Dynamic Constrained Optimization Research Articles

Performance Analysis of TBR Tire Curing Process

Numerical algorithms and computer programs have been developed to determine optimal cure steps in a tire curing process. A dynamic constrained optimization problem was formulated with the following ingredients: (1) an objective function that measures product quality in terms of final state of cure and temperature history at selected points in a tire; (2) constraints that consist of a process model and temperature limits imposed on cure media; (3) B-spine representation of a time-varying profile of cure media temperature. The optimization problem was solved using the complex algorithm along with a finite element model solver. Numerical simulations were carried out to demonstrate the procedure of determining optimal cure steps for a truck/bus radial tire. © 1999 John Wiley & Sons, Inc. J Apple Polymer Sic 74: 2063–2071, 1999.

Dynamic constrained evolutionary optimization based on deep Q-network

Dynamic constrained optimization problems (DCOPs) are common and important optimization problems in real-world, which have great difficulty to solve. Dynamic constrained evolutionary algorithms (DCEAs) are widely used methods for solving DCOPs. However, existing DCEAs often struggle with convergence, particularly for DCOPs with drastic dynamic changes or intricate constraints. To address this issue, this paper proposes a novel DCEA called DCEA-DQN, which leverages the powerful perception and decision-making capabilities of Deep Q-Network (DQN). DCEA-DQN integrates two DQNs to enhance its performance. The first DQN is designed to adaptively respond to dynamic changes, enabling effective handling of DCOPs with various types and degrees of changes. It provides a high-quality re-initialized population for subsequent static optimization, resulting in faster and improved convergence. The second DQN is introduced to guide the mutation direction during offspring generation. It steers the population towards better feasible regions or directs it towards the optimal individual within the current feasible region. Moreover, a penalty mechanism is employed to handle constraints during offspring generation. To evaluate the performance of DCEA-DQN, comprehensive empirical studies are conducted using a new test suite called C-GMPB and a dynamic flexible job-shop scheduling problem. The experimental results, using two commonly used metrics EB and EO in the field of DCOPs, demonstrate that DCEA-DQN outperforms six state-of-the-art DCEAs and achieved optimal performance on 80% and 75% of all 24 test problems, respectively. The source code for DCEA-DQN is available at https://github.com/CIA-SZU/YRT.

Multi-Population Evolution based Dynamic Constrained Multiobjective Optimization under Diverse Changing Environments

Dynamic constrained multiobjective optimization involves irregular changes in the distribution of the true Pareto-optimal fronts, drastic changes in the feasible region caused by constraints, and the movement directions and magnitudes of the optimal distance variables due to diverse changing environments. To solve these problems, we propose a multi-population evolution based dynamic constrained multiobjective optimization algorithm. In this algorithm, we design a tribe classification operator to divide the population into different tribes according to a feasibility check and the objective values, which is beneficial for driving the population toward the feasible region and Pareto-optimal fronts. Meanwhile, a population selection strategy is proposed to identify promising solutions from tribes and exploit them to update the population. The optimal values of the distance variables vary differently with dynamic environments, thus, we design a dynamic response strategy for solutions in different tribes that estimates their distances to approach the Pareto-optimal fronts and regenerates a promising population when detecting environmental changes. In addition, a scalable generator is designed to simulate diverse movement directions and magnitudes of the optimal distance variables in real-world problems under dynamic environments, obtaining a set of improved test problems. Experimental results show the effectiveness of test problems, and the proposed algorithm is impressively competitive with several chosen state-of-the-art competitors.

Evolutionary Dynamic Constrained Multiobjective Optimization: Test Suite and Algorithm

Evolutionary Dynamic Constrained Multiobjective Optimization: Test Suite and Algorithm

Experiment Analysis of TBR Tire Curing Process

The optimization problem was solved using the complex algorithm along with a finit element model solver. Numerical simulations were carried out to demonstrate the procedure of determining optimal cure steps for a truck/bursa dial tire. © 1999 John Wiley & Sons, Inc. J App Poly m Sci 74: 2063–2071, 1999 dynamic constrained optimization problem was formulated with the following ingredients: (1) an objective function that measures product quality in terms of Final state of cure and temperature history a at selected points in a tire; (2) constraints that consist of a process model and temperature limits imposed on cure media; (3) B-splines representation of a time-varying Profile of cure Media temperature

A dynamic constrained multiobjective evolutionary algorithm based on decision variable classification

