Assignment model with multi-objective linear programming for allocating choice ranking using recurrent neural network

Classic linear assignment method is a multi-criteria decision-making approach in which criteria are weighted and each rank is assigned to a choice. In this study, to abandon the requirement of calculating the weight of criteria and use decision attributes prioritizing and also to be able to assign a rank to more than one choice, a multi-objective linear programming (MOLP) method is suggested. The objective function of MOLP is defined for each attribute and MOLP is solved based on absolute priority and comprehensive criteria methods. For solving the linear programming problems we apply a recurrent neural network (RNN). Indeed, the Lyapunov stability of the model is proved. Results of comparing the proposed method with TOPSIS, VICOR, and MOORA methods which are the most common multi-criteria decision schemes show that the proposed approach is more compatible with these methods.

A Novel Spherical Fuzzy Bi-Objective Linear Assignment Method and Its Application to Insurance Options Selection

Spherical fuzzy sets are the latest extension of the ordinary fuzzy sets. The main characteristic of the spherical fuzzy sets is satisfying the condition that the squared sum of the membership, nonmembership, and hesitancy degrees must be at least zero and at most one. In this research, by extending the classical linear assignment method to bi-objective linear assignment and integrating it with cosine similarity measure, we presented a novel beneficial method for solving multiple criteria group decision-making problems in the spherical fuzzy environment. A new concept for weighting the criteria, which is composed of positive and negative impacts (weights), is introduced. The proposed bi-objective model tries to maximize positive impacts and minimize the negative impacts simultaneously. In order to solve the bi-objective linear assignment model, [Formula: see text]-constraint method is applied. Therefore, a trade-off solution is formed between maximizing positive impacts and minimizing negative impacts. The applicability and validity of the proposed method are shown through an insurance options selection problem. To test the reliability and validity of the proposed method, comparative and sensitivity analysis are performed.

Design and fabrication of a freeform mirror generating a uniform illuminance distribution in a rectangular region

The design of a freeform mirror generating a uniform illuminance distribution in a rectangular region with angular dimensions of 30°x15° is presented. The design method is based on the formulation of the problem of calculating the "ray-mapping" as a Monge-Kantorovich mass transportation problem and its subsequent reducing to a linear assignment problem. We describe a mirror fabrication process with the use of milling technology and present results of experimental measurements of the light distribution generated by the mirror. The experimental results are in good agreement with the results of numerical simulations and thus confirm the manufacturability of mirrors designed by the method proposed.

Decentralizing Coordination in Open Vehicle Fleets for Scalable and Dynamic Task Allocation

One of the major challenges in the coordination of large, open, collaborative, and commercial vehicle fleets is dynamic task allocation. Self-concerned individually rational vehicle drivers have both local and global objectives, which require coordination using some fair and efficient task allocation method. In this paper, we review the literature on scalable and dynamic task allocation focusing on deterministic and dynamic two-dimensional linear assignment problems. We focus on multiagent system representation of open vehicle fleets where dynamically appearing vehicles are represented by software agents that should be allocated to a set of dynamically appearing tasks. We give a comparison and critical analysis of recent research results focusing on centralized, distributed, and decentralized solution approaches. Moreover, we propose mathematical models for dynamic versions of the following assignment problems well known in combinatorial optimization: the assignment problem, bottleneck assignment problem, fair matching problem, dynamic minimum deviation assignment problem, Σk-assignment problem, the semiassignment problem, the assignment problem with side constraints, and the assignment problem while recognizing agent qualification; all while considering the main aspect of open vehicle fleets: random arrival of tasks and vehicles (agents) that may become available after assisting previous tasks or by participating in the fleet at times based on individual interest.