A Novel Binary Firefly Algorithm for the Minimum Labeling Spanning Tree Problem

Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-hard combinatorial optimization problem,which is widely applied in communication networks,multimodal transportation networks,and data compression.Some approximation algorithms and heuristics algorithms have been proposed for the problem.Firefly algorithm is a new meta-heuristic algorithm.Because of its simplicity and easy implementation,it has been successfully applied in various fields.However,the basic firefly algorithm is not suitable for discrete problems.To this end,a novel discrete firefly algorithm for the MLST problem is proposed in this paper.A binary operation method to update firefly positions and a local feasible handling method are introduced,which correct unfeasible solutions,eliminate redundant labels,and make the algorithm more suitable for discrete problems.Computational results show that the algorithm has good performance.The algorithm can be extended to solve other discrete optimization problems.

NeuroPrim:An attention-based model for solving NP-hard spanning tree problems

Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential time.Recently,there has been growing interest in end-to-end deep neural networks for solving routing problems.However,such methods typically produce sequences of vertices,which make it difficult to apply them to general combinatorial optimization problems where the solution set consists of edges,as in various spanning tree problems.In this paper,we propose NeuroPrim,a novel framework for solving various spanning tree problems by defining a Markov decision process for general combinatorial optimization problems on graphs.Our approach reduces the action and state space using Prim's algorithm and trains the resulting model using REINFORCE.We apply our framework to three difficult problems on the Euclidean space:the degree-constrained minimum spanning tree problem,the minimum routing cost spanning tree problem and the Steiner tree problem in graphs.Experimental results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 vertices.Additionally,we find that our model has strong generalization ability with no significant degradation observed on problem instances as large as 1,000.Our results suggest that our framework can be effective for solving a wide range of combinatorial optimization problems beyond spanning tree problems.

Island partition of the distribution system with distributed generation

In this paper, a novel optimum island partition model based on Tree Knapsack Problem (TKP) is presented for the distribution system integrated with distributed generation (DG), and a Depth-first Dynamic Programming Algorithm (DPA) is used to solve this model. With the considerations of the load priority, controlled/uncontrolled loads, and the constraints of power balance, voltage and equipment capacity, the model can meet the practical engineering requirements very well. The island partition problem of the distribution system integrated with multiple DGs is first decomposed into multiple TKPs, each of which is solved by DPA respectively. Then, the initial optimum island partition scheme is gained through an island combination procedure, and the final island partition scheme is obtained after feasibility checking and adjustment. Since the algorithm proposed owns the advantages of strong theoretical foundation and low computational complexity, it can find the approximate optimal solution within a limited time. The results of examples demonstrate the validity of the new model and algorithm.