Data Pattern Pro

Optimization

Optimization resources

The original reference set from Data Pattern Pro: how to choose an optimization method, how optimization problems are classified, whether linear or integer programming fits your problem, memoization, and MILP reframed as a policy.

Resource 01

Optimization Methods Decision Flowchart

Resource on how to select the optimization method depending on your problem situation and goals. The following is a taxonomy and flowchart for selecting your model along with several software packages that can be used to implement the model.

Optimization decision framework flowchart. Optimization methods split into combinatorial and continuous branches; combinatorial into exact or optimal methods (mixed-integer linear programming, dynamic programming, branch and bound) and approximate methods (heuristics such as nearest neighbor, greedy algorithms and hill climbing; metaheuristics such as simulated annealing, tabu search and evolutionary algorithms); continuous into linear (simplex, interior point) and nonlinear (gradient-based, gradient-free, global and local search), each annotated with software packages such as Gurobi, CPLEX, OR-Tools, PuLP, AMPL, SciPy and Pyomo.
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Resource 02

Optimization Classification Hierarchy

The world of optimization is vast and intriguing! This hierarchy can help professionals quickly grasp the various facets of optimization problems. If you're in a role that deals with decision-making, this is fundamental knowledge!

Optimization classification hierarchy. Optimization problems classified by number of objectives (single, multi-objective), number of constraints (unconstrained, equality, inequality), function forms (linear, nonlinear), landscape of objective functions (unimodal, multimodal), design variable types (discrete, continuous, mixed), and certainty in variables and objectives (deterministic, stochastic), with definitions, implications and examples for each.
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Resource 03

Is Linear/Integer Programming Suitable?

Use the following guide to determine if you can use linear/integer programming.

Decision guide: Is linear or integer programming suitable? If the objective function is not linear, or the constraints are not linear, consider nonlinear programming or other methods. If all decision variables are continuous, use linear programming. If some are integer or binary, use mixed-integer programming (MIP); if all are integer or binary, use integer programming (IP); otherwise consider other methods.
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Resource 04

Memoization

A simple example of memoization optimization technique using Fibonacci Numbers

Memoization illustrated with Fibonacci numbers: the recursive definition F(0)=0, F(1)=1, F(n)=F(n-1)+F(n-2); a Python fib function that stores results in a memo dictionary; and the recursion tree for Fib(6), in which repeated subproblems such as Fib(4) and Fib(3) are computed once and then retrieved. Memoization reduces the time to compute Fibonacci numbers from exponential to linear, at the cost of some memory.
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Resource 05

Rethinking MILP as a Policy

Article here: Rethinking MILP as a Policy: Embedding MILP in Sequential Decision Analytics

A 30-page paper (version 1.1, July 18, 2025) on treating a mixed-integer program not as a one-shot plan but as one component of a decision policy that is re-solved as information arrives, evaluated in simulation, and tuned like any other policy.

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