Objective Optimization Problem Research Articles

Adaptive decomposition-based evolutionary algorithm for many-objective optimization with two-stage dual-density judgment

In order to better balance the convergence and diversity of MOEA/D for many objective optimization problems (MaOPs) with various Pareto fronts (PFs), an adaptive decomposition-based evolutionary algorithm for MaOPs with two-stage dual-density judgment is proposed. To solve the problem that weighted Tchebycheff decomposition may produce weakly Pareto optimal solutions when the solution is not unique or the uniqueness is difficult to guarantee, an augmented weighted Tchebycheff decomposition is adopted. To balance the convergence and diversity of non-dominated solutions in the external archive, different sparsity-level evaluations using vector angles or Euclidean distances are used to measure the distribution of solutions at different stages. To improve the diversity of solution sets obtained by MOEA/D for various PFs, an adaptive weight vector adjustment method based on two-stage dual-density judgment is presented. For weight vector addition, the potential search area is found according to the two-stage density judgment, and then a two-stage sparsity level judgment on the solutions of this area is performed for a second density judgment. For weight vector deletion, the degree of crowding is used to delete the weight vectors with a high crowding degree. Compared with nine advanced multi-objective optimization algorithms on DTLZ and WFG problems, the results demonstrate that the performance of the proposed algorithm is significantly better than other algorithms.

Optimal siting and sizing of battery energy storage systems in unbalanced distribution systems: A multi objective problem under uncertainty

In this paper the siting and sizing problem of battery energy storage systems in unbalanced active distribution systems is formulated as a mixed-integer, non-linear, constrained multi objective (MO) optimization problem under uncertainties. The problem is cumbersome from the computational point of view due to the presence of intertemporal constraints, a great number of state variables and the presence of uncertainties in the problem input data. A new approach based on the trade-off/risk analysis is proposed to obtain with acceptable computational efforts a solution that may not be the optimal solution but represents a reasonable and robust compromise. We use the trade-off/risk analysis, because it was specifically developed for power system planning problems in which we deal with a wide range of options, with possible conflicting objectives, and with uncertainty and risk. The proposed approach includes new procedures to select an adequate set of planning alternatives to be considered in the trade-off/risk analysis framework and to assist the planning engineer when difficulties arise in setting probabilities of the input data. Numerical applications to an IEEE unbalanced test system demonstrate the effectiveness of the proposed procedure and indicate the best alternatives of storage systems in the range from 450 kW to 600 kW globally installed in a reduced set of nodes.

Pareto-critical equilibrium condition for non-linear multiobjective optimization problems with applications

The new (necessary) Pareto-critical equilibrium condition (PCEC) discussed in this study is based on the Pareto-critical condition for non-linear optimization problems. The proposed condition is evaluated by defining a multiobjective optimization problems (MOOPs) subject to a set of constraints. Then this MOOPs is converted to a single objective optimization problem by using the available optimization techniques, for instance, the weighted sum method, and solved by the non-linear Nelder-Mead simplex method. The obtained solution points satisfy the proposed PCEC of an unconstrained multiobjective optimization problem (MOOPs) under the convexity assumption. This PCEC is evaluated in a search that either results in a point inside the feasible region or a point for which the PCEC holds. The resulting Pareto-critical equilibrium condition is globally valid for convex problems. Numerical experiments are carried out in order to clarify the proposed condition's validity. Moreover, the proposed PCEC is used to place a downlink transmit beamforming system base station in an ideal position as a first application and is also employed in situations where there are multiple agents working towards a common goal as a second application.

