Traditional Multi-objective Optimization Algorithms Research Articles

A novel probabilistic forecasting system based on quantile combination in electricity price

In the electricity market, the accuracy of electricity price forecasting is significant for real-time control; however, the complexity and volatility of electricity prices make this a challenge. Existing forecasting models focus on deterministic forecasting and rarely address the uncertainty in electricity price forecasting. Therefore, this study fills this knowledge gap by introducing a novel combined probability forecasting system (CPFS) and creatively incorporating probability density estimation based on kernel functions in a multi-objective optimization algorithm. In addition, to effectively integrate the forecasting components, the tuna optimization algorithm was enhanced to overcome the limitations of traditional multi-objective optimization algorithms. Finally, the validity of the CPFS is confirmed through two electricity price cases, considering three equally important aspects: reliability, resolution, and sharpness. From a comprehensive perspective, CPFS outperformed the most advanced benchmark by more than 5.66% and 38.93% in AIS and by more than 13.41% and 3.55% in quantile loss on the NSW and Singapore datasets, respectively. The experimental results demonstrate that the CPFS provides an effective range for electricity price fluctuations. Furthermore, given that probabilistic forecasting is essential for risk management, it offers important implications for the electricity market.

Uniformity-Comprehensive Multiobjective Optimization Evolutionary Algorithm Based on Machine Learning

When solving real-world optimization problems, the uniformity of Pareto fronts is an essential strategy in multiobjective optimization problems (MOPs). However, it is a common challenge for many existing multiobjective optimization algorithms due to the skewed distribution of solutions and biases towards specific objective functions. This paper proposes a uniformity-comprehensive multiobjective optimization evolutionary algorithm based on machine learning to address this limitation. Our algorithm utilizes uniform initialization and self-organizing map (SOM) to enhance population diversity and uniformity. We track the IGD value and use K-means and CNN refinement with crossover and mutation techniques during evolutionary stages. Our algorithm’s uniformity and objective function balance superiority were verified through comparative analysis with 13 other algorithms, including eight traditional multiobjective optimization algorithms, three machine learning-based enhanced multiobjective optimization algorithms, and two algorithms with objective initialization improvements. Based on these comprehensive experiments, it has been proven that our algorithm outperforms other existing algorithms in these areas.

Research on the Multiobjective and Efficient Ore-Blending Scheduling of Open-Pit Mines Based on Multiagent Deep Reinforcement Learning

In order to solve the problems of a slow solving speed and easily falling into the local optimization of an ore-blending process model (of polymetallic multiobjective open-pit mines), an efficient ore-blending scheduling optimization method based on multiagent deep reinforcement learning is proposed. Firstly, according to the actual production situation of the mine, the optimal control model for ore blending was established with the goal of minimizing deviations in ore grade and lithology. Secondly, the open-pit ore-matching problem was transformed into a partially observable Markov decision process, and the ore supply strategy was continuously optimized according to the feedback of the environmental indicators to obtain the optimal decision-making sequence. Thirdly, a multiagent deep reinforcement learning algorithm was introduced, which was trained continuously and modeled the environment to obtain the optimal strategy. Finally, taking a large open-pit metal mine as an example, the trained multiagent depth reinforcement learning algorithm model was verified via experiments, with the optimal training model displayed on the graphical interface. The experimental results show that the ore-blending optimization model constructed is more in line with the actual production requirements of a mine. When compared with the traditional multiobjective optimization algorithm, the efficiency and accuracy of the solution have been greatly improved, and the calculation results can be obtained in real-time.

