Complicated Multi-objective Optimization Problem Research Articles

Evolutionary feature selection based on hybrid bald eagle search and particle swarm optimization

Feature selection is a complicated multi-objective optimization problem with aims at reaching to the best subset of features while remaining a high accuracy in the field of machine learning, which is considered to be a difficult task. In this paper, we design a fitness function to jointly optimize the classification accuracy and the selected features in the linear weighting manner. Then, we propose two hybrid meta-heuristic methods which are the hybrid basic bald eagle search-particle swarm optimization (HBBP) and hybrid chaos-based bald eagle search-particle swarm optimization (HCBP) that alleviate the drawbacks of bald eagle search (BES) by utilizing the advantages of particle swarm optimization (PSO) to efficiently optimize the designed fitness function. Specifically, HBBP is proposed to overcome the disadvantages of the originals (i.e., BES and PSO) and HCBP is proposed to further improve the performance of HBBP. Moreover, a binary optimization is utilized to effectively transfer the solution space from continuous to binary. To evaluate the effectiveness, 17 well-known data sets from the UCI repository are employed as well as a set of well-established algorithms from the literature are adopted to jointly confirm the effectiveness of the proposed methods in terms of fitness value, classification accuracy, computational time and selected features. The results support the superiority of the proposed hybrid methods against the basic optimizers and the comparative algorithms on the most tested data sets.

A localized decomposition evolutionary algorithm for imbalanced multi-objective optimization

Multi-objective evolutionary algorithms based on decomposition (MOEA/Ds) convert a multi-objective optimization problem (MOP) into a set of scalar subproblems, which are then optimized in a collaborative manner. However, when tackling imbalanced MOPs, the performance of most MOEA/Ds will evidently deteriorate, as a few solutions will replace most of the others in the evolutionary process, resulting in a significant loss of diversity. To address this issue, this paper suggests a localized decomposition evolutionary algorithm (LDEA) for imbalanced MOPs. A localized decomposition method is proposed to assign a local region for each subproblem, where the inside solutions are associated and the solution update is restricted inside (i.e., solutions are only replaced by offspring within the same local region). Once off-spring are generated within an originally empty region, the best one is reserved for this subproblem to extend diversity. Meanwhile, the subproblem with the largest number of associated solutions will be found and one of its associated solutions with the worst aggregated value will be removed. Moreover, to speed up convergence for each subproblem while balancing the population's diversity, LDEA only evolves the best-associated solution in each subproblem and correspondingly tailors two decomposition methods in the environmental selection. When compared to nine competitive MOEAs, LDEA has shown the advantages in tackling two benchmark sets of imbalanced MOPs, one benchmark set of balanced yet complicated MOPs, and one real-world MOP.

Ensemble of selection operators for decomposition-based multi-objective evolutionary optimization

Decomposition-based multi-objective evolutionary algorithms (MOEA/D) have demonstrated competitive performance in solving complicated multi-objective optimization problems. The two mainstream selection operators of MOEA/D for updating populations, i.e., neighborhood-based and best-fitness-based selection operators, perform differently in balancing diversity and convergence. This paper explores the properties of the two mainstream selection operators and designs an ensemble approach, striving to integrate their merits and complement each other’s weaknesses. In this ensemble approach, each selection operator manipulates a population, and the offspring solutions reproduced by any population update two populations concurrently. In this way, high-quality offspring solutions reproduced by one population have opportunities to improve the convergence or diversity of another population. Moreover, this ensemble approach includes a novel adaptive strategy to pick up mating solutions from each population according to their contributions during previous generations. Thus, the population with a higher contribution will receive more evolution opportunities to reproduce solutions with better convergence and diversity. Finally, we compare the proposal with twelve baseline algorithms on 43 test cases from four frequently-used test suites and the real-world application of cloud service compositions. The comparison results demonstrate the superiority of the proposal in balancing diversity and convergence.

