Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or ...

组合优化问题 (Combinatorial optimization problem，COP) 是一类在离散状态下求 极值 的最优化问题，其数学模型如下所示： \text {min}F (x) \\ \text {s.t.} G (x) \geq 0 \\ x \in D \\ 其中 x 为决策变量、 F (x) 为 目标函数 、 G (x) 为约束条件， D 表示离散的决策空间，为有限个点组成的集合。 ... 其决策空间为 有限点集，直观上可以通过 穷举法 得到问题的最优解，但是由于可行解数量随问题规模呈指数型增长，无法在 多项式时间 内穷举得到问题的最优解。

组合优化的主要目标是设计出解决这类问题的有效算法。 在计算机科学中，只要算法的基本步骤数在输入的大小上增长为多项式，算法就被称为“有效的”。 NP问题： 不能确定能否在多项式时间内找到解，但是可以在多项式时间内验证解是否正确。 赞同 258. 6 条评论. 分享. 喜欢. 收藏. 申请转载. 主要是参考以下三篇文章： [1] Learning Combinatorial Optimization on Graphs: A Survey with Applications to Networking [2] 基于深度强化学习的组合优化研究进展 [3] Learning to Solve …

组合优化（Combinatorial Optimization）问题的目标是从组合问题的 可行解 集中求出 最优解，通常可描述为：令Ω= {s1，s2，…，sn}为所有状态构成的 解空间，C (si)为状态si对应的 目标函数 值，要求寻找最优解s*，使得对于所有的si∈Ω，有C (s*)=minC (si)。

linear program is an optimization problem over real-valued variables, while this course is about combinatorial problems, that is problems with a nite number of discrete solutions. The reasons why we will study linear programming are that.

Therefore, to solve the problem, we need only to study partitions of this special type, i.e., a combinatorial optimization problem. Due to above, we do not make a clear cut to exclude other parts of dis-crete optimization. Actually, this book is methodology-oriented. Problems are selected to illustrate methodology.

组合优化 （英語： Combinatorial optimization）是数学优化的一个子领域，在应用数学和理论计算机科学的领域中，组合优化是在一个有限的对象集中找出最优对象的一类问题。

Combinatorial optimization is an emerging field at the forefront of combinatorics and theoretical computer science that aims to use combinatorial techniques to solve discrete optimization problems. A discrete optimization problem seeks to determine the best possible solution from a finite set of possibilities.

Combinatorial Optimization problem Given a set of elements E = {1, 2, ..., n} Set of feasible solutions F Each element of F is a subset of E. Objective function f(x): F ®R. In the minimization version the problem consists in Finding x*Î F, such that f(x*) £ f(x) " x Î F. Discrete Optimization Graph models Combinatorial Optimization 2

Combinatorial optimization is a field of mathematical optimization that deals with problems where the objective is to find the best solution from a finite set of possible solutions. These problems ...