Search

A new scheme to solve the issue of premature convergence of differential evolution.New test functions to evaluate constrained min-max optimization algorithms (CMMOA).An improved CMMOA to achieve a quite satisfied success rate. In system design, the best system designed under a simple experimental environment may not be suitable for application in real world if dramatic changes caused by uncertainties contained in the real world are considered. To deal with the problem caused by uncertainties, designers should try their best to get the most robust solution. The most robust solution can be obtained by constrained min-max optimization algorithms. In this paper, the scheme of generating escape vectors has been proposed to solve the problem of premature convergence of differential evolution. After applying the proposed scheme to the constrained min-max optimization algorithm, the performance of the algorithm could be greatly improved. To evaluate the performance of constrained min-max optimization algorithms, more complex test problems have also been proposed in this paper. Experimental results show that the improved constrained min-max optimization algorithm is able to achieve a quite satisfied success rate on all considered test problems under limited accuracy.

This paper improves the performance of adaptive neuro-fuzzy inference system (ANFIS) using extreme learning machines (ELM) concept and particle swarm optimization (PSO). The proposed learning machine, particle swarm optimization (PSO) based regularized extreme learning adaptive neuro-fuzzy inference system (PSO-RELANFIS), has the advantages of reduced randomness, reduced computational complexity and better generalization. The fuzzy membership function parameters of the proposed system are randomly selected with in constraint ranges. A regularized loss function is developed using constrained optimization and the optimized regularization parameter is obtained using PSO technique. Performance analysis on regression and classification problems shows that proposed algorithm achieves similar or better generalization performance compared to well-known kernel based methods and ELM based neuro-fuzzy systems.

Achieving robustness with a limited distortion level is a challenging design problem for watermarking systems in multimedia applications with a guaranteed quality requirement. In this paper, we provide an intelligent system for watermarking through incorporating a meta-heuristic technique along with an embedding method to achieve an optimized performance. The optimization objective is to provide the maximum possible robustness without exceeding a predetermined distortion limit. Hence, the quality level of the watermarking method could be guaranteed through that constraint optimization. A new fitness function is defined to provide the required convergence toward the optimum solution for the defined optimization problem. The fitness function is based on dividing its applied solution population into two groups, where each group is ranked according to a different objective. Thus, the multi-objectives in the problem are decoupled and solved through two single-objective sub-problems. Unlike existing watermarking optimization techniques, the proposed work does not require weighting factors. To illustrate the effectiveness of the proposed approach, we employ a recent watermarking technique, and then use it as the embedding method to be optimized. The Artificial Bee Colony is selected as the meta-heuristic optimization method in which the proposed fitness function is used. Experimental results show that the imposed quality constraint is satisfied, and that the proposed method provides enhanced robustness under different attacks for various quality thresholds. The presented approach offers a robust solution that can be applied to numerous multimedia applications such as film industry, intelligent surveillance and security systems.

Bio-inspired computing is an emerging paradigm which is based on the basics and inspiration of natural phenomena to design new and robust competing techniques. Various nature science areas have motivated the inspiration for the design of new intelligent systems. Chemical engineering is one of them. In Chemistry, the vapor-liquid equilibrium process describes the distribution of chemical species combining two essential phases: vapor phase and liquid phase. Using a binary system of compounds is possible to simulate a search process based on the equilibrium between both phases. In this paper, we propose a new algorithm inspired by this chemical phenomenon for solving a new patient bed assignment problem. This problem consists of assigning patients to beds by considering relevant medical requirements trying to maximize the most covered soft constraints. For that, we take a traditional model, and we transform it by using the constraint optimization paradigm. We test our algorithm on 30 benchmarks taken of Chilean health services. To verify results, we perform statistical comparatives with artificial bee algorithm, ant colony optimization, the bat method, cuckoo search, genetic algorithm, particle swarm optimization, and a random strategy. Computational experiments illustrate that the VLE algorithm properly solved 30 instances, finding all global optimal. In nineteen instances, VLE converged towards the best solution in its median value. In ten instances, the median, the average and the best value, all of them achieved the global optimal. Now, when comparing VLE against other techniques, we can note that VLE is surpassed by the artificial bee colony in two instances only. The rest of the results show VLE as a robust algorithm able to suppress classical, such as genetic algorithm and particle swarm optimization.

