External Archive Research Articles

Multi-Objective Teaching-Learning-Based Optimization for Structure Optimization

ABSTRACT Teaching–learning-based optimization is a specific parameter-free and powerful algorithm. However, in large and diverse spaces it often gets trapped in local optima and faces criticism of premature convergence particularly while solving multi-objective problems. The present work proposed a novel multi-objective teaching–learning-based optimization (MOTLBO) based on the framework of non-dominated sorting and solution storage in an external archive. These techniques improve the algorithm’s speed of search and convergence rate. Moreover, this mechanism also assists in obtaining a Pareto optimal set near to the true Pareto solutions while simultaneously maintaining the diversity among non-dominated solutions within one run. The present work proposed a novel MOTLBO. To determine feasibility for practical applications, perceived structure design problems are exposed to multiple and diverse weight minimization and maximization of nodal deformation objectives. The suggested algorithm is employed to five challenging optimization issues of the structure having discrete design variables and subject to multiple constraints. For a performance check, the suggested algorithm is contrasted with two prominent multi-objective algorithms. The performance gauge for all considered test examples is the Pareto front hypervolume and front spacing-to-extent test. MOTLBO shows its promise with coherence and diversification of solutions for producing the desired Pareto fronts.

Bi-objective no-wait multiproduct multistage product scheduling problem with flexible due dates based on MOIDE- MA

This paper deals with the no-wait multiproduct multistage product scheduling problem (NWMMSP) with minimum makespan and maximum mean customer’s satisfaction level criteria. The mean customer’s satisfaction level criterion related to flexible due date is introduced to approach an imprecise or flexible nature of the data in a practical manufacturing environment. A novel discrete multi-objective evolutionary algorithm combined with an improved differential evolution algorithm and memetic algorithm (MOIDE-MA) is proposed to solve the multi-objective NWMMSP. The improved discrete differential evolution algorithm (IDE) mainly focuses on the edge area of the Pareto front (PF) space and the single objective guide strategy to construct better reference points. Meanwhile, an information-sharing strategy is introduced in IDE to improve the information diversity and enhance the search capabilities for the whole PF. A novel memetic algorithm (MA) based on genetic algorithm (GA) and local search related to the researched scheduling problem is developed to improve the distribution uniformity and accuracy of the non-dominated solutions obtained by IDE further. IDE gains some useful information extracted from the external archive of MA to speed up its search. Computational and simulation results show that the improvement strategy proposed in the algorithm can effectively improve the performance of MOIDE-MA. Furthermore, the proposed algorithm is compared with three other multi-objective scheduling optimization approaches based on different scale multi-objective NWMMSP instances. The experimental results show the effectiveness of the proposed MOIDE-MA.

Improved ensemble of differential evolution variants.

In the field of Differential Evolution (DE), a number of measures have been used to enhance algorithm. However, most of the measures need revision for fitting ensemble of different combinations of DE operators—ensemble DE algorithm. Meanwhile, although ensemble DE algorithm may show better performance than each of its constituent algorithms, there still exists the possibility of further improvement on performance with the help of revised measures. In this paper, we manage to implement measures into Ensemble of Differential Evolution Variants (EDEV). Firstly, we extend the collecting range of optional external archive of JADE—one of the constituent algorithm in EDEV. Then, we revise and implement the Event-Triggered Impulsive (ETI) control. Finally, Linear Population Size Reduction (LPSR) is used by us. Then, we obtain Improved Ensemble of Differential Evolution Variants (IEDEV). In our experiments, good performers in the CEC competitions on real parameter single objective optimization among population-based metaheuristics, state-of-the-art DE algorithms, or up-to-date DE algorithms are involved. Experiments show that our IEDEV is very competitive.

