A Research on Flowshop Scheduling Problems With Column Generation

Author(s):  
H. Tanohata ◽  
T. Kaihara ◽  
N. Fujii

Column generation is a method to calculate lowerbound for combinatorial optimization problems, although a feasible schedule is generally obtained with the upperbound. Therefore, in this paper, a new method is proposed to solve the flowshop scheduling problems with column generation, which is composed of the local search and duality gap termination condition. The neighborhood of the local search is composed of columns, and the method is applied in column generation to improve the upperbound and lowerbound. The effectiveness of the proposed method is verified by computational experiments.

Author(s):  
Yousef K. Qawqzeh ◽  
Ghaith Jaradat ◽  
Ali Al-Yousef ◽  
Anmar Abu-Hamdah ◽  
Ibrahim Almarashdeh ◽  
...  

In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBC’s effectiveness in assignment and scheduling problems. Where it was enhanced by incorporating an elite pool of diverse and high quality solutions; a simple descent heuristic as a local search method; implicit recombination; Euclidean distance; dynamic population size; and elitism strategies. Those strategies provide a balanced search of diverse and good quality population. The investigation is conducted by comparing the proposed BBBC with similar metaheuristics. The BBBC is tested on three different classes of combinatorial optimization problems; namely, quadratic assignment, bin packing, and job shop scheduling problems. Where the incorporated strategies have a greater impact on the BBBC's performance. Experiments showed that the BBBC maintains a good balance between diversity and quality which produces high-quality solutions, and outperforms other identical metaheuristics (e.g. swarm intelligence and evolutionary algorithms) reported in the literature.


2018 ◽  
Vol 27 (05) ◽  
pp. 1850021 ◽  
Author(s):  
Ines Sghir ◽  
Ines Ben Jaafar ◽  
Khaled Ghédira

This paper introduces a Multi-Agent based Optimization Method for Combinatorial Optimization Problems named MAOM-COP. In this method, a set of agents are cooperatively interacting to select the appropriate operators of metaheuristics using learning techniques. MAOM-COP is a flexible architecture, whose objective is to produce more generally applicable search methodologies. In this paper, the MAOM-COP explores genetic algorithm and local search metaheuristics. Using these metaheuristics, the decision-maker agent, the intensification agents and the diversification agents are seeking to improve the search. The diversification agents can be divided into the perturbation agent and the crossover agents. The decision-maker agent decides dynamically which agent to activate between intensification agents and crossover agents within reinforcement learning. If the intensification agents are activated, they apply local search algorithms. During their searches, they can exchange information, as they can trigger the perturbation agent. If the crossover agents are activated, they perform recombination operations. We applied the MAOM-COP to the following problems: quadratic assignment, graph coloring, winner determination and multidimensional knapsack. MAOMCOP shows competitive performances compared with the approaches of the literature.


Author(s):  
Mehedi Hasan

Iterated local search (ILS) is a very powerful optimization method for continuous-valued numerical optimization. However, ILS has seldom been used to solve combinatorial integer-valued optimization problems. In this paper, the iterated local search (ILS) with random restarts algorithm is applied to solve combinatorial optimization problems, e.g., the classical weapon-target allocation (WTA) problem which arises from the military operations research. The mathematical model of the WTA problem is explained in detail. Then the idea of ILS with random restarts is explained. A comparison of the algorithm with several existing search approaches shows that the ILS outperforms its competitors on the tested WTA problem.


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