External Archive Set Research Articles

Multiobjective visual evolutionary neural network and related convolutional neural network optimization

Biological visual systems intrinsically include a variety of direction-selective neurons capable of detecting changes in visual motion. Some of the neurons have been used to construct computational models for problem-specific engineering applications. However, it remains unclear how these neurons' visual response mechanisms can serve an interdisciplinary topic - visual evolutionary neural networks. In this study, we draw inspiration from swarm evolution and the fly's visual response and attention mechanisms to develop a fast multiobjective visual evolutionary neural network for solving multiobjective optimization problems, specifically focusing on convolutional neural network optimization. Our approach involves designing a multi-channel input visual neural network that outputs global and local learning rates for state transition, proposing a new population-like state update strategy to move current states toward the Pareto front as quickly as possible, and exploiting a point-to-plane distance model to control the size of the external archive set. The computational complexity of the evolutionary neural network mainly depends on the size of the external archive set and the number of fitness evaluations. Comparative experiments demonstrate that our network is an extremely competitive optimizer, effectively solving multiple kinds of benchmark examples. Especially, when optimizing the 8,248 parameters of a conventional convolutional neural network, our approach quickly achieves large-scale optimization.

A multi-objective discrete differential evolution algorithm for energy-efficient two-stage flow shop scheduling under time-of-use electricity tariffs

In response to the appeal for environmental protection and the efficient utilization of energy, local governments in China actively promote time-of-use (TOU) electricity tariffs for manufacturing enterprises. Motivated by a real-life industrial scenario of large special-purpose pressure vessel production, this paper addresses an energy-efficient two-stage flow shop scheduling problem under TOU tariffs to minimize the total electricity cost and the mean tardiness. Since the problem is computationally intractable, we focus on developing a multi-objective discrete differential evolution (MDDE) algorithm. Specifically, based on the optimal properties of the problem, we tailor an encoding scheme that consists of two job sequences and an idle time vector. The novel mutation and crossover operators are designed to generate the trail individuals, and the hypervolume contribution indicator is incorporated into the bi-criteria selection operator to measure the quality of the solution. Furthermore, two neighborhood structures are designed to iteratively improve the non-dominated solutions in the external archive set. We evaluate the performance of the MDDE algorithm via extensive computational experiments. The experimental results indicate that the MDDE algorithm can obtain the good approximate Pareto front, and it outperforms the well-known NSGA-II, SPEA2 and MOEA/D algorithms in solution quality.

Evolutionary convolutional neural network for image classification based on multi-objective genetic programming with leader–follower mechanism

As a popular research in the field of artificial intelligence in the last 2 years, evolutionary neural architecture search (ENAS) compensates the disadvantage that the construction of convolutional neural network (CNN) relies heavily on the prior knowledge of designers. Since its inception, a great deal of researches have been devoted to improving its associated theories, giving rise to many related algorithms with pretty good results. Considering that there are still some limitations in the existing algorithms, such as the fixed depth or width of the network, the pursuit of accuracy at the expense of computational resources, and the tendency to fall into local optimization. In this article, a multi-objective genetic programming algorithm with a leader–follower evolution mechanism (LF-MOGP) is proposed, where a flexible encoding strategy with variable length and width based on Cartesian genetic programming is designed to represent the topology of CNNs. Furthermore, the leader–follower evolution mechanism is proposed to guide the evolution of the algorithm, with the external archive set composed of non-dominated solutions acting as the leader and an elite population updated followed by the external archive acting as the follower. Which increases the speed of population convergence, guarantees the diversity of individuals, and greatly reduces the computational resources. The proposed LF-MOGP algorithm is evaluated on eight widely used image classification tasks and a real industrial task. Experimental results show that the proposed LF-MOGP is comparative with or even superior to 35 existing algorithms (including some state-of-the-art algorithms) in terms of classification error and number of parameters.