Latency-aware scheduling for data-oriented service requests in collaborative IoT-edge-cloud networks

Edge computing facilitates the collaboration of physical devices at the network edge to support nearby computing requests, in order to reduce long-distance sensory data transmission from Internet of Things (IoT) devices to the remote cloud. An IoT-edge-cloud network is constructed, where sensory data collected by IoT devices is aggregated to the physically adjacent edge nodes and is transmitted between these edge nodes for achieving task processing, and the cloud acts as a central controller with global scheduling, considering the latency sensitivity of service requests and capacity limitation of physical devices. These service requests are decomposed into multiple data-oriented tasks with certain logical relations, and the satisfaction of service requests is implemented in such a collaborative IoT-edge-cloud network. In this setting, a data-oriented task scheduling mechanism is presented through considering data aggregation, data transmission and task processing in a latency-efficient and energy-saving fashion, which is formulated as a constrained objective optimization problem. We develop an improved Genetic Algorithm-based Task Scheduling (iGATS) approach, where task scheduling decisions are regarded as chromosome codings, fitness function and genetic operators are designed to solve the formulated problem. Simulation experiments are evaluated, and numerical results show that our iGATS outperforms other baseline techniques for reducing response latency, improving temporal satisfaction of service requests, and maintaining load-balancing across the whole network.

Optimizing EDM for titanium alloys: an in-depth comparison of five MCDM techniques

This experimental study investigates the effect of the cutting parameters of the Electrical Discharge Machining (EDM) process of Ti-6Al-4V alloy material on surface roughness (Ra), cutting time (t) and Material Removal Rate (MRR) then solve the Multiple Objective Optimization Problem using separate Multi-Criteria Decision-Making (MCDM) methods namely Entropy-Weighted TOPSIS (E-TOPSIS), MOORA, SAW, VIKOR, and WPM. Focusing on nine 3-levels variants including Operating Voltage (OV), Pulse-On Time (Ton), Pulse-Off Time (Toff), Short-Circuit Off Time (AFF), Secondary Voltage (SV), Feed Rate (WF), Tension (WT), Water Pressure (WL) and Material Cutting Speed (F). Due to the large number of variants studied, the Taguchi L27 experimental design was chosen to reduce the number of experiments while still ensuring reliability in assessing the impact of technological parameters on responses in the study. The optimization results from the different methods indicated two distinct optimal outcomes. According to the E-TOPSIS, MOORA, and SAW, the optimal result is a Ra of 3.27 µm, a t of 7.37 min, and an MRR of 7.45 mm3/min. This result suggests a balanced and harmonious optimization among all criteria. On the other hand, the figures VIKOR and WPM methods are 2.87 µm, 9.57 min, and 5.74 mm3/min, respectively. These results indicate a higher priority for certain criteria, reflected in the lower Ra, longer cutting time, and a smaller MRR in comparison to the figures for the remaining MCDM methods. The different optimal results achieved by various methods highlight that each method is suited to and excels with different sets of values. Therefore, in each specific research or production process, comparing and choosing results calculated by different methods provides a comprehensive view, aiding in making appropriate decisions

An Improved Single Objective Optimization Approach for Double-Layered Multi-Head Weighing Process

In recent years, the double-layered multi-head weighers whose hoppers are arranged in two levels are widely used in the accurate and reliable weighing for packing food products. The weighing processes are mathematically modeled into a single objective optimization problems. The objective of packing problem is to minimize the total weight of combined hoppers for a package under the condition that the total weight must be no less than a specified target weight. This paper proposes a novel single objective optimization approach for double-layered multi-head weighing process. More precisely, relying on a new bound on the optimal weight, this study accurately determines the number of hoppers to be combined at each packing operation, and find the best possible hopper combination using the single-objective algorithm. This method significantly speeds up the packing process as a whole. According to the present approach, the candidate number of hoppers to be combined can be taken one or two integral values. The probability that the accurate number of hoppers to be combined becomes one integral value is explicitly calculated, which is the performance factor to the previous one. In addition, results from the numerical experiments to show the effectiveness of the proposed approach are presented.