New surrogate-assisted ES for constrained multi-objective optimization is developed.Surrogates are used to identify the most promising among many trial offspring.A radial basis function (RBF) model is used to implement the method.Method is tested on benchmark problems and manufacturing and robotics applications.Proposed method generally outperforms an ES and NSGA-II on the problems used. In many real-world optimization problems, several conflicting objectives must be achieved and optimized simultaneously and the solutions are often required to satisfy certain restrictions or constraints. Moreover, in some applications, the numerical values of the objectives and constraints are obtained from computationally expensive simulations. Many multi-objective optimization algorithms for continuous optimization have been proposed in the literature and some have been incorporated or used in conjunction with expert and intelligent systems. However, relatively few of these multi-objective algorithms handle constraints, and even fewer, use surrogates to approximate the objective or constraint functions when these functions are computationally expensive. This paper proposes a surrogate-assisted evolution strategy (ES) that can be used for constrained multi-objective optimization of expensive black-box objective functions subject to expensive black-box inequality constraints. Such an algorithm can be incorporated into an intelligent system that finds approximate Pareto optimal solutions to simulation-based constrained multi-objective optimization problems in various applications including engineering design optimization, production management and manufacturing. The main idea in the proposed algorithm is to generate a large number of trial offspring in each generation and use the surrogates to predict the objective and constraint function values of these trial offspring. Then the algorithm performs an approximate non-dominated sort of the trial offspring based on the predicted objective and constraint function values, and then it selects the most promising offspring (those with the smallest predicted ranks from the non-dominated sort) to become the actual offspring for the current generation that will be evaluated using the expensive objective and constraint functions. The proposed method is implemented using cubic radial basis function (RBF) surrogate models to assist the ES. The resulting RBF-assisted ES is compared with the original ES and to NSGA-II on 20 test problems involving 2-15 decision variables, 2-5 objectives and up to 13 inequality constraints. These problems include well-known benchmark problems and application problems in manufacturing and robotics. The numerical results showed that the RBF-assisted ES generally outperformed the original ES and NSGA-II on the problems used when the computational budget is relatively limited. These results suggest that the proposed surrogate-assisted ES is promising for computationally expensive constrained multi-objective optimization.

Most of the real-life project scheduling cases may involve different types of uncertainties simultaneously such as randomness, fuzziness and dynamism. Based on this motivation, the present paper proposes a novel interval programming and chance constrained optimization based hybrid solution approach for a fully uncertain, multi-objective and multi-mode resource investment project scheduling problem (MRIPSP). The classical discrete-time binary integer programming formulation of the problem is extended by incorporating both the interval-valued and interval-stochastic project parameters as well as variables. In addition to the uncertain project parameters/inputs, the completion times of the activities which represent the project schedule and the availabilities of the renewable project resources are also stated as uncertain project variables and represented by interval numbers. Then, the proposed interval-stochastic multi-mode resource investment project scheduling (IS-MRIPSP) model is converted into its crisp equivalent form by using the proposed approach. The proposed approach is also able to consider different types of project scheduling risks and produces more reliable and risk-free solutions according to the project manager's attitude toward risks. Furthermore, in addition to the classical makespan objective, effective and efficient utilization of the renewable project resources, i.e., human resources, is also targeted. The efficiency and reliability factors of the human resources are also taken into consideration. In order to generate balanced project schedules which tradeoffbetween the project time and total human resource costs, compromise programming approach is adapted. Finally, in order to test the validity and practicality of the proposed approach, a real-life application is presented for an enterprise resource planning (ERP) implementation project scheduling problem of an international industrial software company. (C) 2020 Elsevier Ltd. All rights reserved.