The route problem of multimodal transportation with timetable: stochastic multi-objective optimization model and data-driven simheuristic approach

PurposeDistribution of long-haul goods could be managed via multimodal transportation networks where decision-maker has to consider these factors including the uncertainty of transportation time and cost, the timetable limitation of selected modes and the storage cost incurred in advance or delay arriving of the goods. Considering the above factors comprehensively, this paper establishes a multimodal multi-objective route optimization model which aims to minimize total transportation duration and cost. This study could be used as a reference for decision-maker to transportation plans.Design/methodology/approachMonte Carlo (MC) simulation is introduced to deal with transportation uncertainty and the NSGA-II algorithm with an external archival elite retention strategy is designed. An efficient transformation method based on data-drive to overcome the high time-consuming problem brought by MC simulation. Other contribution of this study is developed a scheme risk assessment method for the non-absolutely optimal Pareto frontier solution set obtained by the NSGA-II algorithm.FindingsNumerical examples verify the effectiveness of the proposed algorithm as it is able to find a high-quality solution and the risk assessment method proposed in this paper can provide support for the route decision.Originality/valueThe impact of timetable on transportation duration is analyzed and making a detailed description in the mathematical model. The uncertain transportation duration and cost are represented by random number that obeys a certain distribution and designed NSGA-II with MC simulation to solve the proposed problem. The data-driven strategy is adopted to reduce the computational time caused by the combination of evolutionary algorithm and MC simulation. The elite retention strategy with external archiving is created to improve the quality of solutions. A risk assessment approach is proposed for the solution scheme and in the numerical simulation experiment.

Self-Adaptive two roles hybrid learning strategies-based particle swarm optimization

Particle Swarm Optimization (PSO) is a simple yet efficient population based evolutionary algorithm, which has been widely applied to solve global optimization problems. Similar to other evolutionary algorithms (EAs), PSO algorithm still suffers from loss of diversity and slow convergence caused by the contradiction between exploration and exploitation abilities. In order to address the drawbacks, we propose Self-Adaptive two roles hybrid learning strategies-based particle swarm optimization (SAHLPSO) to improve optimization performance by using exploration-role and exploitation-role learning strategies with self-adaptively updating parameters manner. The exploration-role learning strategies with external archive adopt comprehensive learning to generate the learning exemplars, which can effectively maintain population diversity and thus avoid premature. On the other hand, the exploitation-role learning strategies utilize elitism learning to generate the learning exemplars so as to improve convergence performance. Considering that the performance improvement of PSO depends on not only the adaptation of different learning strategies but also the reasonable parameter settings, we also develop a self-adaptive parameter updating manner based on success history information. This manner can automatically update the learning parameters to appropriate values and avoid a user’s prior knowledge about the relationship between the parameter settings and the characteristics of optimization problems. In addition, the usage of the linear population size reduction is also helpful to well balance the exploration and exploitation along with the process of evolution. Simulation results on some classical and CEC2013 benchmark functions show that LSAHLPSO is better than other PSO variants or at least comparable to other state-of-the-art evolutionary algorithms.

Improved differential evolution LQG control of active suspension

Aiming at the problem that the value of weighted matrix Q and R in linear quadratic optimal control (LQG) controller depends on the designer’s experience, adaptive differential evolution (JADE) algorithm with optional external archive is introduced to optimize the control parameters of LQG, so as to improve the performance of LQG controller. The dynamics model of 1/4 vehicle active suspension was established as the object, and the LQG objective function was constructed. The simulation experiments were carried out on B-class and C-class roads with the help of Matlab/Simulink.The experimental results show that the RMS values of the vertical acceleration of the vehicle body, the dynamic travel of the suspension and the dynamic displacement of the tire of the active suspension based on JADE optimized LQG controller under different road surfaces are reduced to a large extent compared with that of the passive suspension, which improves the stability of the vehicle and the comfort of the ride.

Optimising the job-shop scheduling problem using a multi-objective Jaya algorithm

This paper presents an effective multi-objective Jaya (EMOJaya) algorithm to solve a multi-objective job-shop scheduling problem, aiming to simultaneously minimise the makespan, total flow time and mean tardiness. A strategy based on grey entropy parallel analysis (GEPA) is developed to assess and select solutions during the search process. To obtain a high-quality reference sequence for GEPA, an opposition-based learning (OBL) strategy is used in parallel. Additionally, the OBL strategy is incorporated into Jaya’s search operation and external archive to enhance the search ability and convergence rate of the algorithm. Computational experiments based on 30 benchmark instances with different scales confirm that GEPA and OBL can significantly improve the performance of our proposed EMOJaya. Experimental results also show that EMOJaya is able to outperform three state-of-the-art multi-objective algorithms in solving the problem at hand in terms of convergence, diversity and distribution. Further, EMOJaya can obtain more high-quality scheduling schemes, which provide more and better options for decision makers.

