Learn in the textbookApplications of Discrete Mathematics (Queuing and Optimization)
DefinitionAn optimization problem (最適化問題) seeks, among the solutions that meet the conditions that must hold (constraints), the one (optimal solution) that makes a measure of goodness (objective function), such as maximum profit or minimum cost, as good as it can be.
ExplanationWhen there are only a few candidate solutions, listing them all and comparing their objective function values reveals the optimal solution. When there are many, methods such as linear programming express the conditions and the goal as equations and solve them. Deciding the order in which to carry out jobs, or the order in which to visit several locations, are also examples of optimization problems.
AnalogyLike choosing what to pack so that your suitcase carries as many useful items as it can hold.
Memory hookThe English word optimization comes from the Latin optimus, meaning “best”. Whether the aim is a maximum or a minimum, both count as the “best”.