Ecological multi-objective joint optimized scheduling of cascade hydropower plants based on improved marine predators algorithm

The joint operation of large cascade hydropower plants changes the natural hydrological regime of the river, thereby reducing the stability of the basin ecosystem. To coordinate the power generation of cascade hydropower plants' demand and ecological environment demand, this paper establishes an ecological multi-objective optimized scheduling model (EMOOSM) for cascade hydropower plants, aiming at the maximum power generation of cascade hydropower plants and the minimum inappropriate ecological water volume. To solve the complex EMOOSM, a marine predators algorithm was introduced, which was improved and extended to the multi-objective solution level. Multi-objective improved marine predators algorithm (MOIMPA) based on Cauchy variation preserves non-dominated solutions by adding an external archive set and maintaining them with a crowdedness-based fast sorting strategy. The optimal dispatching results of a cascade hydropower plant in China's Pearl River system show that MOIMPA can effectively deal with conflicting power generation and ecological goals. The recommended scheme determined according to the fuzzy set theory and the principle of maximum satisfaction can adapt to the change law of ecological demand and reasonably adjust the inappropriate ecological water volume in the stage according to the different ecological sensitivity in the dispatching period. The recommended scheme in the normal year reduces the inappropriate ecological water volume caused by the operation of the cascade reservoir by 1.7156 × 105 m3 at the expense of only 1.12% of the power generation, effectively balancing the power generation and ecological benefits of the cascade hydropower plant operation. Compared with the results of other algorithms, the Pareto solution set obtained by MOIMPA has a better diversity metric (DM) indicator, maximum spread (MS) indicator, and hypervolume (HV) indicator. The research results provide a theoretical basis and reference for the ecological operation research of cascade hydropower plants.

A Two-Population Cooperative Multiobjective Differential Evolution Algorithm for Batching Scheduling Problem

Batch processing machine (BPM) scheduling problem is a NP hard problem for it includes machine allocation, job grouping, and batch scheduling. In this paper, to address the BPM scheduling problem with unrelated parallel machine, a multiobjective algorithm based on multipopulation coevolution is proposed to minimize the total energy consumption and the completion time simultaneously. Firstly, the mixed integer programming model of the problem is established, and four heuristic decoding rules are proposed. Secondly, to improve the diversity and convergence of the algorithm, the population is divided into two populations: each of the populations evolves independently by using different decoding rules, and the two populations will communicate through a common external archive set every certain number of generations. Thirdly, an initialization strategy and a variable neighborhood search algorithm (VNS) are proposed to improve the overall performance of the algorithm. Finally, in order to evaluate the proposed algorithm, a large number of comparative experiments with the state-of-the-art multiobjective algorithms are carried out, and the experimental results proved the effectiveness of the proposed algorithm.

Using Non-dominated Sorting Particle Swarm Optimization Algorithm II for Bi-objective Flow Shop Scheduling Problems

A hybrid particulate swarm optimization (hybrid) combination of an optimization algorithm of the particle swarm and a variable neighborhood search algorithm is proposed for the multi-objective permutation flow shop scheduling problem (PFSP) with the smallest cumulative completion time and the smallest total flow time. Algorithm for hybrid particulate swarm optimization (HPSO) is applied to maintain a fair combination of centralized search with decentralized search. The Nawaz-Enscore-Ham )NEH) heuristic algorithm in this hybrid algorithm is used to initialize populations in order to improve the efficiency of the initial solution. The method design is based on ascending order (ranked-order-value, ROV), applying the continuous PSO algorithm to the PFSP, introducing the external archive set storage Pareto solution, and using a hybrid strategy that combines strong dominance and aggregation distance to ensure the distribution of the solution set. We adopted the Sigma method and the roulette method, based on the aggregation distance, to select the global optimal solution. A variable neighborhood search algorithm was proposed to further search the Pareto solution in the external set. The suggested hybrid algorithm was used to solve the Taillard test set and equate the test results with the SPEA2 algorithm to check the scheduling algorithm’s efficacy.