Trajectory optimization for manipulators based on external archives self-searching multi-objective particle swarm optimization

In order to improve the quality of the non-inferior solutions obtained by multi-objective particle swarm optimization (MOPSO), an improved algorithm called external archives self-searching multi-objective particle swarm optimization (EASS-MOPSO) was proposed and applied to a multi-objective trajectory optimization problem for manipulators. The position curves of joints were constructed by using quartic B-splines; the mathematical models of time, energy and jerk optimization objectives for manipulators were established; and the kinematic constraints of joints were transformed into the constraints of the control vertexes of the B-splines. A self-searching strategy of external archives to make non-inferior solutions have the ability to search the surrounding hyperspace was explored, and a diversity maintaining strategy of the external archives was proposed. The results of several test functions by simulation show that the convergence and diversity of the proposed algorithm are better than those of other 4 selected algorithms; the results of the trajectory optimization problem for manipulators by simulation show that the convergence, diversity and time consumption of the proposed algorithm are significantly better than those of non-dominated sorting genetic algorithm.

Multiple global optima location using differential evolution, clustering, and local search

Multimodal optimization can be divided into two main categories. The first focuses on finding only one global optimum, e.g., one peak, and the second focuses on finding multiple global optima, e.g., multiple peaks, and it is the focus of this work. The first category can be approached by single-solution and population-based metaheuristics, while in the second category, the use of population-based metaheuristics is best suited. Finding multiple global optima is more common in real-world optimization problems where there is no previous information about the number of globally optimal solutions in the search space landscape. Thus, this work proposes a self-adaptive Differential Evolution with DBSCAN algorithm and a two-step exploitation routine, named NCjDE-2LSar, applied to multiple global optima multimodal optimization. The jDE algorithm with Michalewicz mutation strategy is employed as a global optimizer. Candidate solutions are grouped in an external archive using the DBSCAN algorithm. External archive solutions represent possible peaks that will feed the Nelder–Mead and Hooke–Jeeves exploitation algorithms. The peak ratio is used as a performance metric. Six state-of-the-art algorithms are used to compare the results obtained by the proposed approach. Results show that the proposed algorithm outperforms the state-of-the-art algorithms concerning the mean absolute value of the peak ratio evaluation metric. The algorithm also achieved the perfect peak ratio (100%) in 10 out of 20 functions.

A vector angles-based many-objective particle swarm optimization algorithm using archive

Because of the easy implement and fast convergence speed in single objective optimization problems, the particle swarm optimization algorithm has been extended to many-objective optimization problems. When designing a many-objective particle swarm optimization algorithm, archive maintenance strategy and selection of leaders are two crucial issues. To addressing these two problems, this paper proposed a vector angles-based many-objective particle swarm optimization algorithm using archive. In this algorithm, a new method was proposed to make the external archive getting a balance between convergence and diversity, based on the values of vector angles of each solution. Also, we designed a novel strategy based on vector angle and decomposition to select gbest and pbest from the archive to promote evolution of the population. Besides, the shift-based density estimation was used as the standard to clone elite solutions to strengthen the quality of the external archive. The experiment results indicate that our algorithm has competitive performance comparing with the six state-of-the-art many-objective optimization algorithms on three widely used benchmarks DTLZ, WFG, and MaF.

A novel multi-objective group teaching optimization algorithm and its application to engineering design

This paper proposes a novel multi-objective algorithm by extending the recent group teaching optimization algorithm (GTOA) for the solution of multi-objective optimization problems. The proposed algorithm (designated as MOGTOA) is based on the Pareto dominance theory, and uses an external archive to guide the search direction of population. In order to strike a balance between exploration and exploitation of MOGTOA, a variety of improvements were made, including an improved teacher selection strategy, a modified student phase, and a hybrid mechanism of evolutionary search on the external archive population. The performance of the proposed algorithm was verified on 21 benchmark functions in comparison with six well established algorithms. The numerical results show that MOGTOA is comparable or even superior to other algorithms. In addition, the application of MOGTOA to two classic engineering design problems demonstrated its promising potential to solve practical problems.

