An iterative exact algorithm for the weighted fair sequences problem

An efficient implementation of a VNS heuristic for the weighted fair sequences problem

“…(2018) to get rid of them. More recently, Sinnl (2021) proposed to solve the WFSP by solving a sequence of subproblems in which the sequence length is fixed. From that variable fixing, the author demonstrates a series of valid inequalities for those subproblems, allowing his algorithm to increase the number of WFSP benchmark instances solved to optimality.…”

“…As done by Sinnl (2021), the general outline of our heuristic, presented in Algorithm 1, decomposes the WFSP into a series of subproblems of fixed sequence length $$T = n, \ldots ,TMAX$$.…”

“…Very recently, Sinnl (2021) proposed a valid cut for sequence lengths $$t \in \lbrace n,\ldots ,TMAX\rbrace$$ from a feasible WFSP solution S . Let $$$$\begin{equation*} k^*_i(S,t) = \min \lbrace k_i: c(x_i) \lceil t / k_i \rceil < cost(S) ; k_i \in \mathbb {N} \rbrace \end{equation*}$$$$be the minimum number of copies of $$x_i \in X$$ required to yield a solution of cost smaller than $$cost(S)$$ for $$|S|=t$$.…”

“…(2018) proved that the WFSP is NP‐hard and proposed an heuristic method that iteratively solves a constrained version of the WFSP. More recently, Sinnl (2021) developed an iterative exact method that decomposes the WFSP in a series of constrained subproblems. By means of a series of new valid inequalities, the author was able to considerably increase the number of WFSP instances solved to optimality.…”

“…By means of a series of new valid inequalities, the author was able to considerably increase the number of WFSP instances solved to optimality. Our work proposes the first metaheuristic solution approach for the WFSP and compares its performance with the method of Sinnl (2021), both in terms of solution quality and efficiency.…”