The original particle swarm optimization (PSO) is not able to tackle constrained optimization problems (COPs) due to the absence of constraint handling techniques. Furthermore, most existing PSO variants can only perform well in certain types of optimization problem and tend to suffer with premature convergence due to the limited search operator and directional information used to guide the search process. An improved PSO variant known as the constrained multi-swarm particle swarm optimization without velocity (CMPSOWV) is proposed in this paper to overcome the aforementioned drawbacks. Particularly, a constraint handling technique is first incorporated into CMPSOWV to guide population searching towards the feasible regions of search space before optimizing the objective function within the feasible regions. Two evolution phases known as the current swarm evolution and memory swarm evolution are also introduced to offer the multiple search operators for each CMPSOWV particle, aiming to improve the robustness of algorithm in solving different types of COPs. Finally, two diversity maintenance schemes of multi-swarm technique and probabilistic mutation operator are incorporated to prevent the premature convergence of CMPSOWV. The overall optimization performances of CMPSOWV in solving the CEC 2006 and CEC 2017 benchmark functions and real-world engineering design problems are compared with selected constrained optimization algorithms. Extensive simulation results report that the proposed CMPSOWV has demonstrated the best search accuracy among all compared methods in solving majority of problems.

We rebuilt the model of constrained optimization problems, called reversed model.We developed a comparison strategy based on origin and new model.Difference between usual algorithm and proposed one is discussed.Experimental results show the effectiveness of the proposed algorithm. Solving constrained optimization problems (COPs) has been gathering attention from many researchers. In this paper, we defined the best fitness value among feasible solutions in current population as gbest. Then, we converted the original COPs to multi-objective optimization problems (MOPs) with one constraint. The constraint set the function value f(x) should be less than or equal to gbest; the objectives are the constraints in COPs. A reverse comparison strategy based on multi-objective dominance concept is proposed. Compared with usual strategies, the innovation strategy cuts off the worse solutions with smaller fitness value regardless of its constraints violation. Differential evolution (DE) algorithm is used as a solver to search for the global optimum. The method is called multi-objective optimization based reverse strategy with differential evolution algorithm (MRS-DE). The experimental results demonstrate that MRS-DE can achieve better performance on 22 classical benchmark functions compared with several state-of-the-art algorithms.

A constraint-activated differential evolution is proposed to solve constrained min-max optimization problems.Min-max optimization theorems are proposed to provide theoretical understanding for the proposed algorithm.The proposed method with an exploitation strategy attains 100% success rates for five test problems. A constraint-activated differential evolution is proposed to solve constrained min-max optimization problems in this paper. To provide theoretical understanding for these problems, their global optima are specified in the proposed definitions. Based on the definition, we propose theorems to prove that a min-max algorithm can be used to solve a max-min problem without any algorithmic changes. Based on the theorems, we propose a constraint-activated differential evolution to solve constrained min-max problems. The proposed method consists of three components, propagation, constraint activation, and inner level evolution. The propagation provides exploitation power of evolution. The constraint activation directly finds a solution which can best activate constraints. The inner level evolution provides continuous evolutionary behavior to prevent convergence premature. The simulation results show that the proposed method attains 100% success rates for all of the numerical benchmarks with an exploitative mutation strategy.

In the last decades, a number of novel meta-heuristics and hybrid algorithms have been proposed to solve a great variety of optimization problems. Among these, constrained optimization problems are considered of particular interest in applications from many different domains. The presence of multiple constraints can make optimization problems particularly hard to solve, thus imposing the use of specific techniques to handle fitness landscapes which generally show complex properties. In this paper, we introduce a modified Covariance Matrix Adaptation Evolution Strategy (CMA-ES) specifically designed for solving constrained optimization problems. The proposed method makes use of the restart mechanism typical of most modern variants of CMA-ES, and handles constraints by means of an adaptive penalty function. This novel CMA-ES scheme presents competitive results on a broad set of benchmark functions and engineering problems, outperforming most state-of-the-art algorithms as for both efficiency and constraint handling.