Trust region based chaotic search for solving multi‐objective optimization problems

AbstractA numerical optimization technique used to address nonlinear programming problems is the trust region (TR) method. TR uses a quadratic model, which may represent the function adequately, to create a neighbourhood around the current best solution as a trust region in each step, rather than searching for the original function's objective solution. This allows the method to determine the next local optimum. The TR technique has been utilized by numerous researchers to tackle multi‐objective optimization problems (MOOPs). But there is not any publication that discusses the issue of applying a chaotic search (CS) with the TR algorithm for solving multi‐objective (MO) problems. From this motivation, the main contribution of this study is to introduce trust‐region (TR) technique based on chaotic search (CS) for solving MOOPs. First, the reference point interactive approach is used to convert MOOP to a single objective optimization problem (SOOP). The search space is then randomly initialized with a set of initial points. Second, in order to supply locations on the Pareto boundary, the TR method solves the SOOP. Finally, all points on the Pareto frontier are obtained using CS. A range of MO benchmark problems have demonstrated the efficiency of the proposed algorithm (TR based CS) in generating Pareto optimum sets for MOOPs. Furthermore, a demonstration of the suggested algorithm's ability to resolve real‐world applications is provided through a practical implementation of the algorithm to improve an abrasive water‐jet machining process (AWJM).

Dynamic and efficient resource allocation for 5G end‐to‐end network slicing: A multi‐agent deep reinforcement learning approach

SummaryThe rapid evolution of user equipment (UE) and 5G networks drives significant transformations, bringing technology closer to end‐users. Managing resources in densely crowded areas such as airports, train stations, and bus terminals poses challenges due to diverse user demands. Integrating mobile edge computing (MEC) and network function virtualization (NFV) becomes vital when the service provider's (SP) primary goal is maximizing profitability while maintaining service level agreement (SLA). Considering these challenges, our study addresses an online resource allocation problem in an MEC network where computing resources are limited, and the SP aims to boost profit by securely admitting more UE requests at each time slot. Each UE request arrival rate is unknown, and the requirement is specific resources with minimum cost and delay. The optimization problem objective is achieved by allocating resources to requests at the MEC network in appropriate cloudlets, utilizing abandoned instances, reutilizing idle and soft slice instances to shorten delay and reduce costs, and immediately scaling inappropriate instances, thus minimizing the instantiation of new instances. This paper proposes a deep reinforcement learning (DRL) method for request prediction and resource allocation to mitigate unnecessary resource waste. Simulation results demonstrate that the proposed approach effectively accepts network slice requests to maximize profit by leveraging resource availability, reutilizing instantiated resources, and upholding goodwill and SLA. Through extensive simulations, we show that our proposed DRL‐based approach outperforms other state‐of‐the‐art techniques, namely, MaxSR, DQN, and DDPG, by 76%, 33%, and 23%, respectively.

A many‐objective evolutionary algorithm based on bi‐direction fusion niche dominance

SummaryAlthough some many‐objective optimization algorithms (MaOEAs) have been proposed recently, Pareto dominance‐based MaOEAs still cannot effectively balance convergence and diversity in solving many objective optimization problems (MaOPs) due to insufficient selection pressure. To address this problem, a bi‐directional fusion niche domination is proposed. This method merges the strengths of cone and parallel decomposition directions in comparing dominations for nondominance stratification within the candidate population, augmenting the selection pressure of population. Subsequently, the crowding distance is introduced as an additional selection criterion to further refine the selection of nondominated individuals within the critical layer. Lastly, a MaOEA based on bi‐directional fusion niche dominance (MaOEA/BnD) is proposed, utilizing bi‐directional fusion niche dominance and crowding distance as important components of environmental selection. The performance of MaOEA/BnD was compared with five representative MaOEAs in 20 benchmark problems. Experimental results demonstrate that MaOEA/BnD effectively balances convergence and diversity when handling MaOPs with complex Pareto fronts.