A practical regularity model based evolutionary algorithm for multiobjective optimization

It is well known that domain knowledge helps design efficient problem solvers. The regularity model based multiobjective estimation of distribution algorithm (RM-MEDA) is such a method that uses the regularity property of continuous multiobjective optimization problems (MOPs). However, RM-MEDA may fail to work when dealing with complicated MOPs. This paper aims to propose some practical strategies to improve the performance of RM-MEDA. We empirically study the modeling and sampling components of RM-MEDA that influence its performance. After that, some new components, including the population partition, modeling, and offspring generation procedures, are designed and embedded in the regularity model. The experimental study suggests that the new components are more efficient than those in RM-MEDA when using the regularity model. The improved version has also been verified on various complicated benchmark problems, and the experimental results have shown that the new version outperforms five state-of-the-art multiobjective evolutionary algorithms.

CFD Analysis and Optimum Design for a Centrifugal Pump Using an Effectively Artificial Intelligent Algorithm

In this study, we proposed a novel approach to improve centrifugal pump performance with regard to the pump head, pump efficiency, and power. Firstly, to establish constraints, an optimal numerical model that accounted for factors such as pump efficiency and the head was considered. The pump was designed, and an artificial intelligence algorithmic approach was applied to the pump before performing experiments. We considered a set of models by selecting the parameters of the centrifugal pump casing section area, the interference of the impeller, the volute tongue length, and the volute tongue angle. The weights of the factors of safety and displacement on the optimization indices were estimated. The matrix of the weights for the optimal process was less than 38% or greater than 62%. This approach guarantees a complicated multi-objective optimization problem. The results show that the centrifugal pump performances were improved.

Hybrid multiobjective evolutionary algorithm considering combination timing for multi-type vehicle routing problem with time windows

Vehicle routing problem (VRP) has been a classical combinatorial optimization challenge, which has been extensively investigated in recent decades. As a VRP typical variant, multi-type vehicle routing problem with time windows (MT-VRPTW) has been concerned with multiple types of heterogeneous fleets of vehicles, within the delivery time window and limited capacity constraints. For such complicated multiobjective optimization problems, hybrid multiobjective evolutionary algorithm (HMOEA) has become an effective method, however, the research on hybrid algorithms and combination timing is still challenging. This study proposes a hybrid multiobjective evolutionary algorithm based on combination timing (HMOEA-CT) to solve MT-VRPTW with the criteria of minimizing the number of vehicles and wasting time simultaneously. The HMOEA-CT combines a fast convergence in multiple directions (FCMDs)-based global search and a problem-specific difference (PSD)-based local search in different evolutionary stages. The FCMD is assumed to be the global exploration search strategy, which converges faster at the center and edge regions of the Pareto front. The PSD is used to improve the local exploitation search ability by directing poor-performing individuals closer to better-performing individuals. Furthermore, the PSD cooperates with FCMD at the right time according to the different evolutionary stages to improve efficiency. Experimental results on Solomon benchmark problems demonstrate the competitive performance comparison of the HMOEA-CT with traditional multiobjective evolutionary algorithms.

Multi-Objective Evolutionary Algorithm Based on Two Reference Points Decomposition and Historical Information Prediction

Aims: The main goal of this paper is to address the issues of low-quality offspring solutions generated by traditional evolutionary operators, as well as the evolutionary algorithm's inability to solve multi-objective optimization problems (MOPs) with complicated Pareto fronts (PFs). Background: For some complicated multi-objective optimization problems, the effect of the multiobjective evolutionary algorithm based on decomposition (MOEA/D) is poor. For specific complicated problems, there is less research on how to improve the performance of the algorithm by setting and adjusting the direction vector in the decomposition-based evolutionary algorithm. Considering that in the existing algorithms, the optimal solutions are selected according to the selection strategy in the selection stage, without considering whether it could produce the better solutions in the stage of individual generation to achieve the optimization effect faster. As a result, a multi-objective evolutionary algorithm based on two reference points decomposition and historical information prediction is proposed. Objective: In order to verify the feasibility of the proposed strategy, the F-series test function with complicated PFs is used as the test function to simulate the proposed strategy. Method: Firstly, the evolutionary operator based on historical information prediction (EHIP) is used to generate better offspring solutions to improve the convergence of the algorithm; secondly, the decomposition strategy based on ideal point and nadir point is used to select solutions to solve the MOPs with complicated PFs, and the decomposition method with augmentation term is used to improve the population diversity when selecting solutions according to the nadir point. Finally, the proposed algorithm is compared to several popular algorithms by the F-series test function, and the comparison is made according to the corresponding performance metrics. Result: The performance of the algorithm is improved obviously compared with the popular algorithms after using the EHIP. When the decomposition method with augmentation term is added, the performance of the proposed algorithm is better than the algorithm with only the EHIP on the whole, but the overall performance is better than the popular algorithms. Conclusion : The experimental results show that the overall performance of the proposed algorithm is superior to the popular algorithms. The EHIP can produce better quality offspring solutions, and the decomposition strategy based on two reference points can well solve the MOPs with complicated PFs. This paper mainly demonstrates the theory without testing the practical problems. The following research mainly focuses on the application of the proposed algorithm to the practical problems such as robot path planning.

