模拟退火算法解决np_P和NP问题与解决方案| 演算法

模拟退火算法解决np

P问题 (P Problems)

P is the set of all the decision problems solvable by deterministic algorithms in polynomial time.

P是多项式时间内确定性算法可解决的所有决策问题的集合。

NP问题 (NP Problems)

NP is the set of all the decision problems that are solvable by non - deterministic algorithms in polynomial time.

NP是可由多项式时间内的非确定性算法解决的所有决策问题的集合。

Since deterministic algorithms are just the special case of non - deterministic ones, so we can conclude that P is the subset of NP.

由于确定性算法只是非确定性算法的特例，因此我们可以得出结论，P是NP的子集。

Relation between P and NP

P和NP之间的关系

NP难题 (NP Hard Problem)

A problem L is the NP hard if and only if satisfiability reduces to L. A problem is NP complete if and only if L is the NP hard and L belongs to NP.

当且仅当可满足性降低到L时，问题L才是NP难。只有当L是NP难且L属于NP时，问题NP才是完整的。

Only a decision problem can be NP complete. However, an optimization problem may be the NP hard. Furthermore if L1 is a decision problem and L2 an optimization problem, then it is possible that L1 α L2. One can trivially show that the knapsack decision problem reduces to knapsack optimization problem. For the clique problem one can easily show that the clique decision problem reduces to the clique optimization problem. In fact, one can also show that these optimization problems reduce to their corresponding decision problems.

只有决策问题才能完成NP。但是，优化问题可能是NP难题。此外，如果L1是决策问题，L2是优化问题，则L1αL2是可能的。可以简单地表明，背包决策问题可以简化为背包优化问题。对于群体问题，可以很容易地表明，群体决策问题可以简化为群体优化问题。实际上，还可以证明这些优化问题可以简化为相应的决策问题。

NP完整性问题 (NP Completeness Problem)

Polynomial time reductions provide a formal means for showing that one problem is at least as hard as another, within a polynomial time factor. This means, if L1 <= L2, then L1 is not more than a polynomial factor harder than L2. Which is why the “less than or equal to” notation for reduction is mnemonic. NP complete are the problems whose status are unknown.

多项式时间缩减提供了一种形式化的方法，用于显示在多项式时间因子内一个问题至少与另一个问题一样困难。这意味着，如果L1 <= L2，则L1不大于比L2难的多项式因数。这就是为什么“小于或等于”减少表示法是助记符的原因。 NP完全是状态未知的问题。

Some of the examples of NP complete problems are:

NP完全问题的一些示例是：

1. Travelling Salesman Problem:

1. 旅行商问题：

Given n cities, the distance between them and a number D, does exist a tor programme for a salesman to visit all the cities so that the total distance travelled is at most D.

给定n个城市，它们之间的距离与数字D确实存在一个推销员计划，以供销售人员访问所有城市，这样总行驶距离最多为D。

2. Zero One Programming Problem:

2.零编程问题：

Given m simultaneous equations,

给定m个联立方程，

3. Satisfiability Problem:

3.满意度问题：

Given a formula that involves propositional variables and logical connectives.

给定一个涉及命题变量和逻辑连接词的公式。

A language L is the subset [0, 1]* is NP complete if,

语言L是子集[0，1] *是NP完整，如果，

L belongs to NP and

L属于NP
L' ← L for every L' belongs to NP

L'←L每L'都属于NP

All NP complete problems are NP hard, but some NP hard problems are not known to be NP complete.

所有的NP完全问题都是NP困难的，但是某些NP困难问题并不是NP完全的。

If NP hard problems can be solved in polynomial time, then all the NP complete problems can be solved in polynomial time.

如果NP难题可以在多项式时间内解决，那么所有NP完全问题都可以在多项式时间内解决。

翻译自: https://www.includehelp.com/algorithms/p-and-np-problems.aspx

模拟退火算法解决np