This paper develops a multi-objective multi-layer location-pricing (MLLP) model with congested facilities in which the facilities act like a classic queuing system. The customers who arrive to this system receive service at all layers in a predetermined order to fulfill their demands. The goal is to determine (1) optimal number of the facilities required at each layer, (2) optimal allocation of customers to facilities, and (3) optimal price of providing service at each layer. The objective functions are to maximize the total profit of the system and to minimize the sum of travel and waiting times, simultaneously. The problem is formulated as a multi-objective nonlinear integer mathematical programming model. Since the problem is hard to be solved analytically, we present a multi-objective meta-heuristic algorithm (MHA) based on an electromagnetism-like mechanism (ELM) as a solution for multi-objective MLLP. This algorithm used an elitist mechanism to strengthen the structure of search engine in order to find better quality solutions. The results indicate the efficiency and effectiveness of the proposed algorithm in comparison with the traditional ELM.

中文翻译：

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使用类电磁机制算法的面向服务的定位定价模型的双目标优化

本文开发了一种具有拥塞设施的多目标多层位置定价 (MLLP) 模型，其中设施的行为类似于经典的排队系统。到达该系统的客户按照预定的顺序在各个层面接受服务，以满足他们的需求。目标是确定（1）每层所需设施的最佳数量，（2）客户对设施的最优分配，以及（3）每层提供服务的最优价格。目标函数是最大化系统的总利润，同时最小化旅行和等待时间的总和。该问题被表述为一个多目标非线性整数数学规划模型。由于这个问题很难分析解决，我们提出了一种基于类电磁机制 (ELM) 的多目标元启发式算法 (MHA) 作为多目标 MLLP 的解决方案。该算法采用精英机制来加强搜索引擎的结构，以便找到更优质的解决方案。结果表明，与传统 ELM 相比，该算法的效率和有效性。