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This paper addresses the optimal control problems with an interval-valued objective function. We consider a type of total order relationships ≤ adm between two intervals. For each total order relationship, Kuhn–Tucker sufficient conditions for the optimal control problems with an interval-valued objective function are obtained. A numerical example is considered and solved. Kuhn–Tucker sufficient conditions provided under the total order relationship ≤ adm are sufficient conditions under the partial order relationship ⪯ LU for interval-valued optimal control problems. The results of this paper could help construct evolutionary algorithms to solve interval-valued optimal control problems. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of dynamic multi- objective optimization problems (DMOPs), by demonstrating new approaches to change detection and change prediction in an evolutionary algorithm framework. Because the objectives of such problems change over time, the Pareto optimal set (PS) and Pareto optimal front (PF) are also dynamic. First, we propose a new change detection method which achieves greater sensitivity by considering changes in both the PS and the PF, unlike most previous approaches. Second, when changes occur, a second-order (acceleration-based) prediction strategy is proposed to predictively reinitialize the population close to the new set of optima. We compare the performance of the proposed algorithm against two other state-of-the-art algorithms from the literature, using ten different dynamic benchmark problems. Experimental results show that the proposed change detection strategy in this paper can not only consider the effect of the optimal individuals but also can consider the effect of their corresponding objective values. Compared with the other two methods, the DMOPs achieved both the ability of precisely predicting the direction of changes and the ability of predicting the future trend of change direction. So, the DMOPs can also converge to the true PF in much less iterations compared with other methods. After multiple experiments, the proposed method outperforms the other algorithms on most of the test problems. [ABSTRACT FROM AUTHOR]

Generating uniform design tables (UDTs) is the first step to experimenting efficiently and effectively, and is also one of the most critical steps. Thus, the construction of uniform design tables has received much attention over the past decades. This paper presents a new algorithm for constructing uniform design tables: restart discrete dynamical evolutionary algorithm (RDDE). This algorithm is based on a well-designed dynamical evolutionary algorithm and utilizes discrete rounding technology to convert continuous variables into discrete variables. Considering the optimization of UDT is a multi-objective optimization problem, RDDE uses Friedman rank to select the optimal solution with better comprehensive comparison ranking. RDDE also utilizes a simulated annealing-based restart technology to select control parameters, thereby increasing the algorithm's ability to jump out of local optima. Comparisons with state-of-the-art UDTs and two practical engineering examples are presented to verify the uniformity of the design table constructed by RDDE. Numerical results indicate that RDDE can indeed construct UDTs with excellent uniformity at different levels, factors, and runs. Especially, RDDE can flexibly construct UDTs with unequal intervals of factors that cannot be directly processed by other designs of experiment. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is among the best evolutionary algorithms for global optimization. However, the basic DE has several shortcomings, like the slow convergence speed, and it is more likely to be stuck at local optima. Additionally, DE's performance is sensitive to its mutation strategies and control parameters for mutation and crossover. In this scope, we present in this paper three mechanisms to overcome DE limitations. First, two novel mutations called DE/mean-current/2 and DE/best-mean-current/2 are proposed and integrated in the DE algorithm, and they have both exploration ability and exploitation trend. On the other hand, to avoid being trapped in local minima of hard functions, a new exploration operator has been proposed called Weibull flight based on the Weibull distribution. Finally, new adapted control parameters based on the Weibull distribution are integrated. These parameters contribute to the optimization process by adjusting mutation scale and alleviating the parameter setting problem often encountered in various metaheuristics. The efficacy of the proposed algorithms called meanDE, MDEW, AMDE, and AMDEW is validated through intensive experimentations using classical tests, some challenging tests, the CEC2017, CEC2020, the most recent CEC2022, four constraint engineering problems, and the data clustering problem. Moreover, comparisons with several popular, recent, and high-performance optimization algorithms show a high effectiveness of the proposed algorithms in locating the optimal or near-optimal solutions with higher efficiency. The experiments clearly indicate the effectiveness of the new mutations compared to the standard DE mutations. Moreover, the proposed Weibull flight has a great capacity to deal with the hard composition functions of CEC benchmarks. Finally, the use of adapted control parameters for the mutation scale helps overcome the parameter setting problem commonly encountered in various metaheuristics. [ABSTRACT FROM AUTHOR]

Association rule mining (ARM) is a widely used technique in data mining for pattern discovery. However, association rule mining in numerical data poses a considerable challenge. In recent years, researchers have turned to optimization-based approaches as a potential solution. One particular area of interest in numerical association rules mining (NARM) is controlling the length of itemset intervals. In this paper, we propose a novel evolutionary algorithm based on the multi-objective firefly algorithm for efficiently mining numerical association rules (MOFNAR). MOFNAR utilizes Balance, square of cosine (SOC) and comprehensibility as objectives of evolutionary algorithm to assess rules and achieve a rule set that is both simple and accurate. We introduce the Balance measure to effectively control the intervals of numerical itemsets and eliminate misleading rules. Furthermore, we suggest a penalty approach, and the crowding-distance method is employed to maintain high diversity. Experimental results on five well-known datasets show the effectiveness of our method in discovering a simple rule set with high confidence that covers a significant percentage of the data. [ABSTRACT FROM AUTHOR]

Evaluating large-scale multi-objective problems is usually time-consuming due to the vast number of decision variables. However, most of the existing algorithms for large-scale multi-objective optimization require a significant number of problem evaluations to achieve satisfactory results, which makes the optimization process very inefficient. To address this issue, a fast interpolation-based multi-objective evolutionary algorithm is proposed in this paper for solving large-scale multi-objective optimization problems with high convergence speed and accuracy. In the proposed algorithm, decision variables are generated based on a small number of variables using an interpolation function. With this approach, only a small number of variables need to be optimized, so that the convergence speed can be greatly improved to make it possible to obtain satisfactory results with relatively low computation cost. The experimental results verified the superiority of our proposed algorithm over other state-of-the-art algorithms in terms of convergence speed and convergence accuracy on 108 test instances with up to 1000 decision variables. [ABSTRACT FROM AUTHOR]

