While Artificial Intelligence (AI) has been adding value to ours lives in many ways, it remains a tool that can be harmful in case of exaggeration or bad usage. To deal with the second aspect, several big tech corporations initiated AI ethics boards and/or departments. While the role differs from a company to another, these entities are generally supposed to oversee, check, and suggest ethical initiatives that will foster the development of responsible AI. Still, one may wonder whether such entities are playing a significant role or just enhancing the brand image of these companies.

When applied to tackle real life problems, mathematics becomes more beautiful and fascinating. This is the case of operations research, a subfield of applied mathematics, where problems are formulated mathematically before being solved. Over the previous years, this subfield flourished in a parallel to the development of computational power. Nowadays, many organizations are using operations research to design their operational, tactical, and even strategic decisions. If successful, it leads to significant cost reduction and/or profit increase. The problems tackled usually involve assignment, scheduling, routing, pairing, partitioning, as well as other tasks within a specific time and/or space framework.

In this…

There are many exciting questions that anyone can spend a part of his life, if not his whole life, trying to solve. Their prizes are quite attractive. Their complexity is not. Solving some of them equals one million dollar each. In mathematics, the list of unsolved problems, called the millennium prize problems, includes P versus NP, Hodge conjecture, Riemann hypothesis, Yang–Mills existence and mass gap, Navier–Stokes existence and smoothness, and Birch and Swinnerton-Dyer conjecture.

In this article, I want to review the excitement of the first one, i.e. P versus NP problem, which I witness everyday implicitly throughout my research…

There is a huge synergy between Operations Research (OR) and Machine Learning (ML). While some ML researchers are using OR to improve further their learning, some OR researchers are using ML to incorporate learning in the optimization process with the expectation of significant gain in terms of time, gap, as well as other metrics.

In this article, I will go through some stories into which machine learning is leveraged to tackle optimization problems. I like calling it operations research learning (ORL). These stories provide insights about the way synergy is built, transferred among problems as well as prospective improvements opportunities…

Between early morning squirrels and late night raccoons, the Cirque du Soleil city is definitely one of the most exciting “Research/Sport” training spots worldwide, especially in the fields of artificial intelligence (AI) and operations research (OR), which have been thriving over the last decades. Being personally excited about these two topics, and in particular the latter that has many sub-fields, I would go for calling this beautiful city: the **Column Generation** (CG) capital.

In this article, I will go through this extremely powerful algorithm that proved over the previous years its efficiency in tackling large scale optimization problem. …

Humans have been enjoying convex optimization (CO) for many years compared to the few contexts where they had to deal with non-convex optimization (NCO). However, over the last decade, non-convex optimization became more crucial and important than before. In fact, with the emergence of deep learning (DL), researchers needed to deal with non-convex optimization more and more given the benefits hidden behind its complexity.

In this article, I will first present both convex and non-convex optimization before getting into some interesting insights related to non-convex optimization. The objective is highlighting both benefits and challenges and see whether there are trade…

The bottleneck assignment problem is an interesting problem in combinatorial optimization. It has many variants and is as well a variant of the assignment problem. In general, the problem is defined based on a set of agents that must be assigned to a set of tasks while ensuring that each task is done by one agent. Each assignment has a cost and we seek the minimization of the maximum cost within the individual assignments. In other words, we want an assignment that will minimize the maximum individual cost. The same problem definition goes for the profit maximization case. In the…

Humans face different problems either in business or in daily life. The complexity of problems differ based on many factors. Hence, some problems are quite easy to solve while others are more difficult to tackle like the miniature of the vehicle routing problem (VRP) shown in the figure below. Here, we might be interested to find the best solution. For instance, a solution that provides the highest revenue or the lowest cost.

With the interest highlighted above, being a sub-component of applied mathematics, mathematical modeling takes place. Still, it is intriguing to wonder whether: any real world problem can be…

While the end of another decade is approaching, it’s quite interesting to witness how the field of machine learning (ML), especially deep learning (DL), has been evolving over the last years. Furthermore, while reading Neural Networks and Deep Learning, one of the observations caught my attention:

While many of us didn’t witness the structuring of many fields such as mathematics, medicine, we are quite lucky to witness a similar phenomenon in ML, and more broadly artificial intelligence (AI). While it’s is still possible to master several fields of ML, many are shifting towards specializations such as reinforcement learning and convolutional…

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