multi-objective optimization

The ease of converting electricity into other energies has caused human activities to be highly dependent on it. Environmental issues, limited resources, unfair distribution of resources and the strong dependence of countries' economies on energy have caused more attention to be paid to optimizing the mix of electricity producing resources. Also, different goals are proposed in policy-making and comprehensive planning, which are in conflict with each other; so It’s important to optimize the composition of the energy production portfolio based on what purpose. In this research, the electricity generation portfolio is a combination of fossil, renewable and nuclear energy groups, and optimization is done using the genetic algorithm method with MATLAB software in single-objective (GA) and multi-objective (NSGA-II) modes.The comparison of optimization methods showed that the share of energies for single-objective optimization based on economic index is different from modes based on environmental index and Multi-purpose optimization. Through multi-objective optimization, a set of solutions is introduced, each of which fulfills one of the objectives at an acceptable level. In other words, achieving general optimal points is more likely than single-objective mode. single-objective optimization usually introduces local optimal points and leads to misguidance and moving away from the main goal.

This study investigates and optimizes the location of urban service centers in District 3 of Tehran using multi-objective models. The aim is to compare and evaluate the performance of the weighted epsilon-constraint method with genetic algorithms and hybrid particle swarm optimization algorithms to determine the optimal locations for urban service centers and allocate population points to them. The goal is to identify the best locations for a number of service centers that should be established at selected candidate sites.
This model incorporates queueing systems, allowing for a variable number of servers at each center based on customer demand. To address multiple objectives, the epsilon-constraint method is used to solve the model. Finally, metaheuristic methods such as genetic algorithms and particle swarm optimization are employed to assess solution time and model efficiency.
Using these models can reduce waiting times and improve citizens’ access to urban service centers. Moreover, optimizing location and resource allocation can lead to lower operational costs and enhance the overall efficiency of the service delivery system.
The results of this study indicate that employing multi-objective models with a queueing theory approach can effectively improve the location of urban service centers.

Diversifying investment portfolios by incorporating a variety of assets is a well-established strategy for mitigating risk and enhancing returns. Traditionally, mathematical models for portfolio optimization have primarily focused on stock investments within the capital market. However, this study extends the scope of portfolio optimization to encompass both project and stock investments. This is a critical advancement as investors increasingly grapple with allocating budgets across these two asset types simultaneously. Therefore, this paper proposes a novel mixed portfolio optimization model that uses the Mean-SemiVariance-SemiEntropy approach. By incorporating project investments alongside traditional stocks, the proposed model offers more efficient portfolios that can lead to improved return/risk ratios for investors seeking to optimize their overall financial strategy.

Design/methodology/approach:

 An attempt has been made to bridge the gap between the distinct spaces of projects and stocks to facilitate their joint analysis. Subsequently, a Mean-SemiVariance-SemiEntropy approach has been employed to develop a model within a probabilistic framework. For validating this model, a numerical experiment involving three projects and five stocks from the capital market has been tackled, considering the preferences of an investor. Finally, the optimization problem has been solved using three metaheuristic algorithms: Genetic Algorithm (GA), Imperialist Competitive Algorithm (ICA), and Gray Wolfs Optimization (GWO).

The results obtained by solving the model using the above-mentioned metaheuristic algorithms demonstrated that despite the high speed of the GWO algorithm, the solutions provided by the GWO algorithm were not satisfactory compared to the GA and ICA algorithms. On the other hand, the acceptable speed with nondominated solutions was the advantage of the ICA algorithm over the GA algorithm. The evaluation of various performance metrics also revealed that the ICA algorithm outperformed the GA and GWO algorithms in this problem. Also, the inclusion of semi-entropy as a risk assessment metric led to an improvement in the return on the investment portfolios.

Research limitations/implications: 

Incorporating investor constraints and preferences, such as cardinality and boundary constraints, into the model forms an NP-hard problem. Consequently, exact solution methods are replaced by non-exact methods, such as metaheuristic algorithms. Given the diversity of project contracts, this study concentrated solely on projects with cost-plus contracts, where the entire project or a portion can be selected for partnership. Similar to the Markowitz model, the projects' returns such as stocks' returns were assumed to be normally distributed.Practical implications: This study significantly enhanced diversification, increased potential returns, and reduced risk for investors by introducing a novel mixed project-and-stock portfolio optimization model. The proposed approach can be implemented by a wide range of investors and managers of investment units in various organizations, bringing a new perspective to investment management.

