Shadow price based genetic algorithms for the cutting stock problem

The Cutting Stock Problem (CSP) is an integer combinatorial optimisation problem (an NP hard problem). It is an important problem in many industrial applications. In recent years, various traditional algorithms have been applied to the CSP, such as the Linear Programming (LP), the Branch and Cut (BC), the Evolutionary Algorithm (EA), etc. To continue improve performance, this paper proposes a novel Shadow Price based Genetic Algorithm (SPGA) to solve the CSP. The main contribution of this work is to combine distinct methods to generate better solutions. The experimental results have shown that the new SPGA has produced much better solutions than the classic Genetic Algorithm (GA) and other bio-inspired algorithms. This paper also demonstrates the new algorithm's capability of solving multi-objective optimisation problems.