The main objective of this paper is to discuss the usefulness of

The main objective of this paper is to discuss the usefulness of the PSO algorithm for solving the HSP problem. Therefore, based on the LCC approach, an integral mathematical model is presented and PSO algorithm is introduced and improved useful handbook for solving the problem. In the end, the results of the case study suggest the effectiveness of improved particle swarm optimization (IPSO) application to the optimal planning method for heating system.2. Mathematical Formulation2.1. Problem Definition and AssumptionsLCC is related to the systems engineering process, because economic considerations are very important in the process of creating systems. Life cycle economic analyses should be done early in the system or product life cycle, because the outcome of the systems engineering process cannot be influenced very much when the design is completed.

Thus, LCC involves evaluation of all future costs related to all of the phases in the system life cycle including design, construction and/or production, distribution, operation, maintenance and support, retirement, and material disposal, and so on [30].Cost models may range from simple to complex and are essentially predictive in nature. Parameters, such as the system’s physical environment, usage demand, reliability, maintainability, labor, energy, taxes, inflation, and the time value of money, may have a great influence on the life cycle costs [17].The main objective of this paper is to discuss the usefulness of the PSO algorithm for owners in making sustainable heating system investment decisions and to improve their decision-bases for municipal administration.

Therefore, we apply LCC approach to describe the HSP problem.Moreover, HSP considered in this study works under the following definition and assumptions.A heat consuming installation can connect with any heat source but cannot connect with two or more heat sources at the same time.The indirect connection between heat consuming installation and heat source is not allowed.A heat source must be connected with more than one heat consuming installation; otherwise, it will be closed.Any connection between any two heat sources is not allowed.The location of heat consuming installation is fixed.A heat source can be sited in a given region.The elevation difference between heat consuming installation and heat source is ignored.

Heating system planning and optimization can be achieved by changing the number and the heating capacity of heat source and the distance between the heat source and heat consuming installation.The Carfilzomib measure between heat source and heat consuming installation is simplified to the Manhattan (or city block) distance.There is no functional difference between any two heat sources and their products.2.2. NotationThe notations used in the mathematical formulations are given as follows.

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