Many-objective Optimization Algorithm Research Articles

Identifying Pareto Fronts Reliably Using a Multistage Reference-Vector-Based Framework

Evolutionary multi-objective and many-objective optimization (EMO and EMaO) algorithms are increasingly being used to identify the true shape and location of the Paretooptimal front using a few representative well-converged and welldistributed solutions. The reason for their popularity is due to their ability to provide a better understanding of objective relationships for optimal solutions, and also to facilitate the choice of a preferred solution using an interactive or postoptimal multi-criterion decision analysis. However, since EMO and EMaO algorithms are stochastic, a single application may not provide a true representative set with a desired number of Pareto solutions reliably in repetitive runs and importantly with a well-distributed set of solutions. In this paper, we propose a multistage framework involving reference-vector based evolutionary multi-and many-objective algorithms (MuSt-EMO and MuSt-EMaO) that attempts to recursively rectify shortcomings of previous stages by careful executions of subsequent stages so that a prescribed number of well-distributed and well-converged solutions are achieved at the end. The proposed multi-stage approach is implemented to a number of popular reference vector based EMO/EMaO algorithms and is applied on various multiand many-objective test and real-world problems.

A Reference Vector-Assisted Many-Objective Optimization Algorithm with Adaptive Niche Dominance Relation

A Reference Vector-Assisted Many-Objective Optimization Algorithm with Adaptive Niche Dominance Relation

Balancing competing objectives in bigel formulations using many-objective optimization algorithms and different decision-making methods

Many-objective optimization, which deals with balancing multiple competing objectives to find compromised solutions, is essential for solving complex problems. This study explores evolutionary algorithms for optimizing the microstructural, rheological, stability, and drug release properties of bigel systems formulated using structured almond oil, mixed organogelators, and carbopol. The oleogel was identified as the dispersed phase, with droplet sizes ranging from 1.43 µm to 7.37 µm, indicating improved characteristics compared to other bigels. Each formulation exhibited non-Newtonian shear-thinning and thixotropic behaviors, which were positively influenced by the proportions of the excipients. After undergoing multiple stress cycles, highly concentrated bigels exhibited phase separation. Unexpectedly, bigels with lower viscosity exhibited reduced rates of drug release. FT-IR and HPLC analyses confirmed the compatibility and stability of drug-excipient interactions, with impurities remaining below 4%. This study emphasizes the complex interactions within mixed lipid-based bigels, requiring many-objective optimization techniques to address conflicting objectives. The objectives of optimization involve simultaneously minimizing microstructural properties while maximizing structural recovery and drug release properties. This led to conflicting objectives, where achieving higher structural recovery did not align with the desired drug release rate. Additionally, more stable formulations did not meet the optimal microstructural objectives. To resolve these conflicts, an RSM-MaOEAs approach was applied, employing various decision-making methods. Among EAs, RSM-RVEA notably achieved exceptional convergence. Furthermore, three MaOEAs-integrated decision-making methods—WSM, WPM, NED—and the RSM-desirability, offered potential solutions. Overall, this research proposes a robust framework for compromising the bigels’ performance and stability, with broader applications in drug delivery and related fields.

A solution potential-based adaptation reference vector evolutionary algorithm for many-objective optimization

Decomposition-based multiobjective evolutionary algorithms are widely utilized for solving multiobjective optimization problems (MOPs). These algorithms have a higher degree of diversity due to a uniform distribution of the reference vectors in the objective space. However, these algorithms may struggle to select a suitable candidate set for solving many-objective optimization problems (MaOPs) with irregular Pareto fronts (PFs). To solve this problem, a solution potential-based adaptation reference vector evolutionary algorithm (SPARVEA) is proposed in this paper. In the algorithm, a concept called solution potential is presented to assess whether the direction of convergence of the solution to the ideal solution has potential. The solution potential is obtained with an evaluation function to calculate the potentials of the corresponding solutions. A solution potential-based adaptation strategy is then designed for adapting the reference vector to better guide the direction of convergence of the solution when solving MaOPs with irregular PFs. A modified angle penalty distance (mAPD) is adjusted to improve the convergence rate of the solution set in many-objective optimization problems. The proposed algorithm SPARVEA is compared with state-of-the-art many-objective evolutionary algorithms on four test sets with irregular PFs and four practical problems. Experimental results demonstrate the superior performance of SPARVEA on many-objective optimization problems. This contribution helps to advance the development of efficient algorithms for solving many-objective optimization problems.