A stochastic approach for the solution of single and multi–objective optimisation problems of biological processes in sequencing batch reactor

This paper investigates the impact of implementing single and multi-optimisation solutions on the biological treatment process in a sequencing batch reactor (SBR). The research is based on a case study of the water resource recovery facility (WRRF) in Swarzewo, Northern Poland. The paper introduces the adaptive extremum seeking control (ESC) method for dissolved oxygen (DO) concentration control and places it in a layered control structure. Further, it presents the introduction of an optimisation layer for the structure and parameters of the SBR cycle, through the synthesis of stochastic methods: single-objective optimisation (SOO) using a genetic algorithm (GA) and multi-objective optimisation (MOO) using the NSGA-II algorithm. The results were compared to a classical approach with fixed cycle parameters. The paper shows the advantages of optimising cycle parameters, including the number of phases as well as the DO value, on the process flow. These control structures underwent simulation tests in the MATLAB environment with the Simba package. The biochemical processes occurring in the reactor are based on the Activated Sludge Model No. 2d (ASM2d). The optimising control system demonstrates tangible improvements in operational efficiency and significant reductions in electrical energy consumption, highlighting the effectiveness of the proposed methodologies. © 2017 Elsevier Inc. All rights reserved.

Power allocation scheme for sum rate and fairness trade-off in downlink NOMA networks

Non-orthogonal multiple access (NOMA) is an essential enabler technology that is expected to help satisfy the key requirements of increased system throughput in future wireless networks. However, another equally important aspect that should go hand-in-hand with system throughput is user fairness for any network. But, to the best of our knowledge, even though there have been works that look at system throughput or user fairness maximization for NOMA-based networks, they looked at these as a single objective optimization problem, where one is the objective and the other is one of the constraints. However, quite often, joint optimization of both system throughput and user fairness is required to make optimized decisions in the face of trade-offs between these two equally important but conflicting objectives. In this regard, this paper formulates a multi-objective optimization problem to jointly maximize the sum rate and user fairness in a downlink transmission NOMA system, through optimize power allocation (PA), under system-imposed constraints. A weighted sum approach is used to turn the multi-objective optimization problem into a single-objective optimization problem to make it analytically tractable. The optimized PA is then obtained using Lagrange dual decomposition method and Karush–Kuhn–Tucker (KKT) conditions. Using our derived expressions, we propose an iterative PA algorithm that converges fast enough to be employed in practical NOMA networks. We also present simulation results to highlight the effectiveness of the proposed solution. Further, the performance of the proposed method is compared with that of the benchmark methods.

The Multiobjective Control Based on Tolerance Optimization in a Multienergy System

To address the issue of multiobjective control in multienergy systems with diverse operational objectives, a two-stage optimization framework based on expected point tolerance has been proposed in this paper. In the first stage, a single objective function is used for optimization control to obtain the expected point of the multiobjective optimization problem. Then, in the second stage, by defining the allowable deviation between each optimization objective and the expected point, the original multiobjective optimization problem is transformed into a single objective optimization problem solution with tolerance measurement. Finally, in the simulation scene of a multienergy system, it is demonstrated that compared with the optimal results under each single objective method, the proposed method increases power line loss, maximum voltage deviation, new energy consumption, and economy by 2.22, 2.30, 1.02, and 2.45 times, respectively. Compared with the suboptimal results, the proposed method reduces power line loss by 22.26, 1.74, 1.09, and 0.97 times, respectively. Combining the shape of the Pareto frontier, it is demonstrated that the proposed method can comprehensively consider the needs of multiple power optimization objectives for forming a more reasonable and effective system optimization scheduling and also provide a new approach for solving multiobjective optimization problems.