Optimal capacity allocation of wind-light-water multi-energy complementary capacity based on improved multi-objective optimization algorithm

As a basic industry for national economic development, the power industry is closely related to the overall economic and environmental development of China. At present, China is still dominated by thermal power generation. In order to reduce carbon emissions, promote the realization of the “double carbon” goal, and improve the level of clean energy utilization and the operating efficiency of the power system, a wind-light-water storage complementary power generation system is built, and a mathematical model of multi energy complementation is established. The minimum economic cost and the minimum battery capacity are proposed as the objective functions of system capacity configuration. Then a multi-objective evolutionary algorithm based on Pareto optimal space of the NDWA-GA and the PCA is proposed for optimal capacity allocation of multi energy complementary systems in this paper. Compared with the traditional multi-objective optimization algorithm, the correctness and effectiveness of the proposed method are verified. In addition, according to the actual research object, the optimal capacity configuration of the multi energy complementary system is given, which can guide the production and has an important promotion significance for energy saving and emission reduction.

An Adaptive Evolutionary Multi-Objective Estimation of Distribution Algorithm and Its Application to Multi-UAV Path Planning

This paper concerns the multi-UAV cooperative path planning problem, which is solved by multi-objective optimization and by an adaptive evolutionary multi-objective estimation of distribution algorithm (AEMO-EDA). Since the traditional multi-objective optimization algorithms tend to fall into local optimum solutions when dealing with optimization problems in three dimensions, we suggest an advanced estimation of distribution algorithm. The main idea of this algorithm is to integrate the adaptive deflation of the selection rate, adaptive evolution of the covariance matrix, comprehensive evaluation of individual convergence and diversity, and reference point-based non-dominated ranking. A multi-UAV path planning model involving multi-objective optimization is established, and the designed algorithm is simulated and compared with other three high-dimensional multi-objective optimization algorithms. The results show that the AEMO-EDA proposed in this paper has stronger convergence and wider population distribution diversity in applying to the multi-UAV cooperative path planning model, as well as better global convergence. The algorithm can provide an stable path for each UAV and promote the intelligent operation of the UAV system.

Quantile deep learning model and multi-objective opposition elite marine predator optimization algorithm for wind speed prediction

Wind speed prediction accuracy is critical for grid connection safety and intelligent wind farm management. However, most wind speed prediction studies mainly focus on the deterministic prediction, and are rarely discussed in wind speed uncertain prediction. Therefore, this paper proposes a wind speed combined probability prediction system that integrates data denoising technology and creatively introduces the concept of quantile into the deep learning model to construct the wind speed quantile prediction component. To ensemble the prediction components effectively, a novel multi-objective marine predator combination strategy is developed that circumvents the limitations of the traditional multi-objective optimization algorithm. The experimental results based on two wind speed datasets show that the proposed system can improve wind speed prediction accuracy, build a more appropriate wind speed prediction interval, efficiently measure and minimize the uncertainty of the forecast process.

Application of a modified MOPSO algorithm and multi-layer artificial neural network in centrifugal pump optimization

Centrifugal pump optimization problems usually have strong nonlinear characteristics and are sometimes non-differentiable. The traditional multi-objective particle swarm optimization (MOPSO) algorithm was modified to solve this situation, and performed better with respect to both accuracy and search speed in validation experiments. Based on the modified algorithm and multi-layer artificial neural networks, the shape of the impeller blades of an industrial inline pump was optimized to improve the comprehensive performance under multiple operating conditions. The non-uniform rational B-spline was applied in the parametric design of the blade geometry, and 14 design variables of the spline were finally utilized in the iteration. With constraint of the computational head, the efficiencies of the part-load condition, the nominal condition, and the overload condition were selected as the objective functions. After optimization, a dramatic efficiency rise was obtained in all the three specified operating conditions, and correlation between the inflow conditions before the impeller and the performance of the inline pump was indicated.