An Expensive Many-Objective Optimization Algorithm Based on Efficient Expected Hypervolume Improvement

The expected hypervolume improvement (EHVI) is one of the most popular infill criteria for multiobjective optimization problems. Although it has a significant advantage in exploring potential Pareto-optimal solutions, it has rarely been applied in many-objective problems due to its high computational cost. To address this issue, this paper proposes an expensive many-objective optimization algorithm based on the framework of NSGA-III and assisted by the kriging surrogate models. In the proposed algorithm, the Monte Carlo sampling method for EHVI estimation is improved by importance sampling, in which only one sampling process is required during the entire optimization process using a uniform distribution in normalized objective space. Considering the predicted uncertainty from the kriging model, an uncertainty-assisted nondominated sorting approach is proposed to substitute for the conventional approach in NSGA-III. In the proposed method, the predicted uncertainty is incorporated into the objective space as one independent dimension for nondominated sorting, which can enable the exploration of potential points with desirable EHVI values. In addition, the proposed algorithm considers the diversity of the solutions by de-emphasizing the pursuit of the best EHVI. The experimental results on benchmark problems demonstrate that the proposed EHVI calculation method can save computational costs compared with Monte Carlo sampling and indicate the superiority of the proposed algorithm over the others.

An efficient many-objective optimization algorithm for computation offloading in heterogeneous vehicular edge computing network

Vehicular Edge Computing (VEC) provides flexible distributed computing paradigm for vehicular network through computation offloading. With the advent of a growing of modern vehicle applications, the challenge for VEC network to fulfill the expansive demands from various suppliers, users and environments is increasingly prominent. This paper formulates a many-objective computation offloading problem in heterogeneous VEC network aiming to fulfill the diversified optimization requirements, including minimizing the task completion time, energy consumption and resource costs as well as load balance. A many-objective optimization algorithm named MaOITGO-CO is proposed to solve the formulated problem based on ITGO (Invasive Tumor Growth Optimization) by simulating the growth patterns of tumor cells. Specifically, considering the characteristics of computation offloading in VEC scenarios such as mobility, real-time requirements and the variety of tasks and resources, four types of tumor cells are equipped with different search strategies to enhance the search effectiveness and efficiency. The simulation results show that the proposed approach can provide high quality Pareto solutions for computation offloading problem, which outperforms other widely used algorithms in terms of convergency and diversity. Furthermore, the results of scalability experiments validate the availability of MaOITGO-CO when the problem is extended to different scales of both tasks and computing resources.

Enhanced decomposition-based hybrid evolutionary and gradient-based algorithm for many-objective optimization

Enhanced decomposition-based hybrid evolutionary and gradient-based algorithm for many-objective optimization

A game theory based many-objective hybrid tensor decomposition for skin cancer prediction

The development of skin cancer can be influenced by the abnormal expression of certain microRNAs (miRNAs). Current prediction models for miRNA-skin cancer associations have difficulties in maintaining both accuracy and comprehensiveness. To construct a comprehensive and interpretable skin cancer prediction model, various advanced tensor decomposition methods are organically combined, and a many-objective hybrid tensor decomposition model is proposed. In addition, due to the high computational cost of tensor decomposition, a many-objective optimization algorithm based on game theory was designed to solve the model. The game theory was used to dynamically adjust the diversity and convergence of the population, alleviate the pressure of solution selection, and improve the performance of the algorithm. The performance of the proposed algorithm is tested on a benchmark, and the prediction results of the many-objective hybrid tensor decomposition model are evaluated by a fivefold test method, and a case study of the prediction results is also presented. Experimental findings reveal that the proposed model and algorithm enhance overall performance by approximately 5.3%, compared to current advanced models.

Wide-angle and high-efficiency acoustic retroreflectors enabled by many-objective optimization algorithm and deep learning models

Wide-angle and high-efficiency acoustic retroreflectors enabled by many-objective optimization algorithm and deep learning models

Data Collection for Target Localization in Ocean Monitoring Radar-Communication Networks