Social implications: 

The far-reaching implications of this study extend beyond the realm of investment management, permeating social, economic, and political areas. The innovative mixed project-and-stock portfolio problem has the potential to positively transform society using fostering innovation, stimulating economic growth, and enhancing financial knowledge. This paper can foster economic growth and job creation by providing new investment opportunities and increasing investment in productive ventures. In summary, this study has taken a significant step towards improving social and economic well-being by introducing an innovative model for resolving investment challenges.

Originality/value:

 The innovation and strength of this research lies in incorporating projects as a new asset class into the traditional portfolio model. This goes beyond simply adding a new asset to an investment portfolio, as the nature of the projects introduces new complexities to the portfolio management process. For this purpose, this study employs a probabilistic approach based on historical data. In addition, the simultaneous use of two risk measures, i.e., semi-variance and semi-entropy, significantly improves the performance of the model by focusing on different risk aspects. This provides a more comprehensive picture of the risks associated with the portfolio and helps investors make more informed and wise decisions.

Managing energy consumption in smart buildings has become an increasingly important challenge. Efficient energy management can have a positive impact on both micro and macroeconomics. Moreover, it is essential to ensure that the comfort of smart building residents is maintained at an acceptable level. Optimization algorithms can be used to achieve user convenience while minimizing energy consumption. In this study, we propose an optimization approach that utilizes an agent-based architecture. This architecture comprises intelligent agents that communicate with each other via message exchange in a network structure consisting of three layers: (1) The switch layer monitors user preferences and comfort levels. (2) The coordination layer includes a coordinating agent that determines the optimal timing for electrical appliances to minimize electricity consumption costs and maximize user comfort. (3) The execution layer contains performer agents. Our focus in this research is on the coordination layer with the aim of reducing energy consumption costs and peak average rates, while increasing user comfort to the highest possible level. However, this optimization problem is highly complex due to the large number of electrical devices and their capabilities. To address this, we propose a hybrid method based on genetic and bat algorithms. We evaluated its performance based on objective functions and compared it with recent research on SmartHome and CU-Bems datasets. Our results demonstrate an improvement in performance

This paper presents a multi-objective mathematical model for the reverse supply chain of hospital waste management in Iran during the COVID-19 pandemic, incorporating dimensions of sustainability. The objectives of the model are as follows: 1) Minimizing the costs associated with building facilities and waste treatment centers, vehicle fuel costs, and environmental costs due to pollutant emissions; 2) Maximizing the energy generated from the waste combustion process; 3) Minimizing the risk of virus transmission resulting from inadequate waste management; and 4) Maximizing the number of job opportunities in the established centers. It is important to note that existing uncertainties are addressed through the application of fuzzy set theory. Given the multi-objective nature of the model, two multi-objective algorithms, namely the Pareto archive-based Krill Herd Algorithm and Non-dominated Sorting Genetic Algorithm II (NSGA-II), are employed to solve the defined problem. The results indicate that the proposed Krill Herd Algorithm converges to a solution with higher quality and dispersion compared to NSGA-II. Additionally, through a comparison of the spacing index and running time of the two algorithms, it is observed that NSGA-II explores the solution space with higher uniformity and solves the model in less time.

In the present unstable business environment, supply chains are considerably impacted by disruptions, necessitating the implementation of resilience strategies. These strategies, however, pose significant financial challenges for companies. Therefore, financing is essential in developing resilient supply chain networks. In addition to utilizing existing capital, options such as bank loans and trade credit can be employed to alleviate the financial burden and enhance working capital.  The present scholarship has failed to address the issue of financial strain resulting from the adoption of resilience strategies. Additionally, the significance of trade credit and repayment scheduling in all levels of the supply chain network also left under-researched. To fill this research gap, this paper proposes a three-tiered supply chain network consisting of main/support suppliers, factories, and distribution centers under uncertain demand conditions. The network is developed to effectively handle demand uncertainty and achieve optimal net present value and demand estimation. To solve the bi-objective model of the study, a preemptive fuzzy ideal programming approach accompanied by the implementation of the CPLEX solver is utilized. The findings lend support to the importance of securing financial support for support suppliers and establishing effective trade credit agreements across all levels of the supply chain.

Pair trading strategy is one of the oldest and most common statistical arbitrage strategies. Pair formation is an important step in pair trading that examined manually and this method fails in the multivariate mode and does not consider conflicting goals in the problem structure. The main problem in this study is to present a method that creates multivariate pair combinations with multiple contradictory goals and focusing on the integration approach. Therefore, a combination of stocks optimized for two opposite objectives risk (mean-reversion) and return (spread variance) to form a set of profitable multivariate pair trading opportunities. The statistical population is companies listed on the Tehran Stock Exchange. The statistical sample limited by the need for high-frequency transactions from the top 50 companies. The problem developed in the form of a mixed integer-programming model (MIP), and due to non-convex constraints and exponential space, a multi-objective genetic algorithm used to obtain pair combinations. To achieve multiple goals, an advanced type of genetic algorithm; The Chaotic Non-dominated Sorting Genetic Algorithm (CNSGA-II) was used. The Chaos theory used to create the initial population of the genetic algorithm in order to obtain appropriate and high-precision solutions. Research has shown that the use of chaos theory can increase the degree of convergence in evolutionary algorithms. The results of the experiments of this study show that multi-objective pair trading strategies focusing on the integration approach have a significant advantage over the traditional single-objective model.

