Ant colony algorithm is a simulated evolutionary algorithm with the characteristics of positive feedback and distributed computation. It simulate the process of ants foraging to search the optimal solution. But the algorithm fall into local optimum easily and the convergence speed is very slow. After analyzing the disadvantages of ant colony algorithm, we put forward an improved hybrid ant colony algorithm. For each generation of ant colony perform crossover and mutation operations, and accept new individuals with a specified probability according to the Metropolis criterion of simulation annealing algorithm. Through series of simulation experiments' results, it can be found that the proposed algorithm is good at stability and optimization capacity.

The standard particle swarm optimization (PSO) algorithm converges very fast, while it is very easy to fall into the local extreme point. According to waiting effect among particles with mean-optimal position(MP), the quantum-behaved particle swarm optimization (QPSO) algorithm can prevent the particle prematurely from falling into local extreme point, but its convergence speed is slow and convergence precision is still low. In order to further improve the precision of QPSO algorithm, the evaluation method of $delta$ trap characteristic length $L(t)$ of wave function for describing the particle's state is modified. In QPSO, a random weight to each particle in swarm is introduced, and according to the order of the each particle best position's fitting value, there are three evaluation programs for $L(t)$, which are random-weight mean-optimal position(RMP), reverse-order random-weight mean-optimal position(RRMP) and same-order random-weight mean-optimal position(SRMP). Through the test of several typical functions, its result shows that the convergence accuracy of QPSO with RMP and RRMP is better than those of QPSO with MP, so the evaluation of $L(t)$ with RMP and RRMP is feasible and effective

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It is the key of Krusal Algorithm to select edges and judge loop. Though realized path-compression in operation of searching tree of Union-Find Sets Data Structure, and optimized merging-operation which the shallower tree has been merged into the deeper tree, the operation of selecting edges and judging loop in Krusal Algorithm is optimized and the time complexity of algorithm is reduced. Compared with the common way, the programming operation time of the new way has been reduced to some 1/10. Keywords-Kruskal algorithm; union-find sets; path-compression; minimum cost spanning tree 1 INTRODUCTION Kruskal algorithm is used to solve the minimum cost spanning tree (MCST)of one net. The basic idea of this algorithm is choose the edges based on weight from the small to the large in the net of N vertices. if the selected edge does not form a loop with other selected edges, it will be as an edge of spanning tree; if selected edge form a spanning tree loop with other selected, it will be discarded. In accordance with this process continues, the generated tree must be MCST[1][2]until the number of identified edges is N-1.The key to the algorithm is: how to determine whether the selected edge has formed a loop with other edges which have been identified. So the data structure to complete the operation determines the algorithm's time complexity.Union-find sets(UFS) is a tree structure, which is used to deal with the issue of merging and inquiring of disjoint sets.UFS is often expressed as a forest in the using. In this paper, through using UFS to determine whether the selected edge has formed a loop with other identified edges ,we have obtained a good result in the algorithm 's time complexity. UNION-FIND SETSUFS is a data structure which derives from the handling of the equivalence relation and equivalence class. A. Equivalence relation and equivalence classEquivalence relation[3][4] is a common relationship that broadly existed in the real world, and many problems can be transformed into an ad hoc basis by the equivalence relation according to dividing a collection of objects into equivalence class[3][4]in the real world. Throughout this paper ,let S be a collection with N elements, and R be the equivalence relation to S ,let be a dual sequence in R, where x and y are the elements of S. Based on the equivalent relation,the collection is divided into equivalence classes in the general algorithm as follows: Algorithm 1: step 1:Initialize： for each e i ∈S do begin construct the respective single-element set S i ; end; step 2:Divide S's elements into equivalence classes based on the dual sequence in R. Suppose x∈S x ，y∈S y ： for each ∈R do begin if(S x ≠ S y ) then begin