Nonlinear normal modes and optimization of a square root nonlinear energy sink

Since the vibration mitigation of nonlinear energy sinks (NESs) needs multi-objective optimization, this paper aims to address this issue with efficient multi-objective particle swarm optimization (MOPSO) methods. A non-polynomial NES model, namely a square root NES (SRNES), is targeted for multi-objective optimization and dynamical analysis on an impulsively excited linear oscillator (LO) and compared with the corresponding polynomial model. Different MOPSO methods are developed to balance the mass and dissipation efficiency of SRNESs by utilizing weighted ranking, external archive, and non-dominated sorting. And nonlinear normal modes (NNMs) are extended for the analysis of SRNESs. The optimization results show the efficient targeted energy transfer (TET) and high robustness of the bistable SRNES in different LO initial and damping conditions. Specifically, more than 95% energy absorption can be easily witnessed, even in a small mass ratio (around 0.003), but the amplitude of the SRNES can be very large. The principal manifestation of the optimal TET is 1:1 resonance capture along with considerable low-frequency components of the SRNES. The optimization results of the SRNESs and the linear vibration absorbers show high similarities, while with a large mass ratio, the SRNESs possess broader range of spring stiffness. In the comparison of the two NES models, the differences are found in potential energy surfaces, NNMs, in-well motion, and vibration attenuation performance. Besides, the SRNESs can be divided into two groups in terms of the conservative dynamics, which can be explained by the polynomial model. The frequency component of in-phase NNMs dominates in the conservative and dissipative dynamics of the SRNESs, which lead to the transition of NNMs in the dissipative dynamics. In summary, the efficient MOPSO methods can be designed for different needs of vibration suppression and structure cost. Furthermore, it is important to directly analyze the non-polynomial nonlinear vibration, because transforming non-polynomial models into polynomial ones may lead to unreasonable or imprecise results. Finally, the NES damping structure and the NES performance in small mass conditions should be enhanced.

Day-ahead optimal reactive power ancillary service procurement under dynamic multi-objective framework in wind integrated deregulated power system

This paper deals with the investigation of a day-ahead reactive power ancillary service procurement problem to minimize cost and voltage deviation under wind power generation uncertainties in a pool-based deregulated system. This reactive power procurement problem is formulated as a dynamic bi-objective optimization problem and is solved using a developed Pareto-based multi-objective artificial electric field algorithm (MO-AEFA). The developed MO-AEFA utilizes nondominated sorting principle and an external archive to store Pareto optimal solutions. Sign and reorder mutation operators are used to avoid trapping in local optima and enhance population diversity. The numerical results obtained from MO-AEFA are compared with other algorithms to validate the efficacy of proposed approach. The optimization algorithm utilizes a fast Newton power flow employing sparse matrix techniques to diminish computational burden. The capacitor switching is decided with consideration of marginal prices. The proposed methodology has been tested on modified IEEE 30-bus and IEEE 118-bus test systems. The performance of both test systems is analyzed for two studies namely, VAr dispatch without wind integration, and VAr dispatch under wind integration. The analysis with wind integration is further investigated for different wind penetration levels. The convergence characteristic of Pareto solutions is measured through statistical distance and diversity metrics.