Providing financial resources is necessary for the survival of any business. In supply chain networks, bank loans and commercial credits play a crucial role in financing. Supply chain networks are always affected by financial disturbances under uncertainty condition, therefore, the design of supply chain networks considering financial flows leads to the improvement of working capital. In this research, the supply chain network is designed and developed considering commercial credibility. Considering commercial credit at all levels in a three-level supply chain network including suppliers, factories and distribution centers can be stated as the main contribution of this study. In addition, considering the timing for the repayment of commercial credits by the factories and distribution centers in uncertainty conditions is another challenge of the present research. Due to the uncertainty of demand, supply chain planning should be done in such a way that the necessary financial resources for the production operations are incorporated. In this regard, the demand is considered under scenario-based uncertainty in the proposed model in which the maximization of the net present value as well as the demand estimate are the main objectives. The CPLEX solver was used for solving the model in small-sized instances and the Bee Colony and Wale multi-objective metaheuristic algorithms were used for solving the large-sized problems. The results show how commercial credit affects physical flow. Also, the Wale metaheuristic algorithm has a better performance than the other algorithm.

Today, due to the increase and complexity of customers' needs, the products available in the market do not satisfy the needs of the customers. Hence, the most effective way for an organization to achieve its objectives is to create distinction through both developing new products and bringing about variations in those products. This study, while pursuing the objective of evaluating product development design, aims to propose a multi-objective design. This model analyzes the developed design from two perspectives of general criteria and variation capacity norms.
Design/methodology/approach: The current research embarks on identifying general criteria using Balanced Scorecard (BSC). The proposed model offers criteria according to which the required standard measures for the evaluation of the product development design are customized and extracted. After determining the evaluation criteria related to each perspective – general and variation capacity- the mentioned criteria have been validated. Then, by using the existing methods, these criteria have been quantified. Finally, the identified standard measures have been employed in the proposed multi-purpose optimized model. 
In this paper, a real case was studied in the Iran Electronics Industries, and the result of the configuration was illustrated. Quantitative values ​​of validated criteria were determined with the help of academic and industry experts and existing methods. After calculating the quantitative values ​​of the criteria for the evaluation of phased array radar development designs, these values were used in the multi-objective optimization model and measured in terms of the amount of risk, revenue, organizational strategy and the amount of effort towards redesign. Finally, by solving the optimization model using GAMZ win 64 25.1.12 software and the weighted sum method, the best development plan was selected.
Research limitations/implications: The main limitation of this study is the lack of accurate information in the early stages of product development. In this research, it was assumed that the information provided by the experts and designers of the relevant industry is correct and real. It is suggested to use fuzzy data in future studies so that the result has more reliability. For future research, the following subjects can be attractive and the present study can provide the necessary background for researchers who seek to work on such subjects: i) In the current research, the time parameter was not considered. It is suggested to consider time in future research; ii) to identify non-common components between the two current and future generations, the method of calculating the priority of standardization of components and considering the technical and financial ability of the producer was used. It is suggested to decide according to possible technologies in the future; iii) another perspective can be used to categorize and identify criteria; iv) to calculate reliability and maintainability, the lifetime of systems was assumed to be exponential and with a constant failure rate. It is suggested to use Weibull distribution with variable failure rate for a more realistic calculation, and v) it is suggested to compare the results of this study with other studies.
Practical implications: Finding comprehensive criteria to evaluate product development designs and providing an effective mathematical model for evaluation can lead to selecting the best product development designs. Selecting an optimal design can prevent the increase in product modification costs and the effort to redesign and reduce the time to supply new products to the market.
Originality/value: Based on the literature review, particularly the internal research, a method that evaluates product development designs with comprehensive criteria including finance, customer, business and internal work, growth and learning, and variation capacity has not been found. Also, the Design for Variety approach has not been used in the initial phases of research and it is applied when the product is made and released to the market.

