Main Objective Function Research Articles

Multiple Instances QoS Routing in RPL: Application to Smart Grids.

The Smart Grid (SG) aims to transform the current electric grid into a “smarter” network where the integration of renewable energy resources, energy efficiency and fault tolerance are the main benefits. This is done by interconnecting every energy source, storage point or central control point with connected devices, where heterogeneous SG applications and signalling messages will have different requirements in terms of reliability, latency and priority. Hence, data routing and prioritization are the main challenges in such networks. So far, RPL (Routing Protocol for Low-Power and Lossy networks) protocol is widely used on Smart Grids for distributing commands over the grid. RPL assures traffic differentiation at the network layer in wireless sensor networks through the logical subdivision of the network in multiple instances, each one relying on a specific Objective Function. However, RPL is not optimized for Smart Grids, as its main objective functions and their associated metric does not allow Quality of Service differentiation. To overcome this, we propose an objective function with a multi-objective metric that considers the delay and the remaining energy in the battery nodes alongside with the dynamic quality of the communication links. Our function automatically adapts to the number of instances (traffic classes) providing a Quality of Service differentiation based on the different Smart Grid applications requirements. We tested our approach on a real sensor testbed. The experimental results show that our proposal provides a lower packet delivery latency and a higher packet delivery ratio while extending the lifetime of the network compared to solutions in the literature.

Mathematical modeling of electric vehicles contributions in voltage security of smart distribution networks

This paper evaluates the voltage security of the distribution networks in the presence of electric vehicles in the optimization framework. Accordingly, the main objective functions of this optimization problem include maximization of voltage security margin and minimization of operational cost. Also, it is supposed that the electric vehicles are equipped with bidirectional chargers to control active and reactive power in smart distribution networks, simultaneously. The objective functions are subject to the constraints of power flow equations, system operating limits and electric vehicle constraints. The proposed model is implemented on the 33-bus distribution network to evaluate the performance of the proposed optimization scheme for the management of the smart distribution networks in the presence of electric vehicles. The results show that the operational cost and network voltage security margin are reduced in the case of the higher electric vehicle penetration rate when electric vehicles are used for charging active power and reactive power control capability, with respect to the case that does not include electric vehicles.

Solving Reactive Power Dispatch Problem by Using JAYA Optimization Algorithm

This paper proposes a new optimization algorithm called JAYA algorithm for solving the optimal reactive power dispatch (ORPD) problem. Minimizing the real power losses is one of main objective functions of (ORPD) problem. The ORPD problem is subjected to non-linear equality and inequality operational constraints. The proposed JAYA is a recently developed optimization algorithm. The main merit of Jaya algorithm is that the algorithm performance is liberated of specific control parameters adjustment. Therefore, it overcomes the limitations of previous optimization algorithms in terms of achieving the global optima atless computational efforts. The effectiveness of the proposed Jaya algorithm is proven on three standard systems namely IEEE 14-bus, 30-bus and 118-bus test systems. Added to that, Jaya is successively tested on the West Delta Real Network (WDRN) as a real part of the Egyptian grid. The obtained simulation results prove that the proposed JAYA algorithm has significant reduction in power losses for the tested system compared with other optimization algorithms. The obtained results confirm that the proposed JAYA optimization algorithm can make a noticeable enhancement on solving the ORPD problem for small and large-scale power systems.

Enhancing observability in MILP-based optimal joint allocation of PMU channels and conventional measurements with new security concepts

Since buses in power systems have a different number of connected branches, they require Phasor Measurement Units (PMUs) with different number of measuring channels. In this paper, a multi-objective channel-based method is proposed for optimal allocation of PMU base units, PMU measuring channels, and Flow Measurements (FMs) for power system observability. The main objective function encompasses cost of PMU base units and their measuring channels as well as FMs. Unlike previous methods, PMU channels are modeled as binary optimization variables, the optimal assignment of which is decided by the optimization problem. Under this framework, a PMU assigns measuring channels to observe its adjacent buses only if they are economically justified. The second objective function maximizes measurement redundancy at selected buses in a more controlled way. For a more economical solution, existing FMs are employed as network resources along with placing new PMUs and FMs. Moreover, PMU failures and branch outages are modeled using a novel approach that is more cost-effective than existing methods. Furthermore, channel failure is also introduced and modeled as a new type of contingency. Results obtained from the proposed method clarify its efficiency from economic perspective.