Many researchers have shown interest in profile monitoring; however, most of the applications in this field of research are developed under the assumption of normal response variable. Little attention has been given to profile monitoring with non-normal response variables, known as general linear models which consists of two main categories (i.e., logistic and Poisson profiles). This paper aims to monitor Poisson profile monitoring problem in Phase II and develops a new robust control chart using support vector regression by incorporating some novel input features and evolutionary training algorithm. The new method is quicker in detecting out-of-control signals as compared to conventional statistical methods. Moreover, the performance of the proposed scheme is further investigated for Poisson profiles with both fixed and random explanatory variables as well as non-parametric profiles. The proposed monitoring scheme is revealed to be superior to its counterparts, including the likelihood ratio test (LRT), multivariate exponentially weighted moving average (MEWMA), LRT-EWMA and other machine learning-based schemes. The simulation results show superiority of the proposed method in profiles with fixed explanatory variables and non-parametric models in nearly all situations while it is not able to be the best in all the simulations when there are with random explanatory variables. A diagnostic method with machine learning approach is also used to identify the parameters of change in the profile. It is shown that the proposed profile diagnosis approach is able to reach acceptable results in comparison with other competitors. A real-life example in monitoring Poisson profiles is also provided to illustrate the implementation of the proposed charting scheme. [ABSTRACT FROM AUTHOR]

This paper addresses a problem of systemic risk minimization in which the optimization algorithm has to simultaneously minimize the number of companies affected by a wave of bankruptcies simulated on a graph as well as the level of reserves the companies keep to avoid going bankrupt. A MOEA/D-NN algorithm (where NN stands for a neural network) is proposed, which optimizes parameters of a machine learning model (a neural network) used in turn to determine the level of reserves the companies keep, based on several attributes describing each node in the graph. In the experiments, the proposed MOEA/D-NN algorithm was found to outperform comparison methods: evolutionary algorithms optimizing the level of reserves for all companies and a method based on the training of neural networks on a dataset previously collected by an evolutionary algorithm solving "training" instances of the optimization problem. The neural networks optimized by MOEA/D-NN were also tested on problem instances based on REDS graphs generated using varying values of R, E, and S parameters and were found to be applicable to these instances for certain ranges of parameters. The R parameter controlling the possibility of generating long-distance connections was found to have a bigger impact on the performance of the optimized neural networks than the other two parameters. [ABSTRACT FROM AUTHOR]

Particle swarm optimization (PSO) is a simple yet efficient population-based algorithm that handles various optimization problems. Nevertheless, diversity and convergence are two significant PSO limits, particularly when tackling challenging optimization issues. This paper develops a PSO with comprehensive learning and a modified dynamic multi-swarm strategy (CLDMSL-PSO) to solve these problems. In the beginning, each iteration of CLDMSL-PSO splits the total population into two subpopulations, one for exploration and the other for exploitation. The comprehensive learning (CL) strategy builds exemplars for the exploration subpopulation. The modified dynamic multi-swarm (DMS) strategy is equipped with the Quasi-Newton method to create the exploitation subpopulation. Second, a self-regulation nonlinear inertia weight, which considers the search level of different sub-swarms, is developed to accelerate the search speed in the early stage and strengthen the exploitation ability in the latter stage of the exploitation subpopulation. Third, the exploitation subpopulation uses a dynamic regrouping period parameter to regulate the frequency of information exchange among the sub-swarms. Finally, the Cauchy mutation is adopted to prevent falling into local optima during the search process. CLDMSL-PSO has been tested on extensive benchmark functions and a multifilament melt spinning process problem. Experimental results show that CLDMSL-PSO outperforms other state-of-art evolutionary algorithms on most optimization problems. [ABSTRACT FROM AUTHOR]

This paper introduces the Golf Sport Inspired Search (GSIS) algorithm as an evolutionary search method for numerical optimization. Each solution is generated with the aid of the step-length and search direction. The step-length is determined with the aid of the Tait's model of the trajectory of the golf ball, which is a physical model. The search direction is from the current position in the search space toward the position of a different individual or its reflected position. Such a direction determines the movement direction in the optimization process. A crossover operator is introduced to increase exploration at the starting and exploitation at the ending stages of the search. Performance of the GSIS is compared with many algorithms on 23 + 14 unconstrained classic functions, 29 functions of CEC 2017 benchmark suite and six constrained engineering design problems. Experiments indicate that with the aid of its cleverly designed operators, GSIS is able to produce promising results. Besides a cooperative game theoretic approach is introduced, which is able to measure the effectiveness of different operators in reducing the search cost. Such an approach can be used to measure the effectiveness of different operators that an evolutionary or swarm-intelligence algorithm owns. [ABSTRACT FROM AUTHOR]

Following the evolution of big data collection, storage, and manipulation techniques, deep learning has drawn the attention of numerous recent studies proposing solutions for smart cities. These solutions were focusing especially on energy consumption, pollution levels, public services, and traffic management issues. Predicting urban evolution and planning is another recent concern for smart cities. In this context, this paper introduces a hybrid model that incorporates evolutionary optimization algorithms, such as Teaching–learning-based optimization (TLBO), into the functioning process of neural deep learning models, such as recurrent neural network (RNN) networks. According to the achieved simulations, deep learning enhanced by evolutionary optimizers can be an effective and promising method for predicting urban evolution of future smart cities. [ABSTRACT FROM AUTHOR]