One of the common methods of controlling the side erosion and rivers training is the use of spur dikes. It is important to consider several different and conflicting objectives in river engineering studies simultaneously. For this purpose, the optimum design of the dimensions of constructed spur dikes in Zanjanrood was considered with the aim of minimizing the cost and maximizing the sediment discharge. In the model, a combination of morphological model, design and optimization model of multi-objective harmony search algorithm were used and to evaluate the cross-section stability were used hypothetical theories. Calibration and validation of the model were performed by Zanjanrood data with Van Rijn sediment equation and Gill scouring equation. Sensitivity analysis of the model were performed for the parameters of discharge, slope and initial width of the river. By comparing different scenarios obtained from the Pareto front, better answers were provided than the plan implemented in Zanjanrood and the studies of other researchers. Finally, one of the points of the Pareto front must be selected for construction and execution. Choosing the right number depends on the designer's opinion and the existing priorities. in one of scenario that chosen as the optimal design, it has the lowest Euclidean distance compared to other scenarios with the ideal point. This scenario offers 244.58% lower cost and 25.48% more sediment discharge than Zanjanrood plan.

This paper investigates unreliable multi-product assembly lines with mixed (serial-parallel) layout model in which machines failures and repairing probabilities are considered. The aim of this study is to develop a multi-objective mathematical model consisting the maximization of the throughput rate of the system and the minimization of the total cost of reducing mean processing times and the total buffer capacities with respect to the optimal values of the mean processing time of each product in each workstation and the buffer capacity between workstations. For this purpose, in order to configure the structure of the mathematical model, Simulation, Design of Experiments and Response Surface Methodology are used and to solve it, the meta-heuristic algorithms including Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Non-Dominated Ranked Genetic Algorithm (NRGA) are implemented. The validity of the multi-objective mathematical model and the application of the proposed methodology for solving the model is examined on a case study. Finally, the performance of the algorithms used in this study is evaluated. The results show that the proposed multi-objective mathematical model is valid for optimizing unreliable production lines and has the ability to achieve optimal (near optimal) solutions in other similar problems with larger scale and more complexity.

Due to the trend of increasing demand for electricity consumption, the use of current fossil fuel-based electricity production technologies has led to frequent blackouts in the summer and fuel burning in the winter. Therefore, the use of renewable energy sources and especially the construction of solar power plants can be a solution to end the blackout and fuel burning crises. The purpose of this research is the multi-objective optimization of the allocation of solar power plant construction to meet the electricity demand. In the objective functions of the problem of system costs, the amount of disturbances in the lines and the amount of greenhouse gases were minimized, as well as the amount of covered areas was maximized. In this research, the LP metric method has been used to solve the problem of multi-objective optimization in GAMS software. In order to validate the presented mathematical model, the correctness of the presented model was checked by GAMS software.Then, by presenting a numerical example, the complexity of the problem, the effectiveness of the multi-objective genetic algorithm in small and large dimensions were investigated. Finally, a case study regarding the construction of a solar power plant in Kashan, Aran and Bidgol region was investigated  and  According to the given information and the input data of the problem, the situation of the candidate areas for the construction of solar power plants was determined and Also, different areas of demand were assigned to the built solar power plants.

This study aims to optimize the energy supply system of a greenhouse considering twelve different climate conditions in Iran. For this purpose, an integrated two-objective linear energy optimization model has been developed to control the inside temperature and provide the required heating, cooling, and electricity by receiving electricity, gas, and water. The mentioned goals are to minimize operating costs (taking into account the discount rate over twenty years) and the initial cost and minimize the deviation of the inside temperature from the desired value. The initial cost of energy equipment is the result of examining data from domestic manufacturers and obtaining the equipment cost curve. The analysis of the results shows that the best areas for greenhouses construction are Kerman, Tehran, and Arak, respectively, for which the total cost is around ten thousand dollars.

Establishing security in the different borders of the country is one of the most important priorities of the military forces, especially the ground forces. In this article, the security games between a defender and several attackers are investigated and the players' preferences and how to calculate them are described. To solve the problem of the uncertainty of the defender to face the unknown type of attacker, the Bayesian game approach is used. and in order to solve the problem of uncertainty caused by the ambiguity in the understanding of experts and their imprecise judgment, the phase theory has been used as a practical example of this type of games in creating security at land borders, and the model of this problem is expressed as a game. multi-objective security has been investigated, for this purpose we have investigated the movements and actions of the Republic of Azerbaijan in the region and to prevent this country from attacking the common land borders of Iran and Azerbaijan, the appropriate allocation and coverage of four bordering provinces (Gilan, Ardabil) , West Azerbaijan and East Azerbaijan) by the ground units in the operational area. Finally, it can be concluded that many complex military issues can be investigated using security games and the model of its optimal solution can be designed.