Optimal multiple installation of DG and capacitor for energy loss reduction and loadability enhancement in the radial distribution network using the hybrid WIPSO–GSA algorithm

ABSTRACTIn the electric power system, the majority of loads connected to the distribution side are inductive loads, thereby resulting in enhanced energy loss and reduced voltage stability and maximum loadability. In this study, in order to overcome these issues, optimal multiple installation of distributed generation (DG) and capacitor are presented with minimisation of total apparent power loss () taken as the main objective function. The optimal DG and capacitor planning problem are solved using a hybrid configuration of the weight improved particle swarm optimisation (WIPSO) algorithm and gravitational search algorithm (GSA) called the hybrid WIPSO–GSA algorithm. Moreover, the total economic benefit due to optimal DG and capacitor installation are also established by considering essential cost parameters for the total planning period. The proposed methodology is tested on standard 33-bus and Indian 85-bus radial distribution systems. The superiority of the proposed technique is also illustrated by comparing the results with other optimisation techniques.

Multiobjective Optimization Modeling Approach for Multipurpose Single Reservoir Operation

The water resources planning and management discipline recognizes the importance of a reservoir’s carryover storage. However, mathematical models for reservoir operation that include carryover storage are scarce. This paper presents a novel multiobjective optimization modeling framework that uses the constraint-ε method and genetic algorithms as optimization techniques for the operation of multipurpose simple reservoirs, including carryover storage. The carryover storage was conceived by modifying Kritsky and Menkel’s method for reservoir design at the operational stage. The main objective function minimizes the cost of the total annual water shortage for irrigation areas connected to a reservoir, while the secondary one maximizes its energy production. The model includes operational constraints for the reservoir, Kritsky and Menkel’s method, irrigation areas, and the hydropower plant. The study is applied to Carlos Manuel de Céspedes reservoir, establishing a 12-month planning horizon and an annual reliability of 75%. The results highly demonstrate the applicability of the model, obtaining monthly releases from the reservoir that include the carryover storage, degree of reservoir inflow regulation, water shortages in irrigation areas, and the energy generated by the hydroelectric plant. The main product is an operational graph that includes zones as well as rule and guide curves, which are used as triggers for long-term reservoir operation.

LVCI approach for optimal allocation of distributed generations and capacitor banks in distribution grids based on moth–flame optimization algorithm

In recent years, due to growth in electricity demand, distribution networks suffer from increased power losses, decreased voltage levels, and increased power quality problems. The distributed generations (DGs) and shunt capacitor banks (SCBs) are considered the convenient sources of active and reactive power compensation in distribution networks, respectively. Moreover, the optimum allocation of DGs and SCBs plays a sufficient role in improving voltage profile and voltage stability that lead to ameliorate power quality and minimize the system power losses. In this respect, this article provides a novel efficient and vigorous moth–flame optimization (MFO) algorithm for solving the optimization problem of DGs and SCBs allocation. Furthermore, a loss–voltage–cost index (LVCI) approach has been incorporated into the proposed optimization methodology as an effective objective function to enhance the voltage profile and minimize the system power losses and the total annual operating cost. Moreover, the proposed scheme is implemented in two stages. In the first stage, the most candidate buses for installing DGs and SCBs are evaluated using loss sensitivity factors (LSFs). In the second stage, the MFO optimization algorithm is implemented to estimate the optimal placement of DGs and SCBs besides their sizing from the nominated buses based on LVCI as the main objective function. The suggested scheme has been tested on 33-bus and 69-bus IEEE standard radial distribution networks with different load levels. Furthermore, it is applied on a practical case study of Moscow region network that consists of 111-bus radial distribution network under different load levels. To insure the validation and accuracy of the proposed algorithm, the acquired results have been compared with other methods and techniques. The numerical results proved that the suggested optimization scheme has notability with high accuracy to estimate the optimal solution of DGs and SCBs allocation for minimizing the system power losses, enhancing the voltage profile and maximizing the net savings as compared to other techniques.

