evolutionary algorithms

Pharmaceutical Industry in Iran has difficulties such as inappropriate distribution, expired drugs and late drug delivery to patients. To overcome these issues and reach a sustainable development, the environmental and social aspects must be considered beside the economic aspects. In this paper, we address the Pharmaceutical distribution network and design a novel model that helps the distributing companies to decide strategic (determining the main and local distribution centers) and tactical decision (determining the flow) according to the three aspects of sustainability. The solution through the evolutionary algorithms presents the best selection of local distribution centers and the optimum amount of flow of medicine through the network with respect to three aspects of sustainability.
  In order to compete in the universal market, pharmaceutical companies must amend their competency. This coemption market needs to select the certain level of commitment for sustainability aspects to reach the sustainable supply chains. For this purpose, this study considers three aspects of sustainability (i.e. economical, environmental, and social pillars) to design the pharmaceutical distribution network. So, the model has three objective functions. The first function is to minimize the cost of transportation through the network, the second is to minimize the CO2 emissions through the network and the third is to maximize the job creation through the network.
Carter and Rogers (2008) used the concept of ‘true sustainability’. They suggested that the consideration of environmental and social issues should be “coupled with economic objectives” and assist the company’s strategic long-term planning. Mota et al. (2014) considered this research question: “How can sustainability be integrated in to supply chains' design and planning decisions?” Several methods and frameworks have been proposed to evaluate environmental effects.
This model is a multi-objective mixed integer linear programming (MILP) and is NP-hard. We have used the evolutionary algorithms (NSGA-II, MOPSO) to solve the problem and achieve the Pareto frontier. The Taguchi design experimental design has been used in order to tune the parameters of the algorithm. For comparing two evolutionary algorithms’ performance indicators of spacing (S), mean ideal distance (MID), Time and number of solutions (NOS) have been calculated.
As a real case study, the proposed model is used in Darupakhsh. This company is one of the biggest pharmaceutical companies in Iran. The model has been customized with Darupakhsh’s features for selected medicine. This company has a main distribution center and twenty local distribution centers. Twenty important customers have been assumed in this research. Solving the model with the evolutionary algorithms of NSGA-II and MOPSO and comparing to traditional method of weighted sum, highlighted the superior of MOPSO in economical and environmental aspects. The weighted sum method had a better answer in the social aspect. Overall, the power of evolutionary algorithms have been proved because of the Pareto frontier present to the researcher.
This research focused on designing the sustainable pharmaceutical distribution network. The proposed model is a multi-objective mixed integer linear programming (MILP). This model was tested in Darupakhsh Company. In this case, MOPSO had better performance than NSGA-II. The solution presents the best selection of local distribution centers and the optimum amount of flow of medicine through the network with respect to three aspects of sustainability.For further research, studying the uncertain parameters in this model and a suitable approach to deal with uncertainty could be proposed.
References
Ahmadi, A., Mousazadeh, M., Torabi, S. A., & Pishvaee, M. S. (2018). “OR Applications in Pharmaceutical Supply Chain Management”. International Series in Operations Research & Management Science. 262,461–491.
Mota,B., Gomes, Ke., Carvalho, A., & Barbosa-Povoa, A. (2014). “Towards supply chain sustainability: economic, environmental and social design and planning”. Journal of Cleaner Production, 107, 14–27.
Mousazadeh, M., Torabi, S.A., & Zahiri, B. (2015). “A robust Possibilistic Programming approach for pharmaceutical supply chain network design”, Computers and Chemical Engineering, 82, 115- 128.

As an environment-friendly and renewable energy source, biomethane plays a significant role in the supply of sustainable energy. To determine location of reactor and allocate feedstocks, to the reactor in a biomethane production system by minimizing the supply chain cost, a mathematical model is studied in this article. Constraints, such as the limited workforce, the reactors’ demand on the residues, and the deterioration of the residues in the hubs are considered. Two evolutionary Algorithm, Genetic and differential evolutionary algorithms for solving mixed integer nonlinear programming model is proposed. The speed of obtaining the solution is the same but differential evolutionary algorithm finds better solutions than Genetic Algorithm when applied to the given problems.

Selecting the best way to perform the project constituting activities is one of the most important issues in the project scheduling, so time and cost be proportionate with contractor or the employer's perspective to implement the project. The other hand considering that many activities in the majority of project and consequently many Choice options for activity implementation, So this choice does not possess a unique solution, But also includes a set of solutions, are not preferred None of which On the other and is called the Pareto solutions this set. Therefore, in this paper, is presented a mathematical model for project scheduling with multiple objectives based cost payment patterns and resource constraints Since this problem, is considered as combinational optimization in NP-hard problems. metaheuristic algorithm is used to solve the proposed model in project scheduling and has been evaluated for finding optimal solution by using comparable indicators algorithms performance. and ultimately for validation, obtained Solutions by the proposed algorithm were compared with the obtained exact solutions form the GAMS software. show that the obtained results the proposed algorithm are efficient and converges to the optimal solutions.