Introduction to Orion

Q: WHAT IS ORION DESIGNED TO DO?

A: SOLVE COMBINATORIAL OPTIMIZATION PROBLEMS.

Combinatorial optimization is a branch of optimization in applied mathematics and computer science, related to operations research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering.

Combinatorial optimization problems are characterized by having variables that are naturally discrete, where a user wants to find a particular configuration of these variables that optimizes something of importance to the user. There are many applications of combinatorial optimization. Some important applications rely directly on minimizing or maximizing an important optimization objective, including:

• scheduling and logistics
• constraint satisfaction
• optimization of return from portfolios of investment instruments
• supply chain performance
• network optimization

The operations research community has developed many instances of optimization methods that improve the performance of any business process for which quantitative measures are available. You can find a good introduction to optimization at www.scienceofbetter.org.

Combinatorial optimization problems are also often embedded (and are frequently the computational bottleneck) in problems that seem to have nothing to do with optimization. Predictive algorithms that learn from historical data and prior assumptions are, at their core, optimization problems that seek to minimize an appropriately defined error function.

Many search problems are also optimization problems. When searching for an object (perhaps stored in a database or on the web), we can define a compatibility function and seek the object that is most compatible with the search query. In other words, we can maximize the compatibility function over the space of objects.

Current approaches to solving combinatorial optimization problems typically rely on heuristic algorithms like simulated annealing, genetic algorithms, and tabu search.