Title : New Optimization Concept for Combinatorial Problems The Dhouib Matrix
Abstract:
Very recently, we have invented a new optimization concept namely Dhouib-Matrix (DM) in order to solve combinatorial problems. DM gathers several approximative methods subdivided into two categories heuristics and metaheuristics.
We design and develop several heuristics in order to rapidly find an initial basic feasible solution for different combinatorial problems: for the Travelling Salesman Problems which are focused on finding the minimal cycle between several nodes, we create a deterministic heuristic Dhouib-Matrix-TSP1 followed by a stochastic method entitled Dhouib-Matrix-TSP2. Concerning the Assignment Problems which deal with affecting objects to resources (jobs to machines ... etc.), we announce our novel heuristic Dhouib-Matrix-AP1. Also, for the Transportation Problems we propose Dhouib-Matrix-TP1. Furthermore, these problems are optimized under certain and uncertain environments. Thus, we consider these problems with crisp, fuzzy, intuitionistic and neutrosophic parameters.
Moreover, we design several metaheuristics in order to nicely generate the optimal or the near optimal solutions in a reasonable computational time: we design at first the new local search metaheuristic entitled Far-to-Near; followed by a novel iterative metaheuristic namely Dhouib-Matrix-3 (DM3) and an original multi-start metaheuristic entitled Dhouib-Matrix-4 (DM4).
Obviously, the performance of the proposed concept DM is proven based on the simulation results.