Entropy-Driven Global Best Selection in Particle Swarm Optimization for Many-Objective Software Package Restructuring

Many real-world optimization problems usually require a large number of conflicting objectives to be optimized simultaneously to obtain solution. It has been observed that these kinds of many-objective optimization problems (MaOPs) often pose several performance challenges to the traditional multi-objective optimization algorithms. To address the performance issue caused by the different types of MaOPs, recently, a variety of many-objective particle swarm optimization (MaOPSO) has been proposed. However, external archive maintenance and selection of leaders for designing the MaOPSO to real-world MaOPs are still challenging issues. This work presents a MaOPSO based on entropy-driven global best selection strategy (called EMPSO) to solve the many-objective software package restructuring (MaOSPR) problem. EMPSO makes use of the entropy and quality indicator for the selection of global best particle. To evaluate the performance of the proposed approach, we applied it over the five MaOSPR problems. We compared it with eight variants of MaOPSO, which are based on eight different global best selection strategies. The results indicate that the proposed EMPSO is competitive with respect to the existing global best selection strategies based on variants of MaOPSO approaches.

An exploitation-enhanced multi-objective efficient global optimization algorithm for expensive aerodynamic shape optimizations

The traditional multi-objective efficient global optimization (EGO) algorithms have been hybridized and adapted to solving the expensive aerodynamic shape optimization problems based on high-fidelity numerical simulations. Although the traditional EGO algorithms are highly efficient in solving some of the optimization problems with very complex landscape, it is not preferred to solve most of the aerodynamic shape optimization problems with relatively low-degree multi-modal design spaces. A new infill criterion encouraging more local exploitation has been proposed by hybridizing two traditional multi-objective expected improvements (EIs), namely, statistical multi-objective EI and expected hypervolume improvement, in order to improve their robustness and efficiency in aerodynamic shape optimization. Different analytical test problems and aerodynamic shape optimization problems have been investigated. In comparison with traditional multi-objective EI algorithms and a standard evolutionary multi-objective optimization algorithm, the proposed method is shown to be more robust and efficient in the tests due to its hybrid characteristics, easier handling of sub-optimization problems, and enhanced exploitation capability.

A Novel Nonlinear Expanded Dominance Relation Based Evolutionary Algorithm for Many-Objective Optimization Problems

Multi-objective optimization problems exist widely in scientific research and engineering applications. With the number of objectives increasing, the proportion of non-dominated individuals in the population of many-objective optimization problems increases sharply, resulting in a reduction of convergence pressure of the traditional multi-objective optimization algorithms. In some cases, the optimal solutions may be located in the special regions, such as many discrete regions and the regions with very few feasible solutions. In this case, the existing nonlinear expanded evolutionary algorithm can not find the true Pareto fronts. To address the limitation, a novel nonlinear expanded dominance relation based many-objective evolutionary algorithm is proposed to handle many-objective optimization problems. Experimental results show that compared with the state of art algorithms, the proposed algorithm is effective for DTLZs, in terms of IGD, PD and GD metrics.

RSM and ANN Modeling for Production of Newbouldia Laevies Fibre and Recycled High Density Polyethylene Composite: Multi Objective Optimization Using Genetic Algorithm

In this study response surface methodology (RSM), artificial neural network (ANN) and non-dominated sorting genetic algorithm-II (NSGA-II) were used for modeling and multi objective optimization of Newbouldia Laevies Fibre and recycled high density polyethylene (RHDPE) composite for fiberboard application. The fiberboard properties optimized were modulus of rupture (MOR), modulus of elasticity (MOE), internal bonding (IB), thickness swelling (TS) and water absorption (WA) whose values vary in response to changes in production process variables namely: Fibre/RHDPE (%), press pressure, press time and temperature. An experimental design using central composite design (CCD) was used to develop an RSM model for modeling the variations in physical and mechanical properties of the fiberboard in response to variations in process parameters. An ANN model was equally used to predict the properties of the fiberboard. Subsequently the ANN was used as the fitness function for multi objective optimization of the fiberboard using NSGA-II. A comparative algorithm was later developed with a traditional multi objective optimization algorithm known as desirability function using the RSM model. The results of the study showed that RSM and ANN effectively modeled the properties of the fiberboard. The optimized Pareto front of the NSGA-II algorithm was found to be an excellent design guide for practical applications of the composite. The superiority of NSGA-II algorithm over the desirability function as a multi objective optimization tool was demonstrated.

