Optimization Archives

Augmented epsilon constraint method: Multi-goal optimization with Pulp in Python

In previous posts, we have discussed using PuLP in python for the implementation of multi-objective linear optimization methods such as maximizing for one objective, then adding it as a constraint, and solving for the other objective (or applying a scalar […]

Scalarizing multi-objective optimization problems: Method comparison

I already introduced various coding examples implementing multi-objective optimization. In these examples I implemented different strategies for searching a multi-objective optimum. One of these strategies was based on scalarizing multiple objectives into a single objective function using weights for each […]

Optimization for Machine Learning: Shallow and Deep Supervised Learning Models

In this post, I explain how supervised learning models in machine learning use single or multiple neurons in a single layer (shallow learning) or multiple neurons in multiple layers (deep learning) to generate a real, binary, or integer value beneficial […]

Handling deep data uncertainty using robust optimization

In this post, I describe how deeply uncertain parametric data can be controlled in an optimization model to gain conservative solutions and decisions. The investigated robust optimization approach can lead to least, partially, or fully conservative solutions by paying the […]

Constraint programming for work scheduling with Google OR-Tools

In previous posts I have already introduced Google OR tools for linear programming. In this post I want to demonstrate the capabilities of Google OR tools for constraint programming. More specifically, I will solve a job scheduling problem using constraint […]

Linear integer programming with Google ortools in Python

In a several other posts on Google’s ortools module in Python I have already solved the linear optimization problem stated below. The problem is a continuous problem as all optimization variables are from a continuous solution space. I could think […]

Lean coding of simple linear optimization ortools models in Python

In a previous post on Google’s ortools module in Python I solved the linear optimization problem stated below: The code written in my previous post can be reduced to fewer lines of code, resulting in lean code. In this post […]

Simple linear programming with Google ortools in Python

In other posts I have demonstrated how one can solve e.g. linear optimization problems using modules such as SciPy and PuLP in Python. In R I have also demonstrated e.g. the lpSolve package. In this post I want to demonstrate […]

Categorization of optimization problems

In other posts I have e.g. demonstrated how to implement linear programming in R and Python. I have also shared examples on e.g. gradient-descent optimization for non-linear problems. In this post I want to provide an overview of various types […]

Multi-objective linear optimization with weighted sub-problems, using PuLP in Python

In my most recent post on linear programming I applied PuLP for solving below linear optimization problem, using two approaches. Approach #1 was based on solving a sub-problem with one objective only first, then adding the optimal outcome of that […]

Multi-objective linear optimization with PuLP in Python

In some of my posts I used lpSolve or FuzzyLP in R for solving linear optimization problems. I have also used PuLP and SciPy.optimize in Python for solving such problems. In all those cases the problem had only one objective […]

Continuous linear optimization in PuLP (Python)

In a previous post I demonstrated how to solve a linear optimization problem in Python, using SciPy.optimize with the linprog function. In this post I want to provide a coding example in Python, using the PuLP module to solve below […]

Solving linear problem with fuzzy constraints by sampling beta with FuzzyLP in R

In a previous post I demonstrated how to use crispLP to solve a simple linear optimization problem with well-defined objective function and constraints. I have also demonstrated how to solve a fuzzy linear optimization problem with uncertain constraints, i.e. fuzzy constraint […]

Linear optimization with fuzzy constraints conducted in R with FuzzyLP

Using the FuzzyLP package in R I have demonstrated simple linear optimization of a well defined linear problem using the crispLP function in a previous post. In that example basic simplex algorithm was applied to solve the problem. In this […]

Simple linear problem with FuzzyLP, using crispLP and basic simplex

In previous posts I have demonstrated how to solve linear programs in R using lpSolve – or in Python using SciPy.optimize. In this coding example I want to show how to conduct simple linear optimization using the FuzzyLP package. FuzzyLP […]

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