A new global approach for 0-1 polynomial programs

Abstract Given a 0–1 polynomial expression Σk = 1N − 1Σm = k + 1Nxkxm, where xk and xm are 0–1 variables, the famous Glover and Woolsey method required to use N(N − l) 2 additional continuous variables and 2N(N − 1) linear constraints to transform this expression into a linear form. This paper proposes a method which first reformulates the above expression as a new expression Σk = 1Nxkyk, yk = Σm = k + 1Nxm; then to transform the expression into a linear form where xk and yk are separated. The proposed transformation method only required to use 2(N − 1) additional continuous variables and 8(N − 1) linear constraints. Based on the new transformation, a 0–1 polynomial program can be more effectively solved to obtain a global optimum.