With the ongoing changes in global climate, ocean data play a crucial role in understanding the complex variations in the earth system. These variations pose significant challenges to human efforts in addressing the changes. As a data hub for the satellite geodetic technique, unmanned aerial vehicles (UAVs) instill new vitality into ocean data collection due to their flexibility and mobility. At the same time, the dual-functional radar-communication (DFRC) system is considered a promising technology to empower ubiquitous communication and high-accuracy localization. In this paper, we explore a new fusion of UAV and DFRC to assist data acquisition in the ocean surveillance scenario. The floating buoys transmit uplink data transmission to the UAV with non-orthogonal multiple access (NOMA) and attempt to localize the target cooperatively. With the mobility of the UAV and power control at the buoys, the system throughput and the target localization performance can be improved simultaneously. To balance the communication and sensing performance, a two-objective optimization problem is formulated by jointly optimizing the UAV’s location and buoy’s transmit power to maximize the system throughput and minimize the attainable localization mean-square error. We propose a joint communication and radar-sensing many-objective optimization (CRMOP) algorithm to meliorate the communication and radar-sensing performance simultaneously. Simulation results demonstrate that compared with the baseline, the proposed algorithm achieves superior performance in balancing the system throughput and target localization.

A Two-Stage Hypervolume-Based Evolutionary Algorithm for Many-Objective Optimization

Many-objective optimization is a critical research topic in the evolutionary computing community. Many algorithms have been proposed to tackle this problem, with evolutionary algorithms based on the hypervolume being among the most effective ones. However, calculating the hypervolume indicator in high-dimensional objective spaces remains time-consuming. To address this issue, we propose a two-stage hypervolume-based evolutionary algorithm (ToSHV) that separates global search and local search to ensure both convergence and diversity. ToSHV performs a global search in the first stage by generating multiple offspring per generation. We modified the R2HCA method to estimate the overall hypervolume contribution, avoiding the time-consuming nature of updating the hypervolume contribution with the greedy method. In the second stage, only one offspring is produced per generation to emphasize local exploration and enhance population diversity. Furthermore, a stage-switching mechanism is designed to dynamically select the appropriate search mode based on the prevailing population distribution. We evaluate our algorithm on WFG and DTLZ test suites, comparing it with three hypervolume-based algorithms and four state-of-the-art algorithms. Experimental results show that our approach is competitive in most cases.

A many-objective optimization evolutionary algorithm based on hyper-dominance degree

Compared with multi-objective optimization, solving many-objective optimization problems usually require more strong selection pressure. However, too strong selection pressure usually leads to the loss of diversity, while insufficient selection pressure often results in the failure of convergence. How to control the selection pressure to balance convergence and diversity remains a challenge in many-objective optimization. To tackle this challenge, a many-objective optimization evolutionary algorithm based on the hyper-dominance degree is proposed in this paper. In the proposed algorithm, the convergence of each solution is quantified by hyper-dominance degree so that the convergence of the population can be controlled by setting a tolerance to screen solutions. To better balance the convergence and the diversity, a tolerance adjusting strategy is designed to control selection pressure during optimization, an improved reference vectors-based diversity preservation strategy is proposed to make the solutions well-distributed in the objective space, and a population reselection strategy based on hyper-dominance degree is proposed to further improve the convergence. The experimental results on various benchmark problems with up to 20 objectives verify that the proposed algorithm outperforms the state-of-the-art peer many-objective optimization algorithms.

On the interest of artificial intelligence approaches in solving the IoT coverage problem

This survey deals with the 3D indoor deployment in IoT collection networks to identify the right locations of the IoT connected objects and, subsequently, to manage the coverage holes while guaranteeing other objectives such as localization and connectivity of IoT devices. These coverage holes result generally from the initial random distribution of the objects. Unlike the existing studies, the present survey does not only focus on the use cases and applications of the different deployment issues but, it also analyzes the problem of deployment by showing its different models and hypotheses presented in the literature and highlighting the used evaluation and performance criteria. The aim of the study is to highlight the relevance of artificial intelligence techniques; especially meta-heuristics, evolutionary optimization, machine learning and reinforcement learning; in finding coverage solutions, better than other methods. Through experimental validation, the performances of the various deployment and redeployment approaches in a 3D indoor context are compared. These approaches involve computational geometry, virtual force, clustering, mathematical modeling, and evolutionary optimization-based approaches. Afterwards, they are investigated and categorized according to their specifications into different summary tables. Statistical and complexity tests are performed to evaluate the complexity of these approaches. In addition, current 3D deployment trends are presented, and some outstanding deployment issues are discussed. Based on the experimental and simulation findings, the behaviors of evolutionary optimization algorithms are compared to those of the other deployment techniques. The obtained findings demonstrate that using artificial intelligence, specifically many-objective optimization algorithms for 3D deployment of IoT networks is more beneficial as it allows enhancing the quality of deployment compared to the other deployment approaches.

