But continuous method has become a new tendency of the 0 - 1 programming problem in recent years, whose advantage is to avoid inherent characteristics of the combinatorial optimization problem, and no longer limited to the size of the problem. Random search algorithms include genetic algorithm, simulated algorithm, artificial neural network algorithm, etc.
The accurate algorithms include implicit enumeration method, branch and bound algorithm, cutting plane algorithm, dynamic programming method, etc. The classical methods for solving 0 - 1 programming problems are mainly divided into two types: accurate algorithms and random search algorithms.
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Because of the wide application prospect and difficult characteristic of 0 - 1 programming, how to solve this kind of combinatorial optimization problem effectively has been the focus of many scholars. It is well known that 0 - 1 programming problem will increase exponentially with the increase of the scale of the problem, and within limited computer resources and time the traditional solution method will be difficult to realize. However, the continuous method proposed later in this paper is also applicable to the general binary quadratic programming (1), which can be easily accomplished by simple variable transformation. Of course, in the following discussion, we will mainly focus on the so-called 0 - 1 quadratic programming: Matrix, and the objective function can be followed by another linear term, but it can be omitted because there is no substantial influence on the method introduced later. Due to the wide application background of this problem and the difficulties caused by NP (Non-Deterministic Polynomial) hard properties, it is of great academic value to study effective algorithms for solving such problems.īinary quadratic programming can be uniformly written in the following general Considering the feasibility of this transformation, BQP problem has more extensive practical application. have successfully used this transformation method to transform the quadratic knapsack problem into BQP problem for solving. Hammer pointed out that any integer programming problems where the objective function is quadratic or linear and the constraint condition is linear can be described as BQP problems. And many combinatorial optimization problems with constraints can be transformed into BQP problems form by certain transformation, so these problems can be on behalf of kinds of important problems in combinatorial optimization. Binary quadratic programming (BQP) problem is a kind of typical combinatorial optimization problem, and has a variety of applications in computer aided design, traffic management, cellular mobile communication frequency allocation, operations research and engineering.
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