Prospective greedy method for solving 1-neighborhood backpack problem

Abstract

A prospective greedy method for solving a 1-neighborhood backpack problem includes the steps: setting initial vertexes stored in a backpack and a set Z= {v0} of the vertexes currently selected into the backpack; respectively calculating the overall value PZ, the overall weight WZ and the residual capacity CR of the current backpack vertexes; searching a neighborhood of the set Z and placing the vertexes in the neighborhood into a set NB1; placing a neighborhood of the vertex NB1 (i) into a set NBi2; acquiring a ratio Ri (j); finding a maximum value R2 (i) in the Ri (j); keeping the univalence R1 (i) of the vertex with the weight W (i)<=CR of the vertex i unchanged; enabling the R1 (i) of the vertex with the W (i)>CR to be equal to 0; selecting a maximum value Rmax; adding m into the set Z, Z={Z, m}; judging whether the residual capacity CR is larger than the weight W (m) of the vertex m or not; calculating the overall weight WZ and the overall value PZ of the vertexes in the current backpack; exiting a loop. The prospective greedy method has the advantage of higher optimizing capacity and is more suitable for solving the high-dimensional constrained optimization problem of the 1-neighborhood backpack problem.

Description

technical field [0001] The present invention relates to a look-ahead greedy approach. In particular it concerns a look-ahead greedy approach to the 1-neighborhood knapsack problem. Background technique [0002] Sysio M M. Discrete Optimization Algorithms [M]. Englewood Cliffs, New Jersey: Prentice-Hall, 1983. The 0-1 knapsack problem proposed in: Given a knapsack with a capacity of C, N items, and its weight is W( i), the value is P(i), 1<=i<=N, the requirement: put the items into the backpack and maximize the value of the items in the bag. In the 0-1 knapsack problem, the object is either put into the knapsack, or it is not put into the knapsack, there are only two choices. Solving which items to load can maximize the value of the items in the backpack without exceeding the capacity of the backpack. [0003] 1-Neighborhood knapsack problem is a kind of knapsack problem with constraints, Borradaile and Heeringa et al. in Borradaile, G., B.Heeringa and G.Wilfong.The ...

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Problems solved by technology

[0003] 1-Neighborhood knapsack problem is a kind of knapsack problem with constraints, Borradaile and Heeringa et al. in Borradaile, G., B.Heeringa and G.Wilfong.The knapsack problem with neighbor constraints[J].Journal of Discrete Algorithms,2012.16 :p.224-235. In the knapsack problem with neighbor constraints, the knapsack problem with neighbor constraints is classified according to three indicators: undirected graph and directed graph; P, W take any value and P, W take Value homogenization; 1-neighborhood constraints and full-neighborhood constraints are divided into eight cases, because there is no effective solution algorithm,

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