What is the difference between machine learning and combinatorial optimization?
Historically, the term “artificial intelligence” was used to refer to several distinct fields of computer science, including machine learning, computer vision, natural language processing, computational biology, artificial neural networks and combinatorial optimization. But thanks to the meteoric rise of artificial neural network based programs like ChatGPT, neural networks based machine learning has become almost synonymous with AI in the public imagination. As a result of the recent media frenzy surrounding companies like OpenAI and DataRobot, combinatorial optimization has taken a backseat to machine learning. Yet this more subtle form of artificial intelligence has its own unique advantages. Combinatorial optimization is still king in applications like logistics, resource allocation, project scheduling, and network design.
CO vs ML
Machine learning involves the creation of algorithms that can learn patterns and relationships from data without being explicitly programmed. In machine learning, you train a model on a dataset to make predictions or decisions on new, unseen data. The problem with machine learning is that it’s dependent on large data sets for training and evaluation, and its overall performance is greatly influenced by the quality and quantity of the training data. Unlike machine learning, with combinatorial optimization, the optimization process itself is not necessarily data-dependent.
The main objective in combinatorial optimization is to find the best solution from a massive and not easily written down set of possible solutions, given rules for what makes a feasible solution. This typically involves identifying the optimal combination of variables that satisfy certain constraints and optimize a given objective function. Combinatorial optimization focuses on problems where the solution is a combination of discrete variables. It excels at difficult-to-solve problems that become considerably harder to solve with each additional variable, like the traveling salesman problem, job scheduling, and the knapsack problem. Combinatorial optimization employs algorithms that systematically explore the solution space to find the best combination of variables. Common techniques include dynamic programming, integer linear programming, dantzig-wolfe decomposition, greedy algorithms, and metaheuristic approaches.
The primary difference between the two is that a combinatorial optimization product comes with its algorithm pre-built, while a machine learning program has to be continuously trained and refined before it can be of use to anyone, and it still sometimes gets things wrong.
How can combinatorial optimization be used to create an AI scheduling assistant?
With scheduling and logistics, the most desirable outcome is absolute. You want to make as much money as you can with the smallest possible commute and in as little time as possible. This makes it an ideal candidate for combinatorial optimization. The desired goal isn’t subjective, like writing a grad school paper. It can be clearly measured, but getting there isn’t so simple.
Let’s look at personal trainers as an example. A single trainer has multiple clients with limited availability, who train in different locations, and have different budgets. As such, this trainer needs to create a schedule that considers travel, pay, and availability to ensure they’re making as much money as possible. This may sound simple if you have three people training in two locations with flexible schedules and an almost equal ability to pay, but as you add variables like more clients, more training locations, more schedule constraints, and unequal abilities to pay this problem becomes exponentially harder and nearly impossible to solve using mental math — meaning your actual earnings will almost always be less than your potential earnings.
Because we’re given tangible constraints (cost, distance, wages, etc.) and a clearly defined goal, finding one set of algorithms that solves everyone’s problem in absolute terms is possible. Granted it’s extremely difficult, but it can be done, eliminating the need for machine learning.
Using a set of well formulated algorithms, you can then construct an interface for scheduling that would be able to provide the optimal schedule for all service providers (or at least service providers within a certain niche). This is what large firms like Amazon and UPS use to manage their scheduling and logistics like clockwork work. And for the first time ever, this same technology is now available to small service providers through Hiero AI.
How does this technology make Hiero unique from existing scheduling apps, like Calendly and Google Calendar?
Right now, almost no other scheduling service uses AI to create your schedule. Instead scheduling happens randomly and as a result can make scheduling even more difficult. This also means prices are charged at a flat rate and not adjusted by demand, and that commuters might waste time and gas by zig zagging back and forth across the city.
Google and Calendly plan to roll out AI updates that will most likely use ML to create your schedule, but will lack the exactitude of combinatorial optimization.
Conclusion
By using combinatorial optimization to create their schedules, small service providers can lower costs and maximize profits, enabling them to compete with large companies who have access to high-powered logistics tools.
Hiero AI is now available for personal trainers in the form of a mobile app. This app helps trainers find clients and better manage their schedule. Future products are being designed to cater to the specific needs of other small service providers.
About the Author
Dr. Julian Yarkony earned his PhD from the University of California Irvine and has developed multiple novel techniques in optimization and artificial intelligence. For years, Julian has worked as a consultant with large airlines to help them with scheduling, routing, and logistics. Now he has taken a lifetime of experience in optimization and applied it to creating innovative solutions to help small service providers better manage their business. Along with his co-founder, Dr. David Pepper, Julian established Hiero AI in 2022.
