# Optimization of the Multi-Facility Location Problem Using Widely Available Office Software
#### 1.1.7 Solutions Using Genetic Algorithm  
In the study \"A Novel Nondominated Sorting Simplified Swarm Optimization for Multi-Stage Capacitated Facility Location Problems (CFLP) with Multiple Quantitative and Qualitative Objectives,\" [20], a novel solution based on simplified swarm optimization (SSO) and a nondominated sorting technique is proposed to provide Pareto-optimal solutions for enhancing search efficiency and solution quality. To yield feasible solutions, three repairer mechanisms, namely, random repair, cost-based, and utility-based mechanisms, are proposed to enhance the search efficiency and diversity of each population. A fuzzy analytic hierarchy process is used to calculate the weight of qualitative objectives. To evaluate the efficiency and effectiveness of the proposed algorithm, extensive experiments are conducted on benchmark and newly generated instances of the four stages of CFLPs. Then, results are compared with those of the nondominated sorting genetic algorithm-II, multi-objective SSO, and multi-objective particle swarm optimization reported from the literature. The computational results demonstrate that the proposed algorithm is highly competitive and performs well in terms of solution quality and computational time. The Pareto set in the investigated type of facility location problems leads to solutions that may better support decision-making.  
In article [21], a multi-objective multi-facility model of green closed-loop supply chain under uncertain environment is presented. In this model, the proposed green closed-loop supply chain considers three classes in the case of the leading chain and three classes in terms of the recursive chain.  
In the study \"A Hybrid Genetic Algorithm for Multi-emergency Medical Service Center Location-allocation Problem in Disaster Response\" [22], the final patient mortality risk value (injury severity) caused by both initial mortality risk value and travel distance (travel time) is considered to determine the location-allocation of temporary emergency medical service centers.  
According to the article \"Multi-facilities Location and Allocation Problem of Three-Echelon Supply Chain Based on an Improved Genetic Algorithm\" [23], a new mathematics model on multi-facilities location and allocation problem (MLAP) of three-echelon supply chain was built, which mainly took some logistics cost such as inventory cost, carrying cost, transportation cost into consideration. Then, an improved Genetic Algorithm was proposed to solve the MLAP. In this algorithm, the real encoding method was used to encode the solution directly, and meanwhile the crossover and mutation operator were improved. Finally, a numerical experiment showed clearly the feasibility of the IGA method and the effectiveness of the model.  
In [24] the multi-objective facility layout problem is defined in the literature as an extension of the famous quadratic assignment problem (QAP). Most previous mathematical models tried to combine both the quantitative and the qualitative objectives into a single objective by using weighting factors. This paper introduces a multi-objective mathematical model and solves it using the revised Strength Pareto Evolutionary Algorithm. The purpose of work is to find an efficient set of solutions \"Pareto optimal set\" which could be introduced to the decision maker to select the best alternative, while considering conflicting and non-commensurate objectives. A computer program is developed to define the mathematical model, code candidate solutions into genetic form, and use Evolutionary Multi-Objective Optimization algorithms to find the efficient set of solutions.