A hybridized multi-algorithm strategy for engineering optimization problems

This paper presents a new multi-hybrid algorithm (MHA) based on the hybridization concepts incorporated in the naked mole-rat algorithm (NMRA). The new algorithm uses the exploratory concepts of whale optimization algorithm (WOA), moth flame optimization (MFO) and marine predator algorithm (MPA) to enhance the worker phase or the exploration operation in NMRA. In order to overcome the problem of local optima stagnation, a new stagnation phase inspired from the concepts of GWO and cuckoo search (CS) algorithm is also added. Apart from these modifications, self-adaptivity has been incorporated by adapting all the parameters of the proposed algorithm. Here five new mutation strategies including simulated annealing (sa), exponentially decreasing (exp), chaos based (chaotic), linearly decreasing (linear) and oscillatory inertia weight (oscillating) have been exploited for different parameters of all the algorithms under study so that no user based parametric adjustments are required. For performance evaluation, the MHA is subjected to CEC 2005, CEC 2014 benchmark problems and image thresholding problem. The comparison on variable population sizes and dimension size has been done to prove the significance of the proposed algorithm over variable function evaluations and higher dimensional problems. From the experimental results, it can be seen that proposed MHA performs better than adaptive differential evolution with optional external archive (JADE), self adaptive differential evolution (SaDE), opposition and exponential whale optimization algorithm (OEWOA), sine cosine crow search algorithm (SCCSA), fractional-order calculus-based flower pollination algorithm (FA-FPO), success-history based parameter adaption differential evolution (SHADE), SHADE with linear population size reduction hybrid with semi-parameter adaptation of CMA-ES (LSHADE-SPACMA), Laplacian biogeography-based optimization (LX-BBO), random walk grey wolf optimizer (RW-GWO), improved symbiotic organisms search (ISOS), variable neighbourhood bat algorithm (VNBA), improved elephant herding optimization (IMEHO) and others. Statistical results in terms of Wilcoxon’s rank-sum test, Freidman’s test and convergence profiles further validate the superior performance of the proposed MHA algorithm. The source code can be downloaded from https://github.com/rohitsalgotra.

Multiobjective Particle Swarm Optimization Based on Cosine Distance Mechanism and Game Strategy.

The optimization problems are taking place at all times in actual lives. They are divided into single objective problems and multiobjective problems. Single objective optimization has only one objective function, while multiobjective optimization has multiple objective functions that generate the Pareto set. Therefore, to solve multiobjective problems is a challenging task. A multiobjective particle swarm optimization, which combined cosine distance measurement mechanism and novel game strategy, has been proposed in this article. The cosine distance measurement mechanism was adopted to update Pareto optimal set in the external archive. At the same time, the candidate set was established so that Pareto optimal set deleted from the external archive could be effectively replaced, which helped to maintain the size of the external archive and improved the convergence and diversity of the swarm. In order to strengthen the selection pressure of leader, this article combined with the game update mechanism, and a global leader selection strategy that integrates the game strategy including the cosine distance mechanism was proposed. In addition, mutation was used to maintain the diversity of the swarm and prevent the swarm from prematurely converging to the true Pareto front. The performance of the proposed competitive multiobjective particle swarm optimizer was verified by benchmark comparisons with several state-of-the-art multiobjective optimizer, including seven multiobjective particle swarm optimization algorithms and seven multiobjective evolutionary algorithms. Experimental results demonstrate the promising performance of the proposed algorithm in terms of optimization quality.

Multi-Objective Task Scheduling Approach for Fog Computing

Despite the remarkable work conducted to improve fog computing applications’ efficiency, the task scheduling problem in such an environment is still a big challenge. Optimizing the task scheduling in these applications, i.e. critical healthcare applications, smart cities, and transportation is urgent to save energy, improve the quality of service, reduce the carbon emission rate, and improve the flow time. As proposed in much recent work, dealing with this problem as a single objective problem did not get the desired results. As a result, this paper presents a new multi-objective approach based on integrating the marine predator’s algorithm with the polynomial mutation mechanism (MHMPA) for task scheduling in fog computing environments. In the proposed algorithm, a trade-off between the makespan and the carbon emission ratio based on the Pareto optimality is produced. An external archive is utilized to store the non-dominated solutions generated from the optimization process. Also, another improved version based on the marine predator’s algorithm (MIMPA) by using the Cauchy distribution instead of the Gaussian distribution with the levy Flight to increase the algorithm’s convergence with avoiding stuck into local minima as possible is investigated in this manuscript. The experimental outcomes proved the superiority of the MIMPA over the standard one under various performance metrics. However, the MIMPA couldn’t overcome the MHMPA even after integrating the polynomial mutation strategy with the improved version. Furthermore, several well-known robust multi-objective optimization algorithms are used to test the efficacy of the proposed method. The experiment outcomes show that MHMPA could achieve better outcomes for the various employed performance metrics: Flow time, carbon emission rate, energy, and makespan with an improvement percentage of 414, 27257.46, 64151, and 2 for those metrics, respectively, compared to the second-best compared algorithm.