Multireservoir system operation optimization by hybrid quantum-behaved particle swarm optimization and heuristic constraint handling technique

Generally, the multireservoir system operation optimization (MSOO) is classified as a large-scale and multi-stage optimization problem with a set of complex constraints. Here, the goal of MSOO is chosen to determine the optimal operation policy of all the reservoirs to minimize the energy deficit of electrical system. In order to effectively resolve this problem, a hybrid quantum-behaved particle swarm optimization (HQPSO) is developed in this study. In HQPSO, the external archive set conserving the elite particles is used to provide multiple search directions for various agents; the modified evolution strategy and mutation operator are used to enhance the convergence rate of the swarm; while a practical heuristic constraint handling method is employed to address the complex physical constraints imposed on all the hydropower reservoirs. The simulations of 12 benchmark functions indicate that HQPSO can produce better results than several existing evolutionary methods. Then, two multireservoir systems are chosen to verify the performance of the proposed method. The results show that compared with the conventional methods, the HQPSO method can obtain scheduling results with better performances in reducing the energy deficits of power system. Hence, this paper provides an effective tool for the complex multireservoir system operation problem.

Two-Stage Adaptive Constrained Particle Swarm Optimization Based on Bi-Objective Method

For the sake of better balancing the relationship between diversity and convergence when handling constrained optimization problems, a two-stage adaptive constrained particle swarm optimization algorithm based on bi-objective method (TABC-PSO) is proposed. In accordance with different phases of the constraint process, the target-constraint space derived from the angle is partitioned adaptively, and simultaneously the global best particle is selected and the external archive set is safeguarded. In the first stage, the whole space is divided adaptively in term of the angular distribution of individual, and the feasible region is explored comprehensively. In the second stage, local regions are adaptively compartmentalized and in-depth exploitation is carried out. Primary and secondary external archive sets are established to maintain population diversity and accelerate convergence. The two phases are switched adaptively in light of the storage status of the two external archive sets. We evaluated TABC-PSO algorithm on the benchmark functions in CEC 2006 and CEC 2017. The experimental results show that TABC-PSO algorithm compared with other state-of-the-art algorithms can be superior to applied to test functions with different types of constraints and possesses a competitive search capability.

Long-Term Hydropower Generation Scheduling of Large-Scale Cascade Reservoirs Using Chaotic Adaptive Multi-Objective Bat Algorithm

With growing concerns over renewable energy, the cascade hydropower reservoirs operation (CHRO), which balances the development of economic benefits and power supply security, plays an increasingly important role in hydropower systems. Due to conflicting objectives and complicated operation constraints, the CHRO problem considering the requirements of maximizing power generation benefit and firm power output is determined as a multi-objective optimization problem (MOP). In this paper, a chaotic adaptive multi-objective bat algorithm (CAMOBA) is proposed to solve the CHRO problem, and the external archive set is added to preserve non-dominant solutions. Meanwhile, population initialization based on the improved logical mapping function is adopted to improve population diversity. Furthermore, the self-adaptive local search strategy and mutation operation are designed to escape local minima. The CAMOBA is applied to the CHRO problem of the Qingjiang cascade hydropower stations in southern China. The results show that CAMOBA outperforms the multi-objective bat algorithm (MOBA) and non-dominated sorting genetic algorithms-II (NSGA-II) in different hydrological years. The spacing (SP) and hypervolume (HV) metrics verify the excellent performance of CAMOBA in diversity and convergence. In summary, the CAMOBA is demonstrated to get better scheduling solutions, providing an effective approach for solving the cascade hydropower reservoirs operation (CHRO).

Fast multiobjective immune optimization approach solving multiobjective interval number programming

Abstract As an uncertain programming model with multiple conflicting performance indices and bounded uncertain parameter(s), multiobjective interval number programming is a daunting topic in the fields of mathematics and intelligent optimization. Despite its comprehensive engineering application background, it is still open, and further studies are needed on basic theory, model transformation and intelligent optimizers. Therein, this work not only gropes a new shortcut to tackling one such model, but also proposes a novel multiobjective interval number immune optimization algorithm. The intrinsic solution relation between the model and a related natural interval extension one is discovered in terms of the new concept of optimal-value vector solution, by which a fast interval nondominated sorting approach is acquired. The algorithm mainly consists of population division, proliferation, evolution, selection and memory update, in which a co-evolutionary mechanism is designed to promote the current population to move quickly towards the Pareto front with the assistance of the sorting approach and an external archive set. The algorithm's resource consumption depends mainly on the archive's size. Comparative experiments have validated that the optimizer can effectively perform well over the compared approaches and is significantly superior to them with regard to efficiency.