Multi-objective design optimization for graphite-based nanomaterials reinforced cementitious composites: A data-driven method with machine learning and NSGA-Ⅱ

Graphite-based nanomaterials (GNs) are promising conductive fillers for producing highly effective electrically conductive cementitious composites (ECCC) and promoting non-destructive structural health monitoring (SHM) methods. Since acceptable mechanical strength and electrical resistivity are both required, the design of GN-reinforced cementitious composites (GNRCC) is a complicated multi-objective optimization problem (MOOP). The present study proposes a comprehensive data-driven method to address this multi-objective design optimization (MODO) issue for GNRCC using machine learning (ML) techniques and non-dominated sorting genetic algorithm (NSGA-Ⅱ). First, prediction models of uniaxial compressive strength (UCS) and electrical resistivity (ER) of GNRCC are established by Bayesian-tuned XGBoost with prepared experimental datasets. The results show that they have excellent performance in predicting both properties with high R2 (0.95 and 0.92, 0.99 and 0.98) and low mean absolute error (MAE) scores (1.24 and 3.44, 0.15 and 0.22). The influence of critical features on GNRCC’s properties are quantified by ML theories. This helps determine the variables to be optimized and define their constraints for the MODO. Finally, the MODO program is developed on the basis of NSGA-Ⅱ. It optimizes GNRCC’s properties of UCS and ER simultaneously with the proposed prediction models as objective functions. It successfully achieves a set of Pareto solutions, which can facilitate appropriate parameters selections for the GNRCC design.

Efficient control and multi‐criteria energy scheduling of renewable‐based utility grid via pareto‐metaheuristic optimizers

Being a renewable influenced utility grid, the wind integrated hydrothermal system (WHTS) is considered as a future-proof and contemporary energy system to reduce the dependency on depleting fossil fuels. However, due to intermittent nature of wind energy and complex operational constraints, offering the day-ahead operation schedule of WHTS with joint awareness of fuel economy and emissions is classified as a complicated multi-objective optimization problem. The major challenge is to maximize the utilization of clean hydro power to accommodate uncertain wind energy together with reduced dependency on fossils based thermal power. In this context, the paper devises an efficient control and multi-criteria energy scheduling method, essentially comprised of adaptive repair and volume restriction to maximize the utilization of available hydro power. The pareto-metaheuristic optimizer based on non-dominated sorting is exploited for the day-ahead scheduling of WHTS based utility grid. The most appropriate solution from pareto-optimal archive is selected using fuzzy-ranking index. The expected reductions in fuel cost and emissions are reflected using a significant probability scheme. The effectiveness of the proposed approach based on pareto-metaheuristic is appraised by various case studies. The simulation results provide a suitable day-ahead generation schedule of WHTS based grid, considering both economics and environmental aspects.

An Improved Heap-Based Optimizer for Optimal Reactive Power Dispatch

Optimal reactive power dispatch (ORPD) in a typical power system is a complicated multi-objective optimization problem. The proper modeling of the multi-objective optimization problem has a significant impact on system operation and control. In this paper, an Improved Heap-based optimizer (IHBO) is proposed to improve the performance of a recently published technique called Heap-based optimizer (HBO). In addition, two algorithms based on the original HBO and IHBO are developed for solving OPRD problem. Pareto front approach is utilized in the proposed OPRD algorithm with the aim of solving two or three objective functions simultaneously. The performance of HBO is improved by utilizing the chaotic sequences with the aim of improving its global search capability and avoiding getting stuck in a local optimum. Both original HBO and proposed IHBO are applied to determine the optimal settings of the generator’s voltages, shunt capacitor reactive power, and tap settings of transformers. Therefore, this study aims for minimizing three most objective functions of the real power loss, total voltage deviation (TVD) and voltage stability index (VSI), with satisfying different operational constraints. The effectiveness of the IHBO is tested on three test systems IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus test systems. The results of the proposed IHBO are compared with recently published algorithms in the literature. The simulation results proven the superiority and robustness of IHBO in solving the ORPD problem.