From Finite Time to Finite Physical Dimensions Thermodynamics: The Carnot Engine and Onsager’s Relations Revisited

Abstract Many works have been devoted to finite time thermodynamics since the Curzon and Ahlborn [1] contribution, which is generally considered as its origin. Nevertheless, previous works in this domain have been revealed [2], [3], and recently, results of the attempt to correlate Finite Time Thermodynamics with Linear Irreversible Thermodynamics according to Onsager’s theory were reported [4]. The aim of the present paper is to extend and improve the approach relative to thermodynamic optimization of generic objective functions of a Carnot engine with linear response regime presented in [4]. The case study of the Carnot engine is revisited within the steady state hypothesis, when non-adiabaticity of the system is considered, and heat loss is accounted for by an overall heat leak between the engine heat reservoirs. The optimization is focused on the main objective functions connected to engineering conditions, namely maximum efficiency or power output, except the one relative to entropy that is more fundamental. Results given in reference [4] relative to the maximum power output and minimum entropy production as objective function are reconsidered and clarified, and the change from finite time to finite physical dimension was shown to be done by the heat flow rate at the source. Our modeling has led to new results of the Carnot engine optimization and proved that the primary interest for an engineer is mainly connected to what we called Finite Physical Dimensions Optimal Thermodynamics.

Integrated production-distribution planning problem in a competition-based four-echelon supply chain

Abstract Integrated production-distribution (P-D) planning reduces costs, enhances the efficiency of the supply chain, and reduces additional proceedings because of its integrated parts and activities. P-D planning facilitates simultaneous planning of supply chain constituents in order to save more time in planning within a supply chain. Therefore, it plays an important role in supply chain management (SCM). Besides, since the introduction of competition into SCM, it has attracted the attention of many researchers and practitioners. The present work was conducted to investigate an integrated P-D planning problem within a four-echelon supply chain with two main objective functions: minimizing total chain cost and maximizing service level. The considered problem is modeled under two circumstances; no competition and competitive market. In the latter, three kinds of competitions are taken into account: Cournot, Stackelberg, and Quality competitions. To tackle the problem, two mixed integer linear programs (MILPs) are developed, which are proved to be unimodular. Moreover, elastic constraint method is used to solve the two multiobjective models. Finally, numerical experiments are conducted. The results showed that although competition improves chain performance in terms of quality of the delivered products, it might also raise the cost of the chain.

Predicting the accumulation of storage compounds by Rhodococcus jostii RHA1 in the feast-famine growth cycles using genome-scale flux balance analysis.

Feast-famine cycles in biological wastewater resource recovery systems select for bacterial species that accumulate intracellular storage compounds such as poly-β-hydroxybutyrate (PHB), glycogen, and triacylglycerols (TAG). These species survive better the famine phase and resume rapid substrate uptake at the beginning of the feast phase faster than microorganisms unable to accumulate storage. However, ecophysiological conditions favouring the accumulation of either storage compounds remain to be clarified, and predictive capabilities need to be developed to eventually rationally design reactors producing these compounds. Using a genome-scale metabolic modelling approach, the storage metabolism of Rhodococcus jostii RHA1 was investigated for steady-state feast-famine cycles on glucose and acetate as the sole carbon sources. R. jostii RHA1 is capable of accumulating the three storage compounds (PHB, TAG, and glycogen) simultaneously. According to the experimental observations, when glucose was the substrate, feast phase chemical oxygen demand (COD) accumulation was similar for the three storage compounds; when acetate was the substrate, however, PHB accumulation was 3 times higher than TAG accumulation and essentially no glycogen was accumulated. These results were simulated using the genome-scale metabolic model of R. jostii RHA1 (iMT1174) by means of flux balance analysis (FBA) to determine the objective functions capable of predicting these behaviours. Maximization of the growth rate was set as the main objective function, while minimization of total reaction fluxes and minimization of metabolic adjustment (environmental MOMA) were considered as the sub-objective functions. The environmental MOMA sub-objective performed better than the minimization of total reaction fluxes sub-objective function at predicting the mixture of storage compounds accumulated. Additional experiments with 13C-labelled bicarbonate (HCO3−) found that the fluxes through the central metabolism reactions during the feast phases were similar to the ones during the famine phases on acetate due to similarity in the carbon sources in the feast and famine phases (i.e., acetate and poly-β-hydroxybutyrate, respectively); this suggests that the environmental MOMA sub-objective function could be used to analyze successive environmental conditions such as the feast and famine cycles while the metabolically similar carbon sources are taken up by microorganisms.