Evolutionary many-objective assembly of cloud services via angle and adversarial direction driven search

Cloud service composition (CSC) is an effective way to carry out large-scale complicated applications by the ensemble of existing individual services. Each service typically involves several Quality of Service (QoS) criteria contracted for non-functional aspects like time or price, among others, which greatly influence the overall performance of the resulting applications. Service composition approaches have emerged as an important technique in leveraging the quality of composite service efficiently and have attracted significant attention. However, most existing proposals ignore the many-objective nature of CSC and consider up to three objectives, the optimization of diverse QoS aspects of CSC from a many-objective perspective (at least four) still lacks. On another aspect, due to the rapid growth of nondominated solutions in high-dimensional objective spaces, the traditional multi-objective optimization algorithms are usually not capable of handling problems possessing many objectives. To address the above issue, we develop an angle and adversarial direction based optimizer for many-objective CSC scenarios, which evolves a number of subpopulations with adversarial search directions in a parallel paradigm. Additionally, vector angle based selection criterion, which adaptively captures beacon individuals, is utilized to diversify the population. Extensive experiments are carried out on a series of CSC instances utilizing synthetic datasets and the results show that our proposition is competitive and has better versatility compared with the state-of-the-art.

Multi-objective optimization method for spectrum allocation in cognitive heterogeneous wireless networks

In a multi-heterogeneous network dense deployment and convergence environment, the cognitive radio technology dynamically utilizes the idle spectrum resources of each primary network, which can effectively improve the data transmission rate and system capacity, and is also a key technology of the next generation wireless communication network. However, how to efficiently and reasonably select the network and allocate idle spectrum resources to meet the low cost and large traffic demand of users is a difficult problem in the case of dynamic coupling with multiple heterogeneous primary networks overlapping coverage and diversified user requirements. In this paper, with the goal of maximizing the total bandwidth and minimizing the total cost, a multi-objective optimization mathematical model for network selection and idle spectrum allocation is established in the context of comprehensive consideration of the difference of spectrum resource attributes of different primary networks in the network domain and the diversification of secondary user requirements in the user domain, and the complexity of the problem is analyzed. Based on this, two kinds of technical paths to solve the complex network selection and spectrum allocation problem are applied in this paper. The first is the simplification method. By analyzing the relationship between optimization objectives and constraints, simplification method simplifies the objective function and constraints of the mathematical model and transforms the complex allocation problem into a standard form of the 01 programming problem. The second is the intelligent optimization algorithm. By improving the traditional multi-objective optimization algorithm Non-dominated Sorting Genetic Algorithm II (NSGA-II), an improved NSGA-II(INSGA-II) method is proposed, which combines the interference constraints of the primary network and the service quality requirements of the secondary users into the objective value evaluation of NSGA-II algorithm, while making the decision selection on the optimal solution set to select a compromise solution. Finally, the performance of this two methods is compared and analyzed through experiments. The experimental results show that the simplified method has higher efficiency advantages, and the INSGA-II algorithm can often meet the user’s service requirements at a lower cost, especially the cost priority strategy.

Robust kinematics design of MacPherson suspension based on a double-loop multi-objective particle swarm optimization algorithm