Multiobjective Electrical Power Dispatch of Thermal Units with Convex and Non Convex Fuel Cost Functions for 24 Hours Load Demands

There are a host of difficult issues with scheduling, operation, and control of integrated power systems. The electricity sector is changing rapidly, and one of the most important concerns is deciding operational strategies to meet electricity demand. It is a greater challenge to satisfy customer demand for power at a minimum cost. The operating characteristics of all generators may be different. In general, operating cost is not proportionate to the performance of these generators. Therefore challenge for power utilities to balance the total load between generators. For a specific load condition on energy systems, Economic Dispatch(ED) seeks to reduce the fuel costs of power generation units. Moreover, energy utilities have also an important task to reduce gaseous emission. So the ED problem can be recognized as a complicated multi-objective optimization problem (MOOP) with two competing targets, the minimal cost of fuel and the minimum emissions effects. This paper presented an efficient method, hybrid of particle swarm optimization (PSO) and a learning-based optimization (TLBO) for combined environmental issues because of gaseous emission and economic dispatch (CEED) problems. The results were shown and verified by PSO and TLBO for standard 3 and 6-generator frameworks with combined issues of emission and economic dispatch taking into account line losses and prohibited zones (POZs) on hourly demand for 24 hours.

Power Allocation Schemes for Uplink Massive MIMO System in the Presence of Imperfect CSI

In this paper, spectrum efficiency (SE) and energy efficiency (EE) performances of uplink massive multiple-input multiple-output (MIMO) systems with continuous-rate adaptive modulation and imperfect channel state information (CSI) are investigated over Rayleigh fading channels. Given a target BER, closed-form SE and EE expressions are derived. With these results, a constrained non-concave optimization problem of power allocation (PA) to maximize the SE is firstly formulated subject to the maximum transmit power per user. A near-optimal PA scheme with the concave-convex procedure (CCCP) method is then developed, and it can offer nearly optimal performance close to that of the optimal scheme with exhaustive search, but require lower complexity. Since this scheme needs more iterations, we propose a suboptimal scheme with reduced complexity and slight performance loss, which utilizes the property of a large number of receive antennas to approximate the objective function as a concave one, thereby reducing the number of iterations. Secondly, the PA problem for EE maximization under the same constraints is addressed. Based on the CCCP method and fractional programming theory, we propose a near-optimal PA scheme to solve this problem, and it has the EE performance very close to the optimal exhaustive search scheme. However, multi-layer iterations make this scheme have relatively higher complexity. For this reason, we propose a low-complexity suboptimal scheme with small EE loss by using variable transformation and a large number of antennas. Based on the above results, we simultaneously optimize both EE and SE. A multi-objective optimization problem (MOP) subject to the maximum power constraint and proportional data rate constraint is formulated. By means of the weighted sum method, the complicated MOP is transformed into a simple single-objective optimization problem. Then a PA scheme is proposed by using the Lagrange multiplier method to balance the EE and SE effectively. Simulation results validate the effectiveness of the proposed PA schemes in term of high SE and EE, and illustrate the fundamental tradeoff between EE and SE for different parameter settings.

