yet another source of inspiration…
In today’s blog post, let’s dive into the fascinating realm of solving Sudoku puzzles using Mixed Integer Linear Programming (MILP). Check this previous post to see how a sudoku solver can be developed in python using dynamic programming and backtracking. Sudoku, a classic logic-based number placement puzzle, has long captivated minds around the globe with… Read more How to Develop a Sudoku Solver Using Mixed Integer Linear Programming
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
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
In the dynamic world of Python scripting, efficiency is key. Today, let’s delve into the transformative realm of parallelization using Numba’s JIT (Just-In-Time) compiler. Brace yourselves as we explore how this powerful tool not only compiles your code on the fly but also paves the way for parallel execution. Join us on a journey to harness the full potential of your Python scripts through the magic of Numba’s parallelization capabilities.
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
I owe this task to Ruedi, a regular tennis player. The Tennis Court Problem (TCP) is about the following task. At the beginning of outdoor tennis, the court lines must always be cleaned first. The sweeping set is often placed in one of two typical locations, usually either on one side of the net or… Read more The Tennis Court Problem (TCP)
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
In this post I show you how to solve the TSP problem using integer linear programming and Google OR-Tools for mathmatical modelling in Python. If you’re not yet familiar to the TSP and want to dig deeper, find out more here. It is one of the oldest and best explored problems in the field of… Read more Solving a TSP with Linear Programming and Google OR-Tools in Python
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
In another post I demonstrated how to develop a heuristic to solve the knapsack problem. We managed to solve the problem quite well and had an optimality gap of about 1%, that is, our solution was 1% away from the optimal solution. Here I’d like to demonstrate, how simple it is to solve the Knapsack… Read more Find optimal Solution to Knapsack Problem with Linear Programming in R