Table of Contents


In this document
What is Optimization?ExamplesDecision-Making ProblemsOptimization TechniquesExternal ResourcesTextbooksVideosPodcasts

Last Updated: 2/6/2023

Optimization

What is Optimization?

Optimization problems in artificial intelligence involve finding the best solution to a problem given certain constraints or objectives. These problems can be broadly classified into two categories: convex optimization problems and non-convex optimization problems.

  • Convex optimization problems are problems where the objective function is convex, and the constraints are linear. These problems are relatively easy to solve because only one global minimum can be found using algorithms like gradient descent.
  • Non-convex optimization problems are problems where the objective function is non-convex, or the constraints are non-linear. These types of problems can be more difficult to solve, because there may be multiple local minima or maxima that can be found, and it may not be clear which one is the global minimum or maximum.

Many different algorithms and techniques can be used to solve optimization problems in artificial intelligence, and the choice will depend on the problem's specific characteristics and the analysis goals. Some common methods include gradient descent, stochastic gradient descent, and simulated annealing. In summary, optimization problems in artificial intelligence involve finding the best solution to a problem given certain constraints or objectives. These problems can be convex or non-convex, and there are many different algorithms and techniques that can be used to solve them.

Imagine you are planning a road trip, and you want to find the shortest route between two cities. One way you could do this is by using optimization. You could start by defining the objective function, which in this case might be the route's total distance. You might also define constraints, such as the maximum driving time per day, or the maximum budget for fuel and accommodation. You could then use an optimization algorithm, like gradient descent, to find the route that minimizes the distance while satisfying the constraints. This might involve making small adjustments to the route and evaluating the effect on the objective function until you find the shortest route that meets your constraints. By using optimization, you can find the best solution to the problem of finding the shortest route between two cities, given certain constraints and objectives. This is similar to how optimization is used in artificial intelligence to find the best solution to a problem given certain constraints or objectives.

There are many robots that implement optimization to perform tasks or solve problems. Optimization algorithms can be used to find the best way for a robot to achieve a specific goal, given certain constraints and objectives. For example, a robot might use optimization to find the most efficient path between two points or to determine the best way to manipulate an object. Optimization can also be used to adjust the parameters of a robot's control system to improve its performance on a specific task.

Examples

  1. Supply chain optimization: Companies often use artificial intelligence optimization to improve the efficiency of their supply chain operations. For example, a retailer might use optimization to find the best way to stock its stores, based on customer demand, supplier lead times, and transportation costs. This can help the retailer minimize waste and reduce costs while ensuring that it has the right products in the right stores at the right time.
  2. Financial portfolio optimization: Investors and financial advisors can use artificial intelligence optimization to find the best mix of assets for a given investment portfolio. This might involve optimizing for factors like risk, return, and diversification, to maximize the portfolio's performance.
  3. Manufacturing optimization: Manufacturers can use artificial intelligence optimization to improve the efficiency of their production processes. For example, a manufacturer might use optimization to find the best way to schedule its production line, based on factors like machine availability, labor availability, and product demand. This can help the manufacturer reduce costs and improve its overall efficiency.
  4. Traffic optimization: Cities and transportation authorities can use artificial intelligence optimization to improve traffic flow in their communities. This might involve optimizing traffic signals, routing algorithms, and public transportation schedules to reduce congestion and improve overall mobility.
  5. Energy optimization: Companies and individuals can use artificial intelligence optimization to improve the efficiency of their energy use. For example, a building owner might use optimization to find the best way to control the heating, ventilation, and air conditioning systems, based on factors like weather, occupancy, and energy prices. This can help the owner reduce energy costs and reduce its carbon footprint.

Decision-Making Problems

Optimization can solve multi-armed bandit problems, a type of online decision-making problem. In a multi-armed bandit problem, there are multiple options or "arms" available, and the goal is to choose the best arm in each round to maximize a reward over time. Those algorithms are based on balancing exploration (trying out different arms) with exploitation (choosing the best-performing arm based on past observations). These Algorithms can be used to solve a wide range of problems where multiple options are available, and the goal is to maximize a reward over time. Some examples of these types of problems include online advertising, where the goal is to choose the best ad to show to a user in each round to maximize clicks or conversions; and online recommendation systems, where the goal is to choose the best item to recommend to a user in each round to maximize engagement or purchases. Upper Confidence Bound (UCB) and Thompson Sampling are both algorithms that can be used to solve multi-armed bandit problems, and of course that we are going to explain them later.

Optimization Techniques

Here are a few more optimization techniques used in artificial intelligence:

  1. Evolutionary algorithms: Evolutionary algorithms are a class of optimization techniques inspired by natural evolution principles. They involve generating a population of candidate solutions and iteratively improving them over time through selection, reproduction, and mutation. Evolutionary algorithms are often used to solve problems where it is difficult or impossible to use traditional optimization methods.
  2. Particle swarm optimization: Particle swarm optimization is a population-based optimization technique inspired by the behavior of swarms of animals, like birds or bees. It involves generating a population of particles that move around searching for the best solution to a problem. The particles update their position based on the positions of their neighbors and the overall best solution found so far. Particle swarm optimization is often used to solve problems with many local minima or maxima.
  3. Ant colony optimization: Ant colony optimization is a swarm intelligence optimization technique inspired by ants' foraging behavior. It involves generating a population of virtual ants that search for the best solution to a problem by following a series of pheromone trails. The ants update the pheromone trails based on the quality of the solutions they find, and the best solution is chosen based on the strength of the pheromone trails. Ant colony optimization solves problems where the search space is large and complex.
  4. Simulated annealing: Simulated annealing is a probabilistic optimization technique inspired by the process of annealing in metallurgy. It involves generating a random initial solution and improving it over time through random perturbations and accept-or-reject steps. The acceptance probability is based on a temperature parameter that decreases over time, allowing the algorithm to escape from local minima and explore the search space more broadly. Simulated annealing is often used to solve problems where the search space is large and complex.
  5. Nelder-Mead method: The Nelder-Mead method is a simplex-based optimization technique that involves generating a set of points in the search space and iteratively improving them over time through a series of reflections, expand, contract, and shrink steps. The method is based on constructing and iteratively improving a simplex, or a set of points in the search space until it converges to the optimal solution. The Nelder-Mead method is often used to solve problems where the objective function is continuous and differentiable.

External Resources

Textbooks

Chapter 6 (Case Study - The MAB Problem)

Genetic algorithms are one of the tools we can use to apply machine learning to finding good, sometimes even optimal, solutions to problems that have billions of potential solutions. They use biological processes in software to find answers to problems that have really large search spaces by continuously generating candidate solutions, evaluating how well the solutions fit the desired outcome, and refining the best solution.

Videos

Podcasts

In this week's mini episode, Linhda and Kyle discuss Ant Colony Optimization - a numerical / stochastic optimization technique which models its search after the process ants employ in using random walks to find a goal (food) and then leaving a pheremone trail in their walk back to the nest. We even find some way of relating the city of San Francisco and running a restaurant into the discussion.

If modeling is about predicting the unknown, optimization tries to answer the question of what to do, what decision to make, to get the best results out of a given situation. Sometimes that's straightforward, but sometimes... not so much. What makes an optimization problem easy or hard, and what are some of the methods for finding optimal solutions to problems? Glad you asked! May we recommend our latest podcast episode to you?
Prev: Clustering
Next: Coming soon!