A point crowding-degree based evolutionary algorithm for many-objective optimization

A point crowding-degree based evolutionary algorithm for many-objective optimization

A composite surrogate-assisted evolutionary algorithm for expensive many-objective optimization

In many practical many-objective optimization problems, the computational cost of real evaluation is often high. To solve such problems, surrogate-assisted evolutionary algorithms (SAEAs) are effective methods that use low-cost surrogate models to approximate expensive real evaluation and select better-performing individuals for further evaluation. However, existing surrogate models accumulate prediction errors with increasing numbers of objectives, and the computational cost of constructing surrogate models also increases sharply. This paper proposes a composite surrogate-assisted evolutionary algorithm for expensive many-objective optimization. The crux of this method involves categorizing the surrogate models into two distinct types: a global model, constructed based on all costly real evaluations, and local models tailored to subsets derived from clustering all evaluations. Additionally, a new filling sampling criteria is proposed to guide the selection of solutions, considering the requirements of convergence, diversity, and uncertainty. Experimental results on multiple benchmark problems demonstrate that the proposed method is competitive compared to other popular surrogate-assisted evolutionary algorithms in solving expensive many-objective optimization problems within limited computational budgets.

A many-objective evolutionary algorithm with population preprocessing and projection distance-assisted elimination mechanism

Abstract Pareto dominance-based many-objective evolutionary algorithms (MaOEAs) face a significant challenge from many-objective problems (MaOPs). The selection pressure reduces as the number of objectives rises, while the non-dominated solution grows exponentially. Pareto dominance-based MaOEA increases the selection pressure by designing diversity-related environmental strategies. However, it still struggles to strike a good balance between population diversity and convergence. Moreover, the diversity-selection method increases the likelihood that dominance-resistant solutions (DRSs) will be chosen, which is detrimental to the performance of MaOEAs. To address the aforementioned problems, a many-objective optimization algorithm based on population preprocessing and projection distance-assisted elimination mechanism (PPEA) is proposed. In PPEA, first, the population preprocessing method is designed to lessen the negative impacts of DRSs. Second, to further improve the ability to balance population diversity and convergence of Pareto dominance-based MaOEAs, a projection distance-assisted elimination mechanism is proposed to remove the poorer individuals one by one until the population size satisfies the termination condition. The performance of PPEA was compared with seven excellent MaOEAs on a series of benchmark problems with 3–15 objectives and a real-world application problem. The experimental results indicate that PPEA is competitive and can effectively balance the diversity and convergence of the population when dealing with MaOPs.

A Hybrid Many-Objective Optimization Algorithm for Task Offloading and Resource Allocation in Multi-Server Mobile Edge Computing Networks

Mobile edge computing (MEC) is an effective computing tool to cope with the explosive growth of data traffic. It plays a vital role in improving the quality of service for user task computing. However, the existing solutions rarely address all the significant factors that impact the quality of service. To challenge this problem, a trusted many-objective model is built by comprehensively considering the task time delay, server energy consumption, trust metrics between task and server, and user experience utility factors in multi-server MEC networks. We decompose the original problem into task offloading (TO) and resource allocation (RA) to address the model. Then a novel hybrid many-objective optimization algorithm based on cascading clustering and incremental learning is designed to optimize the TO decision solutions. A low-complexity heuristic method is adopted based on the optimal TO decision solutions to optimize the RA problem continuously. To verify the model's validity and the optimisation algorithm's superiority, five other advanced many-objective algorithms are used for comparison. The results show that our algorithm has more than half the number of the superior values for the benchmark problem. And the obtained model solution shows good performance on different indicators metrics for the decomposition problem.

An improved two-archive artificial bee colony algorithm for many-objective optimization

Artificial bee colony (ABC) algorithm has shown good performance on many optimization problems. However, these problems mainly focus on single-objective and ordinary multi-objective optimization problems (MOPs). For many-objective optimization problems (MaOPs), ABC encounters some difficulties. The selection pressure based on Pareto-dominance degrades severely. It is hard to balance convergence and population diversity. To help ABC solve MaOPs, this paper proposes an improved two-archive many-objective ABC (called MaOABC-TA) algorithm. Inspired by the improved two-archive (Two_Arch2) method, MaOABC-TA uses two archives namely convergence archive (CA) and diversity archive (DA) to promote convergence and diversity. Based on CA and DA, three different search strategies are designed to strengthen convergence or diversity in different search stages. In addition, a new probability selection strategy is proposed to choose solutions with good diversity. To verify the performance of MaOABC-TA, it is compared with 10 many-objective evolutionary algorithms (MaOEAs) and 3 many-objective ABCs on DTLZ and MaF benchmark sets with 3, 5, 8, and 15 objectives. Two performance indicators including inverted generational distance (IGD) and hypervolume (HV) and utilized. Experimental results show that MaOABC-TA is more competitive than the compared algorithms in term of the IGD and HV values.

