Find the optimal solution from the feasible solution set of the combination problem
The combinatorial optimization problem isoptimization problem Class of.Optimization problems seem to naturally fall into two categories:continuous variable The other isdiscrete variable Problems.A problem with discrete variables is called combinatorial.In the problem of continuous variables, it is generally to find a group of real numbers, or a function;In the combination problem, it is from aInfinite setOr look for an object in a countable infinite set - typically an integer, a set, a permutation, or a graph.Generally, these two kinds of problems have quite different characteristics, and the methods of solving them are also very different.
Source: Combinatorial Optimization Algorithms and Complexity,Higher Education Press, 1988, C.H. Papadimitriou, K. Steiglitz (translated by Liu Zhenhong and Cai Maocheng)
Chinese name
Combinatorial optimization
Foreign name
Combinatorial Optimization
Interpretation
Find the optimal solution from the feasible solution set of the combination problem
The goal of combinatorial optimization problem is tofeasible solutionCentralized solutionOptimal solution, usually described as: let Ω={s1, s2,..., sn} be composed of all statesSolution space, C (si) is corresponding to state siobjective function Value, it is required to find the optimal solution s *, so that for all si ∈Ω, there is C (s *)=minC (si).Combinatorial optimization is an important branch of operations research, which often involves sorting, classification, screening and other issues.
The description of these problems is very simple and has strong engineeringRepresentativenessHowever, the optimization solution is very difficult, the main reason is that the algorithms for solving these problems need very longRun TimeAnd greatstorage space So that it is impossible to implement it on existing computers, namely the so-called“Combined explosion”。It is the representativeness and complexity of these problems that arouse people's interest in the research of combinatorial optimization theory and algorithms.