An Improved SPEA2 Algorithm with Local Search for Multi-Objective Investment Decision-Making

Enterprise investment decision-making should not only consider investment profits, but also investment risks, which is a complex nonlinear multi-objective optimization problem. However, traditional investment decisions often only consider profit as a goal, resulting in an incorrect decision. Facing the high complexity of investment decision-making space, traditional multi-objective optimization methods pay too much attention to global search ability because of pursuing convergence speed and avoiding falling into local optimum, while local search ability is insufficient, which makes it difficult to converge to the Pareto optimal boundary. To solve this problem, an improved SPEA2 algorithm is proposed to optimize the multi-objective decision-making of investment. In the improved method, an external archive set is set up separately for local search after genetic operation, which guarantees the global search ability and also has strong local search ability. At the same time, the new crossover operator and individual update strategy are used to further improve the convergence ability of the algorithm while maintaining a strong diversity of the population. The experimental results show that the improved method can converge to the Pareto optimal boundary and improve the convergence speed, which can effectively realize the multi-objective decision-making of investment.

Multiobjective Particle Swarm Optimization Algorithm Based on Adaptive Angle Division

It is difficult to balance the convergence and diversity at the same time and select the globally optimal particle (gbest) in the multiobjective particle swarm optimization (MOPSO) process. In this paper, a novel method based on adaptive angle division is proposed targeting at archive maintenance and gbest selection. According to the number of particles in the current archive, the angle region of the target space is adaptively adjusted and uniformly divided. The globally optimal particle is selected from the low-density angle region of the particle distribution; in the meanwhile, the superfluous particles are deleted from the high-density angle region. Consequently, the selection of gbest and update of external archive set which including the generation of the optimal solution set and maintenance of external archive set are synchronized. The convergence and diversity are ensured while improving the uniformity of the optimal solution set. In addition, the current highest non-dominated particles in each angle region are preserved, and the particles in adjacent regions are selected to conduct global guidance for such regions and regions of the particle-free distribution area. Through these two ways, the diversity of the population is maintained while the coverage spreadability of the optimal solution set in the target space is enhanced. Four state-of-the-art evolution multiobjective optimization (EMO) algorithms and the two classic EMO algorithms are selected as the peer algorithms to validate multiobjective particle swarm optimization based on adaptive angle division (AADMOPSO) algorithm. A series of extensive experiments are conducted on five groups of standard test functions. The experimental results show the effectiveness and competitiveness of the proposed AADMOPSO in balancing convergence and diversity.

Wind‐thermal dynamic economic emission dispatch with a hybrid multi‐objective algorithm based on wind speed statistical analysis

Based on the analysis on the uncertain nature of wind power output, the Weibull distribution parameters of regional wind speed at different periods are calculated to obtain the probability density function (PDF) and the cumulative distribution function (CDF) of the wind power. The spinning reserve (SR) requirements for wind power incorporation are determined according to the obtained PDF and CDF, and by converting the wind power into a chance constrained form, a model for dynamic economic emission dispatch with wind power is constructed. A hybrid multi-objective algorithm that integrates differential evolution (DE) and particle swarm optimisation (PSO) algorithm is put forward to solve the proposed model. The algorithm is implemented based on the Pareto dominance theory and a dynamic external archive set, and fully exploits the advantages of DE and PSO. An improved calculation method of crowding distance and Pareto solution set reduction rule are also employed to enhance the performance of the proposed algorithm. Also, three performance indicators are introduced to evaluate the performance of the algorithm. Two distinct test systems are performed to verify the proposed model and algorithm, and the results show that they are effective and reasonable.

