is to estimate the parameters of the model. Parameters are the constants or coefficients that affect the objective function and the constraints. They can be derived from data, expert opinions, or other sources. Domain knowledge can help you determine the most reliable and relevant sources of information, the methods for estimating or updating the parameters, and the ranges and distributions of the parameters. You can use domain knowledge to assess the uncertainty and sensitivity of the parameters, and to incorporate them into your model.

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4 Solution analysis

The fourth step in incorporating domain knowledge into optimization models is to analyze the solution of the model. The solution is the optimal or near-optimal value of the objective function and the decision variables that achieve it. It can be a single point, a set of points, or a range of values. Domain knowledge can help you interpret the solution, evaluate its feasibility and robustness, compare it with alternative solutions, and communicate it to stakeholders. You can use domain knowledge to identify the trade-offs, risks, and opportunities of the solution, and to recommend actions or policies based on it.

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5 Model refinement

The fifth step in incorporating domain knowledge into optimization models is to refine the model based on the feedback and results of the previous steps. Model refinement is an iterative process that involves modifying or improving the model to better reflect the reality and the objectives of the problem. Domain knowledge can help you identify the gaps, errors, or limitations of the model, and suggest ways to overcome them. You can use domain knowledge to test and validate the model, to incorporate new data or information, and to adjust the parameters or constraints of the model.

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6 Model integration

The sixth and final step in incorporating domain knowledge into optimization models is to integrate the model with other tools and systems that support the decision making process. Model integration is the process of linking or embedding the model with data sources, software platforms, user interfaces, or decision support systems that facilitate the use and application of the model. Domain knowledge can help you design and implement the integration, and ensure its compatibility and functionality. You can use domain knowledge to monitor and update the model, to provide feedback and guidance, and to measure and evaluate the impact of the model.

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Jayant Swamy

CTO | Machine Learning | Deep Learning | Artificial Intelligence | Data Engineering | Technologist | Strategy | ex-Accenture
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This is where most process’s fail or worse get lost in the bureaucracy of enterprises IT. Most data scientists don’t hang around or are too busy to wait on that process and it is handed off to other in AI ops - and it doesn’t get fully integrated. Post 8 weeks, the model is already not in sync with changing data streams.

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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?

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What are the best methods for incorporating domain knowledge into optimization models?

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2

3

4

5

6

7

1 Problem formulation

2 Model selection

3 Parameter estimation

4 Solution analysis

5 Model refinement

6 Model integration

7 Here’s what else to consider

Operations Research

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What are the best methods for incorporating domain knowledge into optimization models?

1

2

3

4

5

6

7

1 Problem formulation

2 Model selection

3 Parameter estimation

4 Solution analysis

5 Model refinement

6 Model integration

7 Here’s what else to consider

Operations Research

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