A Hybrid Many-Objective Optimization Algorithm for Job Scheduling in Cloud Computing Based on Merge-and-Split Theory

Scheduling jobs within a cloud environment is a critical area of research that necessitates meticulous analysis. It entails the challenge of optimally assigning jobs to various cloud servers, each with different capabilities, and is classified as a non-deterministic polynomial (NP) problem. Many conventional methods have been suggested to tackle this difficulty, but they often struggle to find nearly perfect solutions within a reasonable timeframe. As a result, researchers have turned to evolutionary algorithms to tackle this problem. However, relying on a single metaheuristic approach can be problematic as it may become trapped in local optima, resulting in slow convergence. Therefore, combining different metaheuristic strategies to improve the overall system enactment is essential. This paper presents a novel approach that integrates three methods to enhance exploration and exploitation, increasing search process efficiency and optimizing many-objective functions. In the initial phase, we adopt cooperative game theory with merge-and-split techniques to train computing hosts at different utilization load levels, determining the ideal utilization for each server. This approach ensures that servers operate at their highest utilization range, maximizing their profitability. In the second stage, we incorporate the mean variation of the grey wolf optimization algorithm, making significant adjustments to the encircling and hunting phases to enhance the exploitation of the search space. In the final phase, we introduce an innovative pollination operator inspired by the sunflower optimization algorithm to enrich the exploration of the search domain. By skillfully balancing exploration and exploitation, we effectively address many-objective optimization problems. To validate the performance of our proposed method, we conducted experiments using both real-world and synthesized datasets, employing CloudSim software version 5.0. The evaluation involved two sets of experiments to measure different evaluation metrics. In the first experiment, we focused on minimizing factors such as energy costs, completion time, latency, and SLA violations. The second experiment, in contrast, aimed at maximizing metrics such as service quality, bandwidth utilization, asset utilization ratio, and service provider outcomes. The results from these experiments unequivocally demonstrate the outstanding performance of our algorithm, surpassing existing state-of-the-art approaches.

Integrated Energy Station Optimal Dispatching Using a Novel Many-Objective Optimization Algorithm Based on Multiple Update Strategies

Regarding the need to decrease carbon emissions, the electric vehicle (EV) industry is growing rapidly in China; the charging needs of EVs require the number of EV charging stations to grow significantly. Therefore, many refueling stations have been modified to integrated energy stations, which contain photovoltaic systems. The key issue in current times is to figure out how to operate these integrated energy stations in an efficient way. Therefore, an effective scheduling model is needed to operate an integrated energy station. Photovoltaic (PV) and energy storage systems are integrated into EV charging stations to transform them into integrated energy stations (PE-IES). Considering the demand for EV charging during different time periods, the PV output, the loss rate of energy storage systems, the load status of regional grids, and the dynamic electricity prices, a multi-objective optimization scheduling model was established for operating integrated energy stations that are connected to a regional grid. The model aims to simultaneously maximize the daily profits of the PE-IES, minimize the daily loss rate of the energy storage system, and minimize the peak-to-valley difference of the load in the regional grid. To validate the effectiveness of the model, simulation experiments under three different scenarios for the PE-IES were conducted in this research. Each object weight was determined using the entropy weight method, and the optimal solution was selected from the Pareto solution set using an order-preference technique according to the similarity to an ideal solution (TOPSIS). The results demonstrate that, compared to traditional charging stations, the daily revenue of the PE-IES stations increases by 26.61%, and the peak-to-valley difference of the power load in the regional grid decreases by 30.54%, respectively. The effectiveness of PE-IES is therefore demonstrated. Furthermore, to solve the complex optimization problem for PE-IES, a novel multi-objective optimization algorithm based on multiple update strategies (MOMUS) was proposed in this paper. To evaluate the performance of the MOMUS, a detailed comparison with seven other algorithms was demonstrated. These results indicate that our algorithm exhibits an outstanding performance in solving this optimization problem, and that it is capable of generating high-quality optimal solutions.