In the traditional design of a vehicle suspension system, mechanical parameters, such as spring stiffness and tire radial stiffness, are determined before optimizing the coordinates of suspension hard-points based on handling and stability. However, the mechanical parameters of vehicle suspension systems vary with repeated changes in ambient temperature and loading conditions. Consequently, the original hard-point coordinates cannot guarantee satisfactory handling and stability after long-term vehicle use. To address this issue, an A0 class vehicle with a MacPherson suspension was modeled in ADAMS/Car and was validated against the results of field tests. The relationships between the maximum absolute values of front wheel alignment parameters during parallel wheel travel analysis and the coordinates of suspension hard-points, spring stiffness, and tire radial stiffness were determined using support vector regression. Next, a multi-objective optimization function was formulated based on the interval analysis method. Finally, a novel double-loop multi-objective particle swarm optimization algorithm was designed for global optimization of hard-point coordinates. The ADAMS simulation results indicated that, compared with the vehicle with the original hard-point coordinates, the double-loop multi-objective particle swarm optimization algorithm, the traditional multi-objective particle swarm optimization algorithm, and the genetic algorithm can effectively reduce the variation ranges of front wheel alignment parameters, regardless of the values of the mechanical parameters. It also showed that the double-loop multi-objective particle swarm optimization algorithm performs better than the traditional multi-objective particle swarm optimization and the genetic algorithm with both the original and changed mechanical parameters. Except for an increase in the variation range of the caster angle by 9.24–10.69%, the variation ranges of the toe angle, camber angle, and kingpin inclination angle under various mechanical parameters using the double-loop multi-objective particle swarm optimization algorithm were observed to be reduced by 50.45–79.39%, 1.84–4.24%, and 2.11–2.96%, respectively. Last but not least, the proposed double-loop multi-objective particle swarm optimization algorithm provided better handling, stability, and ride comfort values than the traditional multi-objective particle swarm optimization algorithm and the genetic algorithm.

Interactive evolutionary multi-objective optimization and decision-making on life-cycle seismic design of bridge

Considering future seismic risk and life-cycle cost, the life-cycle seismic design of bridge is formulated as a preference-based multi-objective optimization and decision-making problem, in which the conflicting design criteria that minimize life-cycle cost and maximize seismic capacity are treated simultaneously. Specifically, the preference information based on theoretical analysis and engineering judgment is embedded in the optimization procedure. Based on reasonable displacement ductility, the cost preference and safety preference information are used to progressively construct value function, directing the evolutionary multi-objective optimization algorithm’s search to more preferred solutions. The seismic design of a reinforced concrete pier is presented as an application example using the proposed procedure for the global Pareto front corresponding with engineering designers’ preference. The results indicate that the proposed model is available to find the global Pareto front satisfying the corresponding preference and overcoming the difficulties of the traditional multi-objective optimization algorithm in obtaining a full approximation of the entire Pareto optimal front for large-dimensional problems as well as cognitive difficulty in selecting one preferred solution from all these solutions.

Multi‐objective Optimization for Cloud Task Scheduling Based on the ANP Model

We propose a multi-objective optimization algorithm for cloud task scheduling based on the Analytic network process (ANP) model to solve the problems in cloud task scheduling, such as the deficiencies of mathematical description, limited optimization abilities of the traditional multi-objective optimization algorithm and the selection of the Pareto optimal solutions. Firstly, we present the mathematical description of cloud task scheduling using matrix theory. Then, the improved Nondominated sorting genetic algorithm II (NSGA-II) multiobjective evolutionary algorithm whose optimization ability is improved by Gene expression programming (GEP) algorithm has been introduced into the cloud task scheduling field to search the Pareto set among multi-objects. Finally, ANP model has been combined with the improved NSGA-II to solve the selection problems of Pareto solutions. Comparing with the multi-objective optimization algorithm based on the weighted polynomial, the proposed algorithm can optimize multiple goals at the same time, and can avoid the additional iterations due to the change of users preferences effectively. The simulation results indicate that the proposed algorithm is effective.

Multi-objective robust optimization of foam-filled tapered multi-cell thin-walled structures