Sizing and placement of solar photovoltaic plants by using time-series historical weather data

The integration of distribution generation (DG) in distribution networks with improper planning adversely influences the quality of the electrical networks. Conventionally, the outputs from the intermittent DGs, such as solar photovoltaic (PV) plants, are assumed dispatchable. The intermittency of solar irradiance on the outputs of the PV modules has been ignored in most studies on the sizing and placement of DGs. By looking at this problem, this paper presents the sizing and placement of a distributed solar photovoltaic plant (DSPP) by using time series historical weather data. To predict the output from the PV modules, 15 years of solar data were modeled with the aid of a beta probability density function. The total energy loss index was formulated as the main objective function, and the optimization problem was solved by mixed integer optimization by using genetic algorithm. By adopting a time-varying commercial load, the proposed algorithm was applied on IEEE 33 bus and IEEE 69 bus distribution networks. The numerical studies on the two distribution networks show the advantages of the proposed approach for minimizing the total energy losses and improving the bus voltage profiles. It was revealed that up to 38% of the total energy losses in distribution networks could be reduced at sites with solar insolation of 5.65 peaks sun hours. In contrast to existing methods, planning for DGs by using weather data provided more realistic results for DSPP in distribution networks.

Multi-stage generation and transmission coordinated planning method with a modified fireworks algorithm facing to energy internet

The integration of energy internet (EI) and electric power system has a profound influence on electric power system planning. Therefore, this paper mainly resolves the EI-oriented multi-stage generation and transmission coordinated planning problem with a modified fireworks algorithm. Firstly, we combined with Stackelberg game theory and focused on subject game theory, system low carbon characteristic and renewable energy generation, a multi-stage generation and transmission coordinated planning model for electric power system is proposed. The model has a main objective function of maximizing the social welfare and two secondary objective functions of maximizing individual profits in the operation stage and maximizing overall profits of generation companies in the planning stage. Then, a modified fireworks algorithm (MFWA) is proposed with good expandability, convergence and adaptability to solve the problem. The MFWA is modified by introducing Gaussian Mutation to improve global search capability. The basic coding method and solution procedure of the MFWA are depicted. Finally, an improved IEEE-24 bus system is used to test the proposed planning method and MFWA. By comparing three scenarios and analysing results, we can verify the validity and feasibility of the proposed method.

A Comparative Analysis of Metaheuristic Approaches for Multidimensional Two-Way Number Partitioning Problem

In this study, a novel usage of four metaheuristic approaches Genetic algorithm (GA), Simulated annealing (SA), migrating bird optimization algorithm (MBO) and clonal selection algorithm (CSA) are applied to multidimensional two-way number partitioning problem (MDTWNPP). MDTWNPP is a classical combinatorial NP-hard optimization problem where a set of vectors have more than one coordinate is partitioned into two subsets. The main objective function of MDTWNPP is to minimize the maximum absolute difference between the sums per coordinate of elements. In order to solve this problem, GA is applied with greedy crossover and mutation operators. SA is improved with dual local search mechanism. MBO is specialized as multiple flock migrating birds optimization algorithms. CSA is applied with problem specific hyper mutation process. Furthermore, all instances are solved using an integer linear programming model which was previously presented in the literature. In the experiments, four metaheuristic approaches and integer linear programming model are used to solve 126 datasets with different sizes and coordinates. As a brief result, the GA and SA approaches designed for this problem outperformed all other heuristics and the integer programming model. Both the performance of GA and SA approaches are in a competitive manner where GA and SA yielded the best solution for 56 and 65 out of 125 datasets, respectively.

VLCI approach for optimal capacitors allocation in distribution networks based on hybrid PSOGSA optimization algorithm

The use of Shunt Capacitor Banks (SCB) as a convenient compensation source of reactive power in distribution networks has an efficient role in enhancement voltage profile, correction of power factor and minimizing the network power losses. In this regard, this article investigates the enforcement of a modern robust and effective hybridization of Particle Swarm Optimization besides a Gravitational Search Algorithm (PSOGSA) as an optimization mechanism for solving the problem of optimum SCB allocation with minimizing the annual operating cost and enhancement of the system power quality. Moreover, a new Voltage-Loss-Cost Index (VLCI) has been associated with the proposed optimization technique as an efficient objective function to increase the voltage levels, minimize active power losses and the annual operating cost of the grid. Furthermore, the implemented methodology is introduced in two stages. Firstly, the most appropriate buses for locating SCB are estimated using Loss Sensitivity Factor (LSF). Then, the hybrid PSOGSA optimization algorithm is structured to detect the optimum sitings of SCB and their sizing from the elected buses based on VLCI as the main objective function. The suggested mechanism has been applied on 33-bus besides 69-bus IEEE radial distribution networks. In addition, it is applied on a practicality case study of 111-bus Moscow region radial distribution network. With a view to making certain of the validation of the suggested methodology, the acquired results have been compared with other mechanisms and techniques. The numerical results demonstrated that the suggested optimization technique has superiority with high performance to deduce the optimum decision of SCB allocation for minimizing the network power losses, enhancing the profile of voltage level, and maximizing the net savings as compared to other different techniques.