During the past decade, solving constrained optimization problems with swarm algorithms has received considerable attention among researchers and practitioners. In this paper, a novel swarm algorithm called the Social Spider Optimization (SSO-C) is proposed for solving constrained optimization tasks. The SSO-C algorithm is based on the simulation of cooperative behavior of social-spiders. In the proposed algorithm, individuals emulate a group of spiders which interact to each other based on the biological laws of the cooperative colony. The algorithm considers two different search agents (spiders): males and females. Depending on gender, each individual is conducted by a set of different evolutionary operators which mimic different cooperative behaviors that are typically found in the colony. For constraint handling, the proposed algorithm incorporates the combination of two different paradigms in order to direct the search towards feasible regions of the search space. In particular, it has been added: (1) a penalty function which introduces a tendency term into the original objective function to penalize constraint violations in order to solve a constrained problem as an unconstrained one; (2) a feasibility criterion to bias the generation of new individuals toward feasible regions increasing also their probability of getting better solutions. In order to illustrate the proficiency and robustness of the proposed approach, it is compared to other well-known evolutionary methods. Simulation and comparisons based on several well-studied benchmarks functions and real-world engineering problems demonstrate the effectiveness, efficiency and stability of the proposed method.

Many problems in scientific research and engineering applications can be decomposed into the constrained optimization problems. Most of them are the nonlinear programming problems which are very hard to be solved by the traditional methods. In this paper, an electromagnetism-like mechanism (EM) algorithm, which is a meta-heuristic algorithm, has been improved for these problems. Firstly, some modifications are made for improving the performance of EM algorithm. The process of calculating the total force is simplified and an improved total force formula is adopted to accelerate the searching for optimal solution. In order to improve the accuracy of EM algorithm, a parameter called as move probability is introduced into the move formula where an elitist strategy is also adopted. And then, to handle the constraints, the feasibility and dominance rules are introduced and the corresponding charge formula is used for biasing feasible solutions over infeasible ones. Finally, 13 classical functions, three engineering design problems and 22 benchmark functions in CEC’06 are tested to illustrate the performance of proposed algorithm. Numerical results show that, compared with other versions of EM algorithm and other state-of-art algorithms, the improved EM algorithm has the advantage of higher accuracy and efficiency for constrained optimization problems.

The purpose of this paper is to develop design scheme based on an easy-to-use meta-heuristic approach with superior reliability and validity for fixed-structure robust controllers, satisfying both multiple control specifications and system stability conditions. For this purpose, a particle swarm optimizer is first developed, which reduces the probability of premature convergence to local optima in the PSO (particle swarm optimization) by exploiting the particle's local social learning based on the idea of cyclic-network topology. Next, it is shown how to obtain a fixed-structure robust controller with constraints on multiple H"~ specifications and system stability based on the developed PSO technique incorporated with a simple constraint handling method. Finally, typical numerical examples are studied to show the applicability of the proposed methodology to the synthesis of fixed-structure robust controllers. These examples clearly verify that the developed design scheme gives a novel and powerful impetus with remarkable reliability to fixed-structure robust controller syntheses.

Several constrained and unconstrained optimization problems have been adequately solved over the years thanks to advances in the metaheuristics area. In the last decades, different metaheuristics have been proposed employing new ideas, and hybrid algorithms that improve the original metaheuristics have been developed. One of the most successfully employed metaheuristics is the Differential Evolution. In this paper it is proposed a Multi-View Differential Evolution algorithm (MVDE) in which several mutation strategies are applied to the current population to generate different views at each iteration. The views are then merged according to the winner-takes-all paradigm, resulting in automatic exploration/exploitation balance. MVDE was tested to solve a set of well-known constrained engineering design problems and the obtained results were compared to those from many state-of-the-art metaheuristics. Results show that MVDE was very competitive in the considered problems, largely outperforming several of the compared algorithms.