Foam-filled multi-cell thin-walled structure has recently gained attentions for its excellent energy absorption capacity. Tapered thin-walled structure is less likely to fail by global buckling, and is more capable of bearing oblique impact loads. Thus, foam-filled tapered multi-cell thin-walled structure (FTMTS) may be an extremely excellent energy absorber candidate in future vehicle body. This paper focuses on the crashworthiness of four kinds of axisymmetric FTMTSs with different cell numbers. According to our study, we find that FTMTSs have very excellent energy absorption capacity as well as strong capacity of avoiding global buckling. According to our investigation, it was found that the crashworthiness of FTMTS was largely affected by design parameters such as geometric sizes and foam density. In order to find optimal designs of FTMTSs, it is very essential to carry out crashworthiness optimization for FTMTSs. However, the conventional deterministic design is likely to become less meaningful or even unacceptable when considering the uncertainties of design parameters due to the manufacturing or installation deviation. In order to overcome this drawback, a multi-objective robust optimization procedure which employs Kriging metamodels, multi-objective particle swarm optimization (MOPSO) algorithm, "k-sigma" robust design theory and Monte Carlo simulation (MCS) was developed. The comparison of the Pareto fronts obtained by the developed multi-objective robust optimization procedure and the traditional multi-objective deterministic optimization algorithm shows that the robust optimization result is more reliable than the deterministic optimization result. The robust optimal design of FTMTS not only has very excellent crashworthiness but also has very high reliability when considering the uncertainty of design parameters.

Non-dominated Sorting Bee Colony optimization in the presence of noise

The paper incorporates new extensional strategies into the traditional multi-objective optimization algorithms to proficiently obtain the Pareto-optimal solutions in the presence of noise in the fitness landscapes. The first strategy, referred to as adaptive selection of sample size, is employed to assess the trade-off between accuracy in fitness estimation and the associated run-time complexity. The second strategy is concerned with determining statistical expectation of fitness samples, instead of their conventional averaging, as the fitness measure of the trial solutions. The third strategy aims at improving Goldberg's approach to examine possible accommodation of a seemingly inferior solution in the optimal Pareto front using a more statistically viable comparator. The traditional Non-dominated Sorting Bee Colony algorithm has been ameliorated by extending its selection step with the proposed strategies. Experiments undertaken to study the performance of the proposed algorithm reveal that the extended algorithm outperforms its contenders with respect to four performance metrics, when examined on a test suite of 23 standard benchmarks with additive noise of three statistical distributions.

A Scalable D Dominant Strategy to Solve Large-Dimensional Multi-Objective Optimization Problems

Solving large-dimensional multi-objective optimization problems is one of the focus research areas of multi-objective optimization evolutionary . When using traditional multi-objective optimization algorithms to solve large-dimensional multi-objective optimization problems,we found that the unsatisfactory optimizing results often exist. To overcome this flaw, in this paper we studied scalable dominant mechanism and proposed a D dominant strategy. According to the superior theory of D strategy ,we improved the current four kinds of typical multi-objective optimization evolutionary algorithms. The numerical comparison test on DTLZ1-6 (20) questions which were solved by the improved algorithms indicated that D strategy had in varying degrees improved the algorithms for solving large-dimensional multi-objective optimization problems .Thus ,we confirmed that the D strategy for solving large-dimensional multi-objective optimization problems is effective.

Uncertainty Management in Differential Evolution Induced Multiobjective Optimization in Presence of Measurement Noise

This paper aims to design new strategies to extend traditional multiobjective optimization algorithms to efficiently obtain Pareto-optimal solutions in presence of noise on the objective surfaces. The first strategy, referred to as adaptive selection of sample size, is employed to balance the tradeoff between quality measure of fitness and run-time complexity. The second strategy is concerned with determining statistical expectation, instead of conventional averaging, of fitness samples as the measure of fitness of the trial solutions. The third strategy attempts to extend Goldberg's method to compare slightly worse trial solutions with its competitor by a more statistically viable comparator to examine possible placement of the former solution in the Pareto optimal front. The traditional differential evolution for multiobjective optimization algorithm has been modified by extending its selection step with the proposed strategies. Experiments undertaken to study the performance of the extended algorithm reveal that the extended algorithm outperforms its competitors with respect to three performance metrics, when examined on a test suite of 23 standard benchmarks with additive noise of three statistical distributions. The extended algorithm has been applied on the well known box-pushing problem, where the forces and torques required to shift the box by two robots are evaluated to jointly satisfy the conflicting objectives on task-execution time and energy consumption in presence of noise on range estimates from the sidewalls of the workspace. The application justifies the importance of the proposed noise-handling strategies in practical systems.