The characteristic of 1. combinatorial optimization problem is to find the optimal solution under given constraints. These constraints can be time constraints, resource constraints, cost constraints and so on. The goal of optimization can be to maximize profit, minimize cost, minimize time and so on.
2. There are usually violent search method, dynamic programming method, backtracking method and greedy algorithm to solve combinatorial optimization problems. Among them, the violent search method is to find the optimal solution by enumerating all possible situations, but this method is usually only suitable for small-scale problems; The rule of dynamic programming is to decompose the problem into subproblems, save the solutions of subproblems and avoid repeated calculation.
3. This method is suitable for large-scale problems; The backtracking method is to find the optimal solution by exploring all possible solutions, but this method is usually only suitable for small-scale problems; Greedy algorithm achieves the global optimal solution by selecting the local optimal solution at each step, but this method does not always get the optimal solution.
The concept of combination
1. combination is an important concept in mathematics. It refers to taking any m(m≤n) elements from n different elements and combining them into a group, which is called taking the combination of m elements from n different elements. The number of all combinations of m(m≤n) elements from n different elements is called the number of combinations of m elements from n different elements.
2. Combination and arrangement are two different concepts. Arrangement refers to taking m elements from n different elements and arranging them in a certain order, which is called arrangement of taking m elements from n different elements; All permutation numbers of m(m≤n) elements from n different elements are called permutation numbers of m elements from n different elements.
3. Combination and permutation are widely used in counting principle, permutation and combination, probability theory and other fields. In combinatorial mathematics, we can calculate the number of possible permutations and combinations through combinatorial formulas and permutation formulas, and then solve various practical problems.