A parallel multi-objective particle swarm optimization for cascade hydropower reservoir operation in southwest China

Due to the expanding system scale and increasing operational complexity, the cascade hydropower reservoir operation balancing benefit and firm output is becoming one of the most important problems in China’s hydropower system. To handle this problem, this paper presents a parallel multi-objective particle swarm optimization where the swarm with large population size is divided into several smaller subswarms to be simultaneously optimized by different worker threads. In each subtask, the multi-objective particle swarm optimization is adopted to finish the entire evolutionary process, where the leader particles, external archive set and computational parameters are all dynamically updated. Besides, a novel constraint handling strategy is used to identify the feasible search space while the domination strategy based on constraint violation is used to enhance the convergence speed of swarm. The presented method is applied to Lancang cascade hydropower system in southwest China. The results show that PMOPSO can provide satisfying scheduling results in different cases. For the variation coefficient of generation in 30 independent runs, the presented method can bettered the serial algorithm with about 66.67% and 61.29% reductions in normal and dry years, respectively. Hence, this paper provides an effective tool for multi-objective operation of cascade hydropower system.

A Multiobjective Evolutionary Algorithm Based on Coordinate Transformation.

In this paper, a novel multiobjective evolutionary algorithm (MOEA/CT) is proposed to better manage convergence and distribution of solutions when MOEAs are used for solving multiobjective optimization problems. The coordinate transformation strategy, an external archive update strategy, and a diversity maintenance strategy are proposed in MOEA/CT. The coordinate transformation strategy in the objective space is designed to find more efficient solutions that can accelerate the convergence process. Based on the coordinate transformation strategy, a novel update strategy and diversity maintenance approach for selecting nondominated solutions from the external archive set are integrated in MOEA/CT for getting better distribution of the solutions. The proposed MOEA/CT is compared with eight state-of-art algorithms on six biobjective and seven tri-objective test problems. In terms of four performance metrics, the comparative experimental results demonstrate that MOEA/CT outperforms the other eight competitors and it can achieve solutions with better distribution and better convergence to the Pareto front. In addition, parameter sensitivity analysis is provided to investigate the effect of a key parameter in MOEA/CT; the proposed three strategies are also studied individually to investigate their contribution to MOEA/CT; the performance analysis along with the capacity of external archive is given to clearly make the influence in MOEA/CT; finally, the scalability performance of MOEA/CT is investigated and compared with five notable many-objective evolutionary algorithms on the DTLZ and WFG test suites with 5, 8, 10, and 15 objectives.

Scheduling of short-term hydrothermal energy system by parallel multi-objective differential evolution

With the growing concerns on energy and environment, the short-term hydrothermal scheduling (SHTS) which minimizes the fuel cost and pollutant emission simultaneously is playing an increasing important role in the modern electric power system. Due to the complicated operation constraints and objectives, SHTS is classified as a multi-objective optimization problem. Thus, to efficiently resolve this problem, this paper develops a novel parallel multi-objective differential evolution (PMODE) combining the merits of parallel technology and multi-objective differential evolution. In PMODE, the population with larger size is first divided into several smaller subtasks to be concurrently executed in different computing units, and then the main thread collects the results of each subpopulation to form the final Pareto solutions set for the SHTS problem. During the evolutionary process of each subpopulation, the mutation crossover and selection operators are modified to enhance the performance of population. Besides, an external archive set is used to conserve the Pareto solutions and provide multiple evolutionary directions for individuals, while the constraint handling method is introduced to address the complicated operational constraints. The results from a mature hydrothermal system indicate that when compared with several existing methods, PMODE can obtain satisfactory solutions in both fuel cost and environmental pollutant, which is an effective tool to generate trade-off schemes for the hydrothermal scheduling problem.

