The Use Of Hill-Climbing Algorithm To Construct Generalized Howell Designs With Small Order

The generalized Howell design is an important research direction of combinatorial design theory.It is a kind of double-resolvable combination design.Generalized Howell design is one of the important tools used in coding theory.It can be used to construct the optimal double-repetition code,multi-repetition code,etc.,and it can be used to construct permutation arrays which are used to construct permutation codes that have important applications in the field of communications.The hill-climbing algorithm is a locally optimized heuristic search algorithm,which is an improvement to the depth-first search.This algorithm chooses a solution from the nearby solution space of the current solution as the current solution until a local optimal solution is reached.Although the hill-climbing algorithm has the defect of falling into the local optimal situation,the efficiency is relatively high.This paper gives the use of hill-climbing algorithm to construct generalized Howell designs with small order.This paper is divided into four chapters:In chapter 1,we briefly introduce the hill-climbing algorithm and summarize the background and current situation of the generalized Howell design.The relevant concepts and notations and some examples constructed by hill-climbing algorithm are given in this chapter.In chapter 2,we introduce the application of climbing algorithm in constructing factorization in detail,the generalized Howell design is actually the result of two orthogonal factorizations,this section gives the method of using hill-climbing algorithm to construct one factorization orthogonal to another factorization,and then to construct generalized Howell designs,meanwhile,some results are given by using this algorithm.In chapter 3,optimizing this algorithm and some details of this algorithm are described and analyzed.In chapter 4,summarizing the main results of this paper.