Effect of soil in controlling the seismic response of three-dimensional PBPD high-rise concrete structures

In the last decades, valuable results have been reported regarding conventional passive, active, semi-active, and hybrid structural control systems on two-dimensional and a few three-dimensional shear buildings. In this research, using a three-dimensional finite element model of high-rise concrete structures, designed by performance based plastic design method, it was attempted to construct a relatively close to reality model of concrete structures equipped with Tuned Mass Damper (TMD) by considering the effect of soil-structure interaction (SSI), torsion effect, hysteresis behavior and cracking effect of concrete. In contrast to previous studies which have focused mainly on linearly designed structures, in this study, using performance-based plastic design (PBPD) design approach, nonlinear behavior of the structures was considered from the beginning of the design stage. Inelastic time history analysis on a detailed model of twenty-story concrete structure was performed under a far-field ground motion record set. The seismic responses of the structure by considering SSI effect are studied by eight main objective functions that are related to the performance of the structure, containing: lateral displacement, acceleration, inter-story drift, plastic energy dissipation, shear force, number of plastic hinges, local plastic energy and rotation of plastic hinges. The tuning problem of TMD based on tuned mass spectra is set by considering five of the eight previously described functions. Results reveal that the structural damage distribution range is retracted and inter-story drift distribution in height of the structure is more uniform. It is strongly suggested to consider the effect of SSI in structural design and analysis.

Battery Storage for the Utility-Scale Distributed Photovoltaic Generations

Batteries are essential for efficiently utilizing the energy from the photovoltaic (PV) modules. However, integration of batteries with PV plants at large scale needs more attention in terms of size, location, and times for the charging and discharging of the batteries. This paper addresses these aspects. It presents a mixed integer optimization using genetic algorithm for determining the optimum size and placement of battery-sourced distributed PV generation (B-SDPVG) in distribution networks. The total energy loss index is formulated as the main objective function and simultaneously, the bus voltage deviations and penetrations of the B-SDPVG are calculated. The yields from the PV plants are estimated using 15 years of weather data modeled with the aid of beta probability density function. Furthermore, a novel charge–discharge control model is developed for determining the choice of the charging and discharging of batteries at each hour. By considering different time varying voltage-dependent load models, the proposed algorithm is applied on the IEEE 33 bus and the IEEE 69 bus test distribution networks. The numerical results of two distribution networks with time-varying loads show the advantages of the proposed methodology. It was revealed that integration of battery storage and intelligent scheduling for charging and discharging of batteries produced much better results and improved the quality of distribution networks. The supply of power from the B-SDPVG during the peak load hours and at night was made possible for each load model. The proposed charge–discharge control model for scheduling the charging and discharging of the batteries was found dynamic. Results of this paper can be of potential importance in planning for the integration of battery storage in distribution networks.

An energy scheduling method for multiple users of residential community connected to the grid and wind energy source

Energy management of residential consumers plays a very important role in the achievement of aim of energy saving, lesser cost of electricity for the residential consumers and highest possible satisfaction of the consumers. In this paper, a common energy scheduler for the multiple users has been designed for energy scheduling of residential consumers having smart appliances. Mathematical modelling of different types of appliances has been done to achieve the required results. Time of use tariff and day ahead real time pricing tariff have been used for energy scheduling. A wind energy source has been considered to reduce the burden of energy demand on the grids and to analyse the effect of renewable energy sources in a small scale energy management problem. A delay factor has been also included in the main objective function of the problem to maintain the satisfaction level of the consumers by reducing cost of waiting. The final designed problem is solved by mixed integer linear programming technique using GAMS software. The time taken for the solution is very less. In this paper, to increase the energy efficiency and the accuracy of the required results, the selected time horizon of 24 h is divided into 96 small time slots, each of 15 min duration. Achievement of the aim of the paper, that is reduction in the cost of electricity and attainment of the highest possible satisfaction level of the users, has been verified by the simulation results. Practical application: Our work is completely applicable in the practical field. This work can be used for the energy scheduling of home appliances.