Multi-objective inverse scheduling optimization of single-machine shop system with uncertain due-dates and processing times

Generally, ideal manufacturing system environments are assumed before determining effective scheduling. However, the original schedule is no longer optimal or even to be infeasible due to many uncertain events. This paper investigates a multi-objective inverse scheduling problem in single-machine shop system with due-dates and uncertain processing parameters. Moreover, in order to more close the addressed problem into the situations encountered in real world, the processing parameters are considered to be uncertain stochastic parameters. First, a comprehensive mathematical model for multi-objective single-machine inverse scheduling problem (MSMISP) is addressed. Second, an effective hybrid multi-objective evolutionary algorithm (HMNL) is proposed to handle uncertain processing parameters (uncertainties) and multiple objectives at the same time. In HMNL, using an effective decimal system encoding scheme and genetic operators, the non-dominated sorting based on NSGA-II is adapted for the MSMISP. In addition, hybrid HMNL are proposed by incorporating an adaptive local search scheme into the well-known NSGA-II, where applies a separate local search process, total six strategies, to improve quality of solutions. Furthermore, an on-demand layered strategy is embedded into the elitism strategy to keep the population diversity. Afterwards, an external archive set is dynamically updated, where a non-dominated solution is selected to participate in the creation of the new population. Finally, 36 public problem instances with different scales and statistical performance comparisons are provided for the HMNL algorithm. This paper is the first to propose a mathematical model and develop a hybrid MOEA algorithm to solve MSMISP in inverse scheduling domain.

Hybrid Multiobjective Differential Evolution Incorporating Preference Based Local Search

AbstractThe performance of Differential Evolution (DE) for multiobjective optimization problems (MOPs) can be greatly enhanced by hybridizing with other techniques. In this paper, a new hybrid DE incorporating preference based local search is proposed. In every generation, a set of nondominated solutions is generated by DE operation. Usually these solutions distribute unevenly along the obtained nondominated set. To get solutions in the sparse region of the nondominated set, a mini population and preference based local search algorithm is specifically designed, and is used to exploit the sparse region by optimizing an achievement scalarizing function (ASF) with the dynamically adjusted reference point. As a result, multiple solutions in the sparse region can be obtained. Moreover, to retain uniformly spread nondominated solutions, an improved e-dominance strategy, which would not delete the extreme points found during the evolution, is proposed to update the external archive set. Finally, numerical result...

Optimal operation of multi-reservoir system by multi-elite guide particle swarm optimization

With increasingly scarce of fossil fuel resources required for energy demand, hydropower has become one of the most important energy resources. As a renewable and sustainable energy, hydropower system has developed rapidly during recent decades. The unprecedented rate of expansion and development scale of hydropower has posed a challenge to the operation of multi-reservoir system (OMRS). The optimal operation of multi-reservoir system is a large-scaled, non-linear and multi-stage problem which subject to a series of hydraulic constraints. The main objective of OMRS is to find out the optimal hourly water discharge rate of each hydro station in the multi-reservoir system to minimize the power deficit and distribute the uniformly deficit if any. In order to solve OMRS problem effectively, in this paper, a multi-elite guide particle swarm optimization (MGPSO) is proposed by introducing archive set into standard particle swarm optimization. External archive set which can preserve elite solutions along the evolution process is employed to provide multi-elite flying directions for particles. Meanwhile, an effective constrain handling method is proposed to handle the operational constraints of OMRS problem. This proposed method is applied to a multi-reservoir system consisting of 10 cascaded hydro plants for case study. Compared with several previous methods, the simulation results of MGPSO can get better solutions with smaller energy deficit, which proves it is an alternative method to deal with OMRS problem.

Optimal Operation of Large-Scale Cascaded Hydropower Systems in the Upper Reaches of the Yangtze River, China

AbstractIn recent decades, there has been a rapid rate of development of hydropower in China. The unprecedented rate of expansion, development scale, and large numbers of hydropower plants have posed a challenge to the operation of large-scale cascaded hydropower systems (OLCHSs), which has become one of the most important factors in ensuring the security and economic operation of the power grid in China. In this paper, a long-term optimal operation model is developed for the purpose of maximizing the total generated energy of cascaded hydropower plants. To solve the OLCHS problem effectively, an elite-guide particle swarm optimization (EGPSO) algorithm is proposed in this paper. An external archive set, which can preserve elite solutions during the evolution process, is employed to provide flying directions for particles. Since the OLCHS problem is a high-dimensional, nonlinear, multistage, and stringent constraint optimal problem, the proposed algorithm introduces three new innovations: a layer-partitio...