Optimization Task

An Optimization Task is a search task for an optimal solution from within a search space based on a utility function.

• AKA: Cost Function Optimization, Numerical Optimization.
• Context:
  • Task Input: Search Space, and a Cost Function.
  • Task Output: Optimal Solution.
  • ...
  • It can range from being a Minimization Task to being a Maximization Task, depending on its optimization goal.
  • It can range from being a Combinatorial Optimization Task to being a Continuous Optimization Task, depending on its variable type.
  • It can range from being an Exact Optimization Task to being an Approximate Optimization Task, depending on its solution precision.
  • It can range from being an Unconstrained Optimization Task to being a Constrained Optimization Task, depending on its solution constraints.
  • ...
  • It can be solved by an Optimization System through optimization algorithms.
  • ...
• Examples:
  • Combinatorial Optimization Tasks, such as:
    • Vehicle Routing Problem for route optimization.
    • Traveling Salesman Problem for path optimization.
    • Minimum Spanning Tree Problem for network optimization.
    • Knapsack Packing Problem for resource allocation.
  • Continuous Optimization Tasks, such as:
    • Linear Programming Task for linear systems.
    • Maximum Likelihood Estimation Task for statistical inference.
  • Parameter Optimizations, such as:
    • Machine Learning Parameter Optimization for model tuning.
    • Control System Parameter Optimization for system response.
  • Industrial Process Optimizations, such as:
    • Manufacturing Process Optimization for production efficiency.
    • Chemical Process Optimization for yield maximization.
  • ...
• Counter-Example(s):
  • Random Search Task, which does not target optimal solutions.
  • Constraint Satisfaction Task, which finds feasible solutions rather than optimal solutions.
  • Classification Task, which categorizes rather than optimizes.
  • Pattern Matching Task, which identifies rather than optimizes.
• See: Constraint Satisfaction, Function Selection Task, Optimization Task Decomposition, Search Algorithm, Mathematical Programming.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/optimization_problem Retrieved:2015-6-13.
  • In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories depending on whether the variables are continuous or discrete. An optimization problem with discrete variables is known as a combinatorial optimization problem. In a combinatorial optimization problem, we are looking for an object such as an integer, permutation or graph from a finite (or possibly countable infinite) set.

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