Development of information support systems for production processes of contractor enterprises through an external electronic archive

The main areas of activity of research and manufacturing associations include the creation of knowledge-based military and civilian products. Having unique competencies in the field of creating knowledge-based products for various fields of industry, research and production enterprises together with cooperative enterprises, including contracting partners, for many years have occupied a leading position in the markets of fuel and energy complex and other industries. Over the past five years, many industrial enterprises have gone from a critical decline in production and bankruptcy to a stable increase in work volumes, while the projects in the field of development of information support systems for industrial production processes have become highly demanded in the process of crisis management.

A Modified Crow Search Optimizer for Solving Non-Linear OPF Problem With Emissions

This paper proposes a modified crow search optimizer (MCSO) for solving the combined economic emission power flow (EEPF) problem. In the proposed approach, the local search ability is enhanced into the crow search optimizer (CSO) and aggregated with a novel bat algorithm (NBA). Close accord between CSO, NBA, and MCSO is employed for solving the single and multi-objective frameworks. Moreover, the proposed MCSO incorporates external archive and dominance comparison to handle multi-objective frameworks while the best compromise solution is extracted by using a fuzzy based mechanism. The proposed MCSO, CSO, and NBA are developed and tested to on IEEE 30 bus and West Delta power grid (WDPG) systems. Added to the that, the proposed methodology is tested on a large-scale power system, IEEE 118-bus test system, for measure the scalability of the proposed method. Their output results are compared with the reported algorithms in the literature to demonstrate the MCSO outperformance in terms of solution quality and robustness. Significant economical solutions of the EEPF problem are achieved with respecting the environment concerns at acceptable emission levels. Added to that, the multi objective framework is assessed with hypervolume indictor that show the high capability of the proposed MCSO compared with CSO.

Multi-objective optimization of space adaptive division for environmental economic dispatch

With the increasingly severe global energy and environmental issues, the traditional economic load dispatching with the single goal of power generation cost has been unable to meet the national macro strategic requirements for energy conservation and emission reduction. This research mainly discusses the multi-objective optimization of spatial adaptive partitioning based on environmental economic dispatch problems. This study uses the method of calculating power generation costs and pollution control costs to select a compromise solution. When initializing the individual optimal position memory bank and the global optimal position memory bank, put the first-generation particle position into the individual optimal position memory bank, and put the optimal position obtained by comparing the first-generation particle into the global optimal position. In the location memory. Then calculate the fitness value corresponding to each objective function of each particle, compare the calculated result with the corresponding results of each Pareto solution in the internal memory bank and the external memory bank, and replace the particle position with the best. In the multi-objective processing strategy, in order to better obtain the Pareto optimal solution set and the Pareto optimal frontier, an external archive is set up to save and update the new elite Pareto optimal solution generated after each iteration. Since the quality of the particles in the random simulation particle swarm algorithm will directly affect the convergence and diversity of the final Pareto optimal solution set, this study selects the historical optimal particles according to the Pareto dominance relationship. When the multi-objective optimized power system economic dispatch research model with wind farms was adopted, the cost of power generation increased by 6.21 million yuan, the cost of polluting gas treatment was reduced by 8.1 million yuan, and the total cost was reduced by 1.89 million yuan. The research results show that the multi-objective optimization model proposed in this research has achieved a relatively satisfactory balance between power generation costs and environmental advantages.

A Multiobjective Particle Swarm Optimization Algorithm Based on Competition Mechanism and Gaussian Variation

In order to solve the shortcomings of particle swarm optimization (PSO) in solving multiobjective optimization problems, an improved multiobjective particle swarm optimization (IMOPSO) algorithm is proposed. In this study, the competitive strategy was introduced into the construction process of Pareto external archives to speed up the search process of nondominated solutions, thereby increasing the speed of the establishment of Pareto external archives. In addition, the descending order of crowding distance method is used to limit the size of external archives and dynamically adjust particle parameters; in order to solve the problem of insufficient population diversity in the later stage of algorithm iteration, time-varying Gaussian mutation strategy is used to mutate the particles in external archives to improve diversity. The simulation experiment results show that the improved algorithm has better convergence and stability than the other compared algorithms.