МОДЕЛИРОВАНИЕ ПРОЦЕССА УПРАВЛЕНИЯ УСТОЙЧИВОСТЬЮ ТРАНСПОРТНОГО ПРЕДПРИЯТИЯ

In management, the modeling method is widely used, which allows to formalize and streamline the process under investigation, to identify problems and to determine the ways to solve them. The problem of adaptation and ensuring sustainability is relevant for economic entities that carry out various activities in the conditions of both the emerging and the already formed market. The stability of the enterprise as a socio-economic system is defined as the ability to preserve the characteristics of an economic entity and ensure the successful fulfillment of the main objective function. For example, for a cargo transportation company, the objective function is to carry out transport work for the carriage of goods. As part of the study of the process of enterprise sustainability management, it is advisable to differentiate the main category, highlighting such types of sustainability as functional, social, financial, economic and environmental. In turn, achieving the sustainability of all the aspects under consideration is an indispensable condition for overall sustainability and, as a result, sustainable development of the enterprise. The process of enterprise sustainability management is presented in the form of a model consisting of two blocks, structural elements of which reflect the complexity and features of the management object. At the same time, special attention should be given to the block of formation of the organizational and methodological base of the model, which presupposes the choice of methods for managing sustainability, the formation of a system of indicators of sustainability and the effectiveness of management of sustainability, etc. In addition, the model provides for clarifying the principles of management, allowing to take into account the specifics of the business. When building the model, it is recommended to use the data obtained as a result of the survey of workers in the industry, as well as the normative and recommended values of individual indicators used in assessing the sustainability of the enterprise through the magnitude of its potential. Building a model allows to create an enterprise management view of the hierarchy of management tasks, how their decisions affect the management object, how the managed organization adapts to changes in the external environment, and what is the basis for adjusting management decisions.

Emission Constraint Profit based Unit Commitment Problem using Improved Bacterial Foraging Algorithm

Objectives: The main objective function is to increase the Generation Companies profit and reduce the GHG gas emission of the thermal generating units. Methods/Analysis: During the most recent few centuries, emission control has become a very big problem of worlds concern due to the frequently increasing pollution of earth’s atmosphere. In order to reach the emission control in this paper the Improved Bacterial Foraging Algorithm (IBFA) is proposed. The Bacterial Foraging Algorithm is formed by foraging behavior of E-coli Bacteria in the human intestine. But the BF algorithm leads to some convergence problem while solving the large problems. So for improving the performance of the large problems the new integer coded Improved Bacterial Foraging Algorithm is proposed. Findings: The proposed method is implemented to the IEEE 39 bus10 unit system with one day time period. This proposed algorithm is simulated using MATLAB software and the output results are compared with traditional Unit Commitment Method. Novelty/Improvement: The restructuring of electric power industry is used to reform the electric supply industry. The generation scheduling of thermal generating units in deregulated environment is named as Profit Based Unit Commitment. In PBUC problem the normal Demand constraint is changed to modified power demand constraint to increase the GENeration Companies (GENCO) profit.

Multi-criteria optimization of a micro solar-geothermal CCHP system applying water/CuO nanofluid based on exergy, exergoeconomic and exergoenvironmental concepts

The main objective of the present study is to perform the thermodynamic, economic and environmental analyses of a solar-geothermal driven combined cooling, heating and power (CCHP) cycle integrated with flat plat collectors containing water/copper oxide (CuO) nanofluid as the absorbing medium. Twelve main parameters are selected as the decision variables of the desired system while the daily exergetic efficiency, total product cost rate and total product environmental impact associated with exergy rate are chosen as the three main objective functions. NSGA-II (Non-dominated Sort Genetic Algorithm-II) is individually applied to obtain the final optimal solutions in the multi-objective optimization of the desired system for four working fluids including R134a, R423A, R1234ze and R134yf from the exergy, exergoeconomic and exergoenviromental points of view. Based on the multi-objective optimization outcomes, R1234ze is the best fluid with 36.82Pts/h total product environmental impact rate so that the maximum nanoparticles volume fraction and minimum collector tilt angle are required. Moreover, R423A with the minimum total product cost rate of 4496 $/year is the best fluid at which minimum collector area is needed. Furthermore, R134a is the best fluid with 4.194% daily exergetic efficiency so that the minimum nanoparticle volume fraction is required compared with other studied fluids.