In dynamic constrained multiobjective optimization problems (DCMOPs), dynamics may arise from time-varying objective functions or/and constraints. To solve these problems, maintaining a good balance among feasibility, convergence and diversity of a population under dynamic environments is a critical challenge. Although appropriately utilizing the characteristic of decision variables can promote algorithms to better track the Pareto optima under dynamic environments, their sensitivity to constraints is neglected. Therefore, a dynamic constrained multiobjective evolutionary algorithm based on decision variable classification (DC-MOEA-DVC) is proposed. Under each environment, decision variables are classified into four types in terms of their influence on convergence, distribution, and constraint violation. Based on them, a new offspring generation method is developed, decision variables with different characteristics are rationally combined to generate offspring, with the purpose of accelerating the convergence of the population. Once an environmental change appears, a hybrid strategy consisting of four change response techniques is introduced for the corresponding types of decision variables, producing a new initial population. The experimental results show that DC-MOEA-DVC is superior to the other five state-of-the-art algorithms.

Penalty and prediction methods for dynamic constrained multi-objective optimization

Penalty and prediction methods for dynamic constrained multi-objective optimization

Modified Differential Evolution Algorithm for Solving Dynamic Optimization with Existence of Infeasible Environments

Dynamic constrained optimization is a challenging research topic in which the objective function and/or constraints change over time. In such problems, it is commonly assumed that all problem instances are feasible. In reality some instances can be infeasible due to various practical issues, such as a sudden change in resource requirements or a big change in the availability of resources. Decision-makers have to determine whether a particular instance is feasible or not, as infeasible instances cannot be solved as there are no solutions to implement. In this case, locating the nearest feasible solution would be valuable information for the decision-makers. In this paper, a differential evolution algorithm is proposed for solving dynamic constrained problems that learns from past environments and transfers important knowledge from them to use in solving the current instance and includes a mechanism for suggesting a good feasible solution when an instance is infeasible. To judge the performance of the proposed algorithm, 13 well-known dynamic test problems were solved. The results indicate that the proposed algorithm outperforms existing recent algorithms with a margin of 79.40% over all the environments and it can also find a good, but infeasible solution, when an instance is infeasible.

EvoDCMMO: Benchmarking and solving dynamic constrained multimodal optimization problems

In the field of evolutionary computation, many dynamic optimization problems whose fitness values and/or constraints are changed over time have been studied. As the research progresses, complex dynamic optimization problems draw the attention of researchers, such as the dynamic constrained optimization problems with constraints and the dynamic multimodal optimization problems with multiple optima in each environment. Dynamic, constrained, and multimodal properties frequently appear in real-world applications, but the dynamic constrained multimodal optimization problems (DCMMOPs) that simultaneously possess all these properties have not been studied yet. This paper is the extended version of our conference work, aiming to investigate the effect of different techniques for solving DCMMOP. Compared with the previous work, we proposed a more challenging benchmark suite and designed a framework called EvoDCMMO to make further research on DCMMOPs. The new challenge of the proposed benchmark problems arises from the additional constraint based on the fitness values. More techniques, including the optimizers, niching methods, constraint handling techniques and dynamic response strategies are implemented in EvoDCMMO to carry out the comparative studies for solving DCMMOPs and discussed in our work.

Evolutionary approach for dynamic constrained optimization problems

The number of research works on dynamic constrained optimization problems has been increasing rapidly over the past two decades. In this domain, many real-life decision problems need to be solved repeatedly with changing data and parameters. However, no research on dynamic problems with changes in the coefficients of the constraint functions has been reported. In this paper, to deal with such problems, a new evolutionary framework with multiple novel mechanisms is proposed. The new mechanisms are for (1) dealing with both linear and non-linear components in the constraint functions, (2) identifying the rate of change in the coefficients of the variables and (3) updating the population efficiently after every change occurs in the problem. To evaluate the performance of the proposed algorithm, we designed a new set of 13 dynamic benchmark problems, each of which consists of 20 dynamic changes and 3 different scenarios. The results demonstrate that the proposed algorithm significantly contributes in achieving good quality solutions, high feasibility rates and fast convergence in rapidly changing environments. In addition, the framework shows its capability of using different meta-heuristics to solve dynamic problems.