Multi-Objective Optimization-Based Virtual Network Embedding Algorithm for Software-Defined Networking

To overcome the drawbacks of traditional Internet architectures, software-defined networking (SDN) technology has been proposed, which is expected to dramatically simplify network control processes and enable the convenient deployment of sophisticated network functions. To achieve highly efficient resource utilization in SDN and offer users with diverse service requirements, virtual network embedding (VNE), which maps various virtual network requests of users to a given substrate network, should be conducted. In this paper, we study the VNE problem in SDN where the substrate SDN switches and links may be subject to malicious attacks. We first propose a hierarchical virtualization-enabled SDN architecture based on which the VNE strategy can be designed. Then, stressing the importance of network load and reliability of the substrate network, we formulate the VNE problem of SDN as a multi-objective optimization problem which jointly minimizes network load and maximizes embedding reliability under the constraints of virtual network requirements and the resource characteristics of substrate network. As the formulated optimization problem is a complicated multi-objective optimization problem which cannot be solved conveniently, we apply the ideal point method. In particular, we first propose virtual node embedding sub-algorithm and virtual link embedding sub-algorithm to determine the locally optimal solution to the two subproblems, i.e., network load minimization subproblem and embedding reliability maximization subproblem. Then, examining the distance between the feasible solutions and the locally optimal solutions, we formulate a single-objective optimization problem and solve the problem to obtain the global VNE strategy by applying discrete particle swarm optimization (DPSO) algorithm. Numerical results demonstrate the effectiveness of the proposed algorithm.

Decomposition-Based Multiobjective Optimization with Invasive Weed Colonies

In order to solve the multiobjective optimization problems efficiently, this paper presents a hybrid multiobjective optimization algorithm which originates from invasive weed optimization (IWO) and multiobjective evolutionary algorithm based on decomposition (MOEA/D), a popular framework for multiobjective optimization. IWO is a simple but powerful numerical stochastic optimization method inspired from colonizing weeds; it is very robust and well adapted to changes in the environment. Based on the smart and distinct features of IWO and MOEA/D, we introduce multiobjective invasive weed optimization algorithm based on decomposition, abbreviated as MOEA/D-IWO, and try to combine their excellent features in this hybrid algorithm. The efficiency of the algorithm both in convergence speed and optimality of results are compared with MOEA/D and some other popular multiobjective optimization algorithms through a big set of experiments on benchmark functions. Experimental results show the competitive performance of MOEA/D-IWO in solving these complicated multiobjective optimization problems.

Path Planning for Multi-UAV Formation Rendezvous Based on Distributed Cooperative Particle Swarm Optimization

This paper studies the problem of generating cooperative feasible paths for formation rendezvous of unmanned aerial vehicles (UAVs). Cooperative path-planning for multi-UAV formation rendezvous is mostly a complicated multi-objective optimization problem with many coupled constraints. In order to satisfy the kinematic constraints, i.e., the maximum curvature constraint and the requirement of continuous curvature of the UAV path, the Pythagorean hodograph (PH) curve is adopted as the parameterized path because of its curvature continuity and rational intrinsic properties. Inspired by the co-evolutionary theory, a distributed cooperative particle swarm optimization (DCPSO) algorithm with an elite keeping strategy is proposed to generate a flyable and safe path for each UAV. This proposed algorithm can meet the kinematic constraints of UAVs and the cooperation requirements among UAVs. Meanwhile, the optimal or sub-optimal paths can be obtained. Finally, numerical simulations in 2-D and 3-D environments are conducted to demonstrate the feasibility and stability of the proposed algorithm. Simulation results show that the paths generated by the proposed DCPSO can not only meet the kinematic constraints of UAVs and safety requirements, but also achieve the simultaneous arrival and collision avoidance between UAVs for formation rendezvous. Compared with the cooperative co-evolutionary genetic algorithm (CCGA), the proposed DCPSO has better stability and a higher searching success rate.

Optimization Model Calculation of Construction Cost and Time Based on Genetic Algorithm

In the process of multi-objective problems, traditional algorithms have certain defects, especially because of the increasing number of conflicts and the increasingly complex application environment. This paper proposes a practical method to solve the multi-objective optimization problem for the duration and cost requirements in the construction project management, in order to reduce the error probability that the optimized project will produce in the actual project. Different from the existing optimization methods, this design modifies the curve of the time cost, and improves the parameters of the traditional genetic algorithm design and operation process design, which greatly increases the degree of fitness between the algorithm and the actual project. The model is based on genetic algorithms and combines different algorithms, so a simple and excellent Pareto solution can be quickly obtained. At the same time, optimization and simulation are carried out in an orderly way during the construction period. This new method is reasonable and effective in the very complicated multi-objective optimization problem of managing construction period and cost through an engineering example.

