This paper introduces the Lagrangian relaxation method to solve multiobjective optimization problems. It is often required to use the appropriate technique to determine the Lagrangian multipliers in the relaxation met...
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This paper introduces the Lagrangian relaxation method to solve multiobjective optimization problems. It is often required to use the appropriate technique to determine the Lagrangian multipliers in the relaxation method that leads to finding the optimal solution to the problem. Our analysis aims to find a suitable technique to generate Lagrangian multipliers, and later these multipliers are used in the relaxation method to solve multiobjective optimization problems. We propose a search-based technique to generate Lagrange multipliers. In our paper, we choose a suitable and well-known scalarization method that transforms the original multiobjective into a scalar objective optimizationproblem. Later, we solve this scalar objective problem using Lagrangian relaxation techniques. We use Brute force techniques to sort optimum solutions. Finally, we analyze the results, and efficient methods are recommended.
An assembly line (AL) is a typical manufacturing process consisting of various tasks in which interchangeable parts are added to a product in a sequential manner at a station to produce a final product. Most of the wo...
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An assembly line (AL) is a typical manufacturing process consisting of various tasks in which interchangeable parts are added to a product in a sequential manner at a station to produce a final product. Most of the work related to the ALs concentrate on the assembly line balancing (ALB) which deals with the allocation of the tasks among stations so that the precedence relations among them are not violated and a given objective function is optimized. From the view point of the real ALB systems, multiobjective ALB with stochastic processing time (S-moALB) is an important and practical topic from traditional ALB problem involving conflicting criteria such as the cycle time, variation of workload, and/or the processing cost under uncertain manufacturing environment. This paper proposes a hybrid multiobjective evolutionary algorithm (hMOEA) to deal with such S-moALB problem with stochastic processing time considering minimization of the cycle time and the processing cost, given a fixed number of stations available. The special fitness function strategy is adopted and a hybrid selection mechanism is designed to improve the convergence and distribution performance. Experimental results with various instances show that hMOEA could get the better convergence distribution performance than existing MOEAs.
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