Solving multi-objectives function problem using branch and bound and local search methods

Document Type : Research Paper


Mathematics Dept, Mustansiriyah University, College of Science/ Baghdad, Iraq


In this paper we consider $1//\sum^n_{j=1}{(E_j+T_j+C_j+U_j+V_j)}$ problem, the discussed problem is called a Multi objectives Function (MOF) problem, As objective is to find a sequence that minimizes the multiple objective functions, the sum earliness, the tardiness, the completion time, the number of late jobs and the late work. The NP-hard nature of the problem, hence the existence of a polynomial time method for finding an optimal solution is unlikely. This complexity result leads us to use an enumeration solution approach. In this paper we propose a branch and bound method to solve this problem. Also, we use fast local search methods yielding near optimal solution. We report on computation experience; the performances of exact and local search methods are tested on large class of test problems.


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Volume 13, Issue 1
March 2022
Pages 1649-1658
  • Receive Date: 17 April 2021
  • Revise Date: 03 July 2021
  • Accept Date: 10 September 2021
  • First Publish Date: 10 November 2021