A search algorithm for constrained engineering optimization and tuning the gains of controllers

In this work, the application of an optimization algorithm is investigated to optimize static and dynamic engineering problems. The methodology of the approach is to generate random solutions and find a zone for the initial answer and keep reducing the zones. The generated solution in each loop is independent of the previous answer that creates a powerful method. Simplicity as its main advantage and the interlaced use of intensification and diversification mechanisms--to refine the solution and avoid local minima/maxima--enable the users to apply that for a variety of problems. The proposed approach has been validated by several previously solved examples in structural optimization and scored good results. The method is also employed for dynamic problems in vibration and control. A modification has also been done on the method for high-dimensional test functions (functions with very large search domains) to converge fast to the global minimum or maximum; simulated for several well-known benchmarks successfully. For validation, a number of 9 static and 4 dynamic constrained optimization benchmark applications and 32 benchmark test functions are solved and provided, 45 in total. All the codes of this work are available as supplementary material in the online version of the paper on the journal website.

Dynamic Optimization in Fast-Changing Environments via Offline Evolutionary Search

Dynamic optimization, for which the objective functions change over time, has attracted intensive investigations due to the inherent uncertainty associated with many real-world problems. For its robustness with respect to noise, Evolutionary Algorithms (EAs) have been expected to have great potential for dynamic optimization. Many dynamic optimization methods such as diversity-driven methods, memory methods, and prediction methods have been proposed based on EAs to deal with environmental changes. However, they face difficulties in adapting to fast changes in dynamic optimization as EAs normally need quite a few fitness evaluations to find a near-optimum solution. To address this issue, this paper proposes a new framework of applying EAs in the context of dynamic optimization to deal with fast changing environments. We suggest that, instead of online evolving (searching) solutions for the ever-changing objective function, EAs are more suitable for acquiring an archive of solutions in an offline way, which could be adopted to construct a system to provide high-quality solutions efficiently in a dynamic environment. To be specific, we formulate the offline search as a static set-oriented optimization problem. Then, a set of solutions is obtained by an EA for this set-oriented optimization problem. After this, the obtained solution set is adopted to do fast adaptation to the corresponding dynamic optimization problem. The general framework is instantiated for continuous dynamic constrained optimization problems, and the empirical results show the potential of the proposed framework. The superiority of the framework is also verified on a dynamic vehicle routing problem with changing demands.

Dynamic Constrained Multi-Objective Optimization with Combination Response Mechanism

Dynamic Constrained Multi-Objective Optimization with Combination Response Mechanism

Elliptical Slot Microstrip Patch Antenna Design Based on a Dynamic Constrained Multiobjective Optimization Evolutionary Algorithm

Most evolutionary optimization algorithms have already been used for antenna design and shown promising results on improving the performance of the antenna. However, for many real-world antenna optimization problems, they are difficult to solve in that there are highly constrained and multimodal difficulty. These difficulties impede the development of antenna design. In this paper, an elliptical slot microstrip patch antenna design with these difficulties is modeled as a constrained optimization problem (COP). To address the problem, a Dynamic Constrained Multiobjective Optimization Evolutionary Algorithm(DCMOEA) is used. The experimental results show that the optimum antenna with satisfying the design requirement is obtained, and as well as we find the radiation patch should be a whole ellipse instead of subtracting with two ellipses.

Elliptical Slot Microstrip Patch Antenna Design Based on a Dynamic Constrained Multiobjective Optimization Evolutionary Algorithm

Most evolutionary optimization algorithms have already been used for antenna design and shown promising results on improving the performance of the antenna. However, for many real-world antenna optimization problems, they are difficult to solve in that there are highly constrained and multimodal difficulty. These difficulties impede the development of antenna design. In this paper, an elliptical slot microstrip patch antenna design with these difficulties is modeled as a constrained optimization problem (COP). To address the problem, a Dynamic Constrained Multiobjective Optimization Evolutionary Algorithm(DCMOEA) is used. The experimental results show that the optimum antenna with satisfying the design requirement is obtained, and as well as we find the radiation patch should be a whole ellipse instead of subtracting with two ellipses.

Self-organizing migrating algorithm using covariance matrix adaptation evolution strategy for dynamic constrained optimization

The dynamic constrained optimization problems can be a challenge for the optimization algorithms. They must tackle global optimum detection, as well as the change of the environment. Recently, a novel test suite for dynamic constrained optimization was introduced. Furthermore, three well-performed evolutionary algorithms were compared based on it. The experimental results show that each algorithm performed best for a different type of optimization problem. The objective of our work was to develop an algorithm reflecting requirements arising from the novel test suite and regarding the results provided by the tested algorithms. In this work, we present a novel evolutionary algorithm for dynamic constrained optimization. The algorithm hybridizes the self-organizing migrating algorithm and the covariance matrix adaptation evolution strategy with constraints handling approach. To avoid premature convergence, the best solutions representing feasible regions do not affect the rest of the population. Two clustering methods, exclusion radius, and quantum particles are used to preserve population diversity. The performance is evaluated on the recently published test suite and compared to the three state-of-the-art algorithms. The presented algorithm outperformed these algorithms in most test cases, which indicates the efficiency of the utilized mechanisms.

