## The use of Construction Heuristics

In this post, we’ll develop a construction heuristic to build reasonable (start) solutions for the knapsack problem. Why use Construction Heuristics? Construction heuristics offer the advantage of quickly leading to acceptable solutions. Unlike more complex optimization algorithms, they are easy to implement and require less computational power. These heuristics are particularly well-suited for handling large… Read more The use of Construction Heuristics

## A Metaheuristic Approach to Solving The Knapsack Problem

In the world of Operations Research and Optimization, solving complex problems efficiently is a constant pursuit. One such problem that has intrigued researchers and practitioners alike is the Knapsack Problem. In this blog post, we’ll delve into the fascinating realm of metaheuristics and guide you through the step-by-step process of applying these technique to tackle… Read more A Metaheuristic Approach to Solving The Knapsack Problem

## Vertex Coloring using ILP

In this post I’ll show you how to solve the vertex coloring problem to optimality using linear programming. Since the problem is NP-complete, there is no algorithm which can solve any problem instance in deterministic polynomial time. In a former post, I used constraint programming to find an optimal (minimal) vertex coloring. A popular greedy… Read more Vertex Coloring using ILP

## Solving Happy Cubes® on A micro:bit

In this post I’ll demonstrate the results of my most recent fun project on the micro:bit: An app to solve Happy Cubes®, a set of puzzles created in 1986 by the Belgian toy inventor Dirk Laureyssens. My kids were playing with these cubes and I was wondering, if the micro:bit could solve these cubes in… Read more Solving Happy Cubes® on A micro:bit

## Map Coloring Problem

This is a similar post as the one on Graph Coloring. However, this in this post I show an application of the graph coloring problem, allowing us to answer practical questions using graph theory. In this post we’ll first tackle a map coloring problem manually, then we’ll use a MiniZinc constraint programming script to validate the solution found.

## Graph Coloring Problem

A node coloring is valid or admissible if any two adjacent nodes do not have the same color. If a graph is colorable, there is a smallest number such that the graph is node colorable. This number is called the chromatic number of the graph and is usually denoted by . The problem to identify… Read more Graph Coloring Problem

## TSP Miller-Tucker-Zemlin Subtour Elimination Constraint

In this post we want to try to provide a solution to solve the Traveling Salesman Problem (TSP) using linear programming. The post is based on this excellent video from Mr. Michel Bierlaire at the EPFL. A good written documentation of the Miller Tucker Zemlin Constraint can be found here. What is a TSP? The… Read more TSP Miller-Tucker-Zemlin Subtour Elimination Constraint

## Solve Knapsack Problem with Heuristics in R

In this post I’ll show a way how to solve the Knapsack Problem applying a simple greedy improvement heuristic and how to implement it in R. What is the Knapsack Problem? On Wikipedia, you find the following definition: “The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a… Read more Solve Knapsack Problem with Heuristics in R

## A Sudoku Solver in a few Lines of Code – Or the Power of Recursive Programming

In this post I want to demonstrate the power of recursive programming by programming a sudoku solver in Python. The complete sourcecode can also be downloaded here. Although I like solving Sudokus by hand, I’m far away from being a professional Sudoku solver. Usually I get the medium-ones solved, however, since I always want to… Read more A Sudoku Solver in a few Lines of Code – Or the Power of Recursive Programming

## Calculate an MST with Ant Colony Optimization in Python

Ant Colony Optimization is an old but still often applied construction heuristic to develop solutions using nature inspired behavior. The heuristic mimics the behavior of ants when finding shortest paths to between their nests and some kind of attraction, i.e. a food-source. The main idea are the pheromone trails, which ants leave behind, when travelling… Read more Calculate an MST with Ant Colony Optimization in Python