Attaining robust performance targets in data envelopment analysis with application to efficiency evaluation of airports

We consider a ratio-based efficiency analysis in view of achieving performance targets by Decision Making Units. The targets refer to the efficiency scores or ranks and the truth of pairwise preference relations. These outcomes can be instantiated for at least one or all feasible weights associated with inputs and outputs. We discuss Multiple Objective Optimization problems that minimize the required reductions of consumed resources or increases of produced results needed to reach the pre-defined aims. The proposed models offer great flexibility to the Decision Maker, who can indicate which factors should be modified and to which extent. The evolutionary optimization algorithm computes a set of solutions that exhibit the trade-offs between expected modifications of various factors. They can serve as the basis for interactively selecting the most preferred solution to be implemented in practice. The use of the proposed framework is illustrated in the problem of analyzing the efficiency of Polish airports.

Finite mixture models for multiscale dynamics in Chinese financial markets

A novel statistical machine learning technique for decomposing, analyzing, and modeling complex time series is presented in this paper. This methodology is based on unsupervised classification methods using finite mixtures, which have been widely used in factor analysis to extract essential information from multivariate static data in a parsimonious manner. Here, they are applied in a purely dynamic framework to create a new family of autoregressive models. The selection of the number of components and appropriate geometric template in these models is based on a set of information criteria that require solving a multiple objective optimization problem. To ensure the most adequate models are selected, the problem is augmented with a simulation instruction, providing a robust criterion for assignment. Experiments on real financial data sampled over the COVID-19 pandemic demonstrate the potential of this approach as a promising alternative to the well-known Box-Jenkins methodology. The proposed method offers flexibility, accuracy, and stability, making it suitable for a variety of applications in financial modeling and other fields where complex time series data analysis is required.

A review on multi objective optimization problems and advancement on its solutions

A plenty of literatures are available for finding solution of optimization problem of single objective. Very few literatures are available for finding solution of optimization problem with multi objective optimization. Many researchers analysing multi objective problems by treating as single objective, keeping rest of variables as constant. With the tremendous rise of innovations in evolutionary computation, that has added feathers to Multi Objective Optimization techniques.

OPTIMAL SIZING OF SOLAR-WIND HYBRID MICROGRID USING IMPROVED GREY WOLF OPTIMIZATION ALGORITHM A CASE STUDY OF KADUNA - NIGERIA

This paper presents an improved grey wolf optimization algorithm (IGWOA) for optimal sizing of an isolated photovoltaic (PV), wind turbine (WT), and battery energy storage (BES) hybrid microgrid. To demonstrate the effectiveness of the proposed approach, atmospheric data sets comprising of wind, solar, and temperature of Kaduna International Airport were collected from Nigerian Meteorological Agency while the load demand data was collected from Kaduna International Airport Electricity Distribution Center. The microgrid optimal sizing was formulated as a constrained single objective optimization problem. Constraints including, loss of power supply probability (LPSP), power balance, generation limits and battery state of charge (SOC) were imposed. Three simulation scenarios were considered. Firstly, the target allowable maximum LPSP was fixed at 25% and the algorithm was able to determine the optimal sizing of the hybrid microgrid components and minimize the initial cost from 169,880.00 USD to 112,356.40 USD per annum resulting in 34% savings in cost. Secondly, the effect of the target allowable maximum LPSP variation was investigated, and it was found that the total installed capacity of the system decreases with increase in LPSP thereby decreasing the total cost. Additionally, a novel electricity price index (EPI) was introduced in order to quantify the degree of optimality of the solution. The EPI was found to increase exponentially with increase in LPSP, resulting in an EPI of < 0.05USD/kWh at 20% LPSP. Lastly, to validate the proposed approach, a comparative analysis between the IGWOA and other algorithms was carried out, and the proposed IGWOA proved applicable.