An adaptive immune-inspired multi-objective algorithm with multiple differential evolution strategies

Most multi-objective immune algorithms (MOIAs) adopt clonal selection to speed up convergence, as this operator only clones the best individuals during the search process. However, this approach somehow deteriorates the population diversity, which may cause a MOIA to be trapped in a local optimum and could also lead to premature convergence when tackling some complicated multi-objective optimization problems (MOPs). In order to overcome this problem, an adaptive immune-inspired multi-objective algorithm (AIMA) is presented in this paper, in which multiple differential evolution (DE) strategies having distinct advantages are embedded into a conventional MOIA. Our proposed approach strengthens the exploration capabilities of a MOIA while also improving its population diversity. At each generation, based on the current search stage, an adaptive selection method is designed to choose an appropriate DE strategy for evolution. The core idea is to effectively combine the advantages of three DE strategies when solving different MOPs. A number of comparative experiments are conducted on the well-known and frequently-used WFG and DTLZ test problems. Our experimental results validate the superiority of our proposed AIMA, as it performs better than some state-of-the-art multi-objective optimization algorithms and some state-of-the-art MOIAs.

A novel adaptive control strategy for decomposition-based multiobjective algorithm

Recently, evolutionary algorithm based on decomposition (MOEA/D) has been found to be very effective and efficient for solving complicated multiobjective optimization problems (MOPs). However, the selected differential evolution (DE) strategies and their parameter settings impact a lot on the performance of MOEA/D when tackling various kinds of MOPs. Therefore, in this paper, a novel adaptive control strategy is designed for a recently proposed MOEA/D with stable matching model, in which multiple DE strategies coupled with the parameter settings are adaptively conducted at different evolutionary stages and thus their advantages can be combined to further enhance the performance. By exploiting the historically successful experience, an execution probability is learned for each DE strategy to perform adaptive adjustment on the candidate solutions. The proposed adaptive strategies on operator selection and parameter settings are aimed at improving both of the convergence speed and population diversity, which are validated by our numerous experiments. When compared with several variants of MOEA/D such as MOEA/D, MOEA/D-DE, MOEA/D-DE+PSO, ENS-MOEA/D, MOEA/D-FRRMAB and MOEA/D-STM, our algorithm performs better on most of test problems.

Self-adaptive step fruit fly algorithm optimized support vector regression model for dynamic response prediction of magnetorheological elastomer base isolator

Parameter optimization of support vector regression (SVR) plays a challenging role in improving the generalization ability of machine learning. Fruit fly optimization algorithm (FFOA) is a recently developed swarm optimization algorithm for complicated multi-objective optimization problems and is also suitable for optimizing SVR parameters. In this work, parameter optimization in SVR using FFOA is investigated. In view of problems of premature and local optimum in FFOA, an improved FFOA algorithm based on self-adaptive step update strategy (SSFFOA) is presented to obtain the optimal SVR model. Moreover, the proposed method is utilized to characterize magnetorheological elastomer (MRE) base isolator, a typical hysteresis device. In this application, the obtained displacement, velocity and current level are used as SVR inputs while the output is the shear force response of the device. Experimental testing of the isolator with two types of excitations is applied for model performance evaluation. The results demonstrate that the proposed SSFFOA-optimized SVR (SSFFOA_SVR) has perfect generalization ability and more accurate prediction accuracy than other machine learning models, and it is a suitable and effective method to predict the dynamic behaviour of MRE isolator.

Adaptive composite operator selection and parameter control for multiobjective evolutionary algorithm

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) has shown a superior performance in tackling some complicated multiobjective optimization problems (MOPs). However, the use of different evolutionary operators and their various parameter settings has a significant impact on its performance. To enhance its algorithmic robustness and effectiveness, this paper proposes an adaptive composite operator selection (ACOS) strategy for MOEA/D. Four evolutionary operator pools are used in ACOS and their advantages are combined to provide stronger exploratory capabilities. Regarding each selected operator pool, an online self-adaptation for the parameters tuning is further employed for performance enhancement. When compared with other adaptive and improved strategies designed for MOEA/D, our proposed algorithm is found to be effective and competitive in solving several complicated MOPs.