When most existing multiobjective evolutionary algorithms tackle continuous multiobjective optimization problems, they pay more attention to the population distribution in the objective space and neglect the potential...
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When most existing multiobjective evolutionary algorithms tackle continuous multiobjective optimization problems, they pay more attention to the population distribution in the objective space and neglect the potential of high-quality solutions in the decision space. In fact, it has been demonstrated that a good approximation of both Pareto optimal set (PS) and Pareto front (PF) is capable of facilitating decision making, especially when preferences are not clearly defined by the decision-maker. However, since different problems may have different internal structures, achieving trade-offs between exploration and exploitation while accelerating convergence toward the PS and PF remains challenging. To address this issue, we propose an evolutionary algorithm that explicitly exploits the regularity properties of the multiobjective optimization problem in the decision space and the objective space. A feedback loop can be formed directly between two spaces, which aims to approximate the PS and the PF by approximating the PS manifold and the PF manifold, respectively. In addition, the uniform distribution of population is guaranteed by two mutually reinforcing diversity maintenance mechanisms. Our experimental results on a variety of benchmark problems and real -world problems demonstrate that the proposed method performs remarkable on problems with regularities but suffers from some limitations when solving some real-world problems.
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.
In this paper, the waste collection problem (WCP) of a city in the south of Spain is addressed as a multiobjective routing problem that considers three objectives. From the company's perspective, the minimization ...
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In this paper, the waste collection problem (WCP) of a city in the south of Spain is addressed as a multiobjective routing problem that considers three objectives. From the company's perspective, the minimization of the travel cost is desired as well as that of the total number of vehicles. Additionally, from the employee's point of view, a set of balanced routes is also sought. Four variants of a multiobjective hybrid algorithm are proposed. Specifically, a GRASP (greedy randomized adaptive search procedure) with a VND (variable neighborhood descent) is combined. The best GRASP-VND algorithm found is applied in order to solve the real-world WCP of a city in the south of Spain.
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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