Efficient Multi-Objective Simulation Metamodeling for Researchers

Solving multiple objective optimization problems can be computationally intensive even when experiments can be performed with the help of a simulation model. There are many methodologies that can achieve good tradeoffs between solution quality and resource use. One possibility is using an intermediate “model of a model” (metamodel) built on experimental responses from the underlying simulation model and an optimization heuristic that leverages the metamodel to explore the input space more efficiently. However, determining the best metamodel and optimizer pairing for a specific problem is not directly obvious from the problem itself, and not all domains have experimental answers to this conundrum. This paper introduces a discrete multiple objective simulation metamodeling and optimization methodology that allows algorithmic testing and evaluation of four Metamodel-Optimizer (MO) pairs for different problems. For running our experiments, we have implemented a test environment in R and tested four different MO pairs on four different problem scenarios in the Operations Research domain. The results of our experiments suggest that patterns of relative performance between the four MO pairs tested differ in terms of computational time costs for the four problems studied. With additional integration of problems, metamodels and optimizers, the opportunity to identify ex ante the best MO pair to employ for a general problem can lead to a more profitable use of metamodel optimization.

MOEA/D with customized replacement neighborhood and dynamic resource allocation for solving 3L-SDHVRP

Split delivery heterogeneous vehicle routing problem with three-dimensional loading (3L-SDHVRP) is a critical issue in manufacturing logistics. Current mainstream research formulates this problem as a single objective optimization problem, which fails to reveal the relationship among multiple conflicting objectives and cannot provide various trade-off solutions for decision-makers in real-world logistics scenarios. This paper concentrates on a multi-objective 3L-SDHVRP and proposes a multi-objective evolutionary algorithm based on decomposition with customized replacement neighborhood and dynamic resource allocation (called MOEA/D-RD) to deal with it. The numerical experiments on the dataset from the 11th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2021) show the superior performance of the proposed method over some state-of-the-art ones. The source code of MOEA/D-RD is available at https://github.com/CIAM-Group/EvolutionaryAlgorithm_Codes/tree/main/MOEAD-RD.

New Approach to Solving Fuzzy Multiobjective Linear Fractional Optimization Problems

In this paper, an iterative approach based on the use of fuzzy parametric functions is proposed to find the best preferred optimal solution to a fuzzy multiobjective linear fractional optimization problem. From this approach, the decision-maker imposes tolerance values or termination conditions for each parametric objective function. Indeed, the fuzzy parametric values are computed iteratively, and each fuzzy fractional objective is transformed into a fuzzy non-fractional parametric function using these values of parameters. The core value of fuzzy numbers is used to transform the fuzzy multiobjective non-fractional problem into a deterministic multiobjective non-fractional problem, and the ε-constraint approach is employed to obtain a linear single objective optimization problem. Finally, by setting the value of parameter ε, the Dangtzig simplex method is used to obtain an optimal solution. Therefore, the number of solutions is equal to the number of used values, and the optimal solution is chosen according to the preference of the decision-maker. We have provided a didactic example to highlight the step of our approach and its numerical performances.

Accurate identification and confidence evaluation of automatic generation control command execution effect based on deep learning fusion model

With the increasing complexity of the power grid, the precision of the thermal power units' execution of automatic generation control (AGC) commands is gradually increasing the impact on the online regulation of the power grid. The deviation between the actual output of thermal power units and the AGC command of the grid will not only affect the consumption of new energy output, but also endanger the safe operation of the grid. This paper introduces “deep learning” technology to solve the problem. Firstly, an AGC command execution effect identification and confidence evaluation algorithm (ACEEI-CEA) is proposed. The algorithm builds a neural network model to accurately predict the unit output and the confidence evaluation of the prediction results. Next, a high-dimensional input preprocessing strategy based on variational autoencoder (VAE) is proposed to reduce the dimensionality of the model input attributes, improving the convergence and accuracy of the model. Finally, an AGC optimal command fast inversion solution method (AOCFISM) is designed. This method transforms the unit output deviation problem into an objective optimisation problem. And improve the efficiency of solving the optimal AGC command value by constraining the unit command value. The calculation results show that the error of the prediction results of the model proposed in this paper is 5% lower than that of the traditional neural network. The difference between the output value of the optimal AGC command and the expected output value obtained is less than 0.5 MV, which can support AGC online decision-making.© 2017 Elsevier Inc. All rights reserved.