The generation of priority vectors from pairwise comparison matrices is an essential part of the Analytic Hierarchy Process. Perhaps the most popular approach for deriving the priority weights is the right eigenvalue method (REV) which was proposed by Saaty. Despite its popularity some shortcomings of the REV have been reported in literature. Among the alternative approaches one can find the statistical estimation techniques, methods founded on constrained optimization models and models based on fuzzy description of decision maker preferences. In this paper new optimization techniques for deriving priority weights are introduced. In the proposed approach, the constrained optimization models are based on the same idea which underlies the REV. The properties of the resulting prioritization techniques are studied via computer simulations. This study demonstrates that the new methods perform very well in comparison with other popular techniques known from literature. What is especially important, the new approach provides the decision maker with a meaningful index that can be used to measure consistency of his/her judgments. The new index is closely related to the well-known Saaty's consistency index CI, but in difference to the latter, it can be applied to both reciprocal as well as nonreciprocal comparison matrices. Hence the new index can be considered as a natural extension of the CI to all types of matrices. Some additional advantages resulting from the new approach are discussed and illustrated by numerical examples.

Over the years, several metaheuristics have been developed to solve hard constrained and unconstrained optimization problems. In general, a metaheuristic is proposed and following researches are made to improve the original algorithm. In this paper, we evaluate a not so new metaheuristic called differential evolution (DE) to solve constrained engineering design problems and compare the results with some recent metaheuristics. Results show that the classical DE with a very simple penalty function to handle constraints is still very competitive in the tested problems.

A directed searching optimization algorithm (DSO) is proposed to solve constrained optimization problems in this paper. The proposed algorithm includes two important operations - position updating and genetic mutation. Position updating enables the non-best solution vectors to mimic the best one, which is beneficial to the convergence of the DSO; genetic mutation can increase the diversity of individuals, which is beneficial to preventing the premature convergence of the DSO. In addition, we adopt the penalty function method to balance objective and constraint violations. We can obtain satisfactory solutions for constrained optimization problems by combining the DSO and the penalty function method. Experimental results indicate that the proposed algorithm can be an efficient alternative on solving constrained optimization problems Refereed/Peer-reviewed

Constrained optimization problems are very important in that they frequently appear in the real world. A constrained optimization problem consists of the optimization of a function subject to constraints, in which both the function and constraints may be nonlinear. Constraint handling is one of the major concerns when solving constrained optimization problems by hybrid Nelder-Mead simplex search method and particle swarm optimization, denoted as NM-PSO. This paper proposes embedding constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, in NM-PSO as a special operator to deal with satisfying constraints. Experiments using three benchmark function and three engineering design problems are presented and compared with the best known solutions reported in the literature. The comparison results with other evolutionary optimization methods demonstrate that NM-PSO with the embedded constraint operator proves to be extremely effective and efficient at locating optimal solutions.

WOS: 000259432600018, Soft computing is the state-of-the-art approach to artificial intelligence and it has showed an excellent performance in solving the combined optimization problems. In this paper, issues related to the implementation of the soft computing techniques are highlighted for a successful application to solve economic dispatch (ED) problem, which is a constrained optimization problem in power systems. First of all, a survey covering the basics of the techniques is presented and then implementation of the techniques in the ED problem is discussed. The soft computing techniques, namely tabu search (TS), genetic algorithm (GA), Hopfield neural network (HNN) and multi-layered perceptron (MLP) are applied to solve the ED problem. The techniques are tested on power systems consisting of 6 and 20 generating units and the results are compared to highlight the performance of the soft computing techniques. Future directions and open-ended problems in implementation of soft computing techniques for constrained optimization problems in power system are indicated. Suggestions are presented to improve soft computing techniques. (C) 2007 Elsevier Ltd. All rights reserved.