Transient analysis of systems exhibiting inverse response and their control with CSTR as a case study

<span>In this paper the phenomenon of inverse response from systems was investigated and its transient response thoroughly analyzed. Inverse response is shown by non-minimum phase systems and some minimum phase systems. Transient analysis of these systems is lacking in literature A case study was done for a non-linear, non-minimum phase CSTR (Continuous Stirred Tank Reactor), which was identified and a novel optimized trajectory for temperature feed was synthesized, which is a non-linear dynamic constrained optimization problem solved using ACADO for a particular chemical reaction. Different control schemes were also implemented on other systems as well, which exibhit inverse responses, including model reference adaptive control. The finding shows that PID-ZN goes with the inverse response, is unable to suppress it and requires large control effort which can have serious hardware limitations. Robustness is another area where PID is lacking with these systems. MRAC shemes were able to overcome all these issues. For CSTR also, these findings hold true thus points at using advance stratigies in process control industries for maximzing product yield.</span>

Sensitivity-Based Change Detection for Dynamic Constrained Optimization

In dynamic constrained optimization, changes may occur in either the objective function or constraint functions, or both. However, although research on dynamic optimization has been growing significantly, it is centered mainly around unconstrained problems. On the other hand, research on dynamic constrained problems has considered simple extensions of those conducted on unconstrained ones. These approaches are usually computationally expensive and exhibit slow convergence in changed environments. To develop an effective algorithm for dynamic constrained problems with changes occurring in only the constraint's space, in this research, we propose a sensitive constraint detection mechanism that provides valuable information for determining the movements of solutions in changing environments. As, by incorporating it with a search process, the convergence of an algorithm can be accelerated, it is adopted with a multi-operator evolutionary type of algorithm which is then tested on a set of constrained dynamic problems. The experimental results clearly demonstrate the benefits of this proposed approach.

A Novel Evolutionary Algorithm for Dynamic Constrained Multiobjective Optimization Problems

To promote research on dynamic constrained multiobjective optimization, we first propose a group of generic test problems with challenging characteristics, including different modes of the true Pareto front (e.g., convexity–concavity and connectedness–disconnectedness) and the changing feasible region. Subsequently, motivated by the challenges presented by dynamism and constraints, we design a dynamic constrained multiobjective optimization algorithm with a nondominated solution selection operator, a mating selection strategy, a population selection operator, a change detection method, and a change response strategy. The designed nondominated solution selection operator can obtain a nondominated population with diversity when the environment changes. The mating selection strategy and population selection operator can adaptively handle infeasible solutions. If a change is detected, the proposed change response strategy reuses some portion of the old solutions in combination with randomly generated solutions to reinitialize the population, and a steady-state update method is designed to improve the retained previous solutions. The experimental results show that the proposed test problems can be used to clearly distinguish the performance of algorithms, and that the proposed algorithm is very competitive for solving dynamic constrained multiobjective optimization problems in comparison with state-of-the-art algorithms.

Evolutionary dynamic constrained optimization: Test suite construction and algorithm comparisons

Many real-world applications can be modelled as dynamic constrained optimization problems (DCOPs). Due to the fact that objective function and/or constraints change over time, solving DCOPs is a challenging task. Although solving DCOPs by evolutionary algorithms has attracted increasing interest in the community of evolutionary computation, the design of benchmark test functions of DCOPs is still insufficient. Therefore, we propose a test suite for DCOPs. A dynamic unconstrained optimization benchmark with good time-varying characteristics, called moving peaks benchmark, is chosen to be the objective function of our test suite. In addition, we design adjustable dynamic constraints, by which the size, number, and change severity of the feasible regions can be flexibly controlled. Furthermore, the performance of three dynamic constrained optimization evolutionary algorithms is tested on the proposed test suite, one of which is presented in this paper, named dynamic constrained optimization differential evolution (DyCODE). DyCODE includes three main phases: 1) the first phase intends to enter the feasible region from different directions promptly via a multi-population search strategy; 2) in the second phase, some excellent individuals chosen from the first phase form a new population to search for the optimal solution of the current environment; and 3) the third phase combines the memory individuals of the first two phases with some randomly generated individuals to re-initialize the population for the next environment. From the experiments, one can understand the strengths and weaknesses of the three compared algorithms for solving DCOPs in depth. Moreover, we also give some suggestions for researchers to apply these three algorithms on different occasions.