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Single-objective optimization problem

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

An optimization problem with one objective function whose value is optimized.

A single-objective optimization problem has one objective function to maximize or minimize. In ticket pricing, profit is the sole objective: a quadratic profit function produces an optimal ticket price of $155 and net profit of $130,500. section 1.3.2

The distinction is the number of objectives. Designing an electric vehicle with both acceleration time and EPA driving range creates a multi-objective problem, especially when the objectives conflict. section 1.3.2

Political districting

A genetic algorithm assigns neighborhoods to districts while minimizing overpopulated and underpopulated districts. The model uses one objective, three constraints, integer decision variables, population data, an adjacency matrix, and an allowable population margin. Ideally, the objective reaches zero. section 8.8

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes
Defines the single-versus-multiple-objective distinction and demonstrates mathematical and genetic-algorithm implementations.
Examples
Uses ticket pricing, electric-vehicle design, and political districting as concrete optimization examples.
What you can do after
Apply it via pymoo by defining one objective, constraints, variable bounds, and a genetic algorithm.
How it connects
Connects objective functions with decision variables, constraints, genetic algorithms, and multi-objective optimization.

Related concepts

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.