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Linear optimization main concepts and implementation in PythonPhoto by Patrick Fore on UnsplashNumerical optimization is a fundamental tool in quantitative decision-making processes. To optimize a given goal, one must select values for interrelated decision variables under some prescribed set of circumstances. The format of the mathematical equations that describe the objective and the constraints of the problem is used to distinguish optimization problems between two major categories: Linear and Nonlinear…

Mathematical modeling and Python implementation of the classical sequencing problem using PyomoPhoto by Guillaume Bolduc on UnsplashThe job-shop scheduling problem (JSSP) is a widely studied optimization problem with several industrial applications. The goal is to define how to minimize the makespan required to allocate shared resources (machines) over time to complete competing activities (jobs). As for other optimization problems, mixed-integer programming can be an effective tool to provide good solutions, although for…

The classical inventory management optimization problem solved in Python using PyomoPhoto by CHUTTERSNAP on UnsplashLot sizing problems are production planning problems with setups between production lots. By reason of these setups, it is often too costly to produce a given product in every period (Suwondo & Yuliando, 2012). In contrast, fewer setups are associated with higher holding inventory costs. Therefore, to obtain optimal costs, one should balance these operational aspects.Throughout this article, the problem…

The most fundamental integer and mixed-integer programming algorithm explained with PythonPhoto by Viktor Talashuk on UnsplashNumerical optimization problems are a fundamental tool in quantitative decision-making processes. Suppose a system can be described by a set of mathematical equations that adequately encompasses the impact of decision variables in objectives and constraints. In that case, one might search for the values of those decision variables that produce the best possible outcome using optimization…

Linear least-squares explained in detail and implemented from scratch in PythonPhoto by Ferdinand Stöhr on UnsplashMultiple linear regression is one of the most fundamental statistical models due to its simplicity and interpretability of results. For prediction purposes, linear models can sometimes outperform fancier nonlinear models, especially in situations with small numbers of training cases, low signal-to-noise ratio, or sparse data (Hastie et al., 2009). In these models, as their name suggests, a predicted (or…

Learn how to solve optimization problems in Python using scipy and pyomoPhoto by Denisse Leon on UnsplashThe knapsack problem is probably one of the first problems one faces when studying integer programming, optimization, or operations research. In this problem, from a given set of items, one must choose the most valuable combination to fit in a knapsack of a certain capacity (weight, volume, or both).Throughout this article, we will implement the knapsack problem in a relaxed form using scipy and in an integer form…

Solve single- and multi-objective optimization problems using Differential Evolution algorithmsPhoto by Brendan Church on UnsplashDifferential evolution (DE) (Storn & Price, 1997) was originally designed for scalar objective optimization. However, because of its simple implementation and efficient problem-solving quality, DE has been modified in different ways to solve multi-objective optimization problems.Throughout this article, we will see the algorithms and operators available in the Python package pymoode with…