A hybrid integral RNN framework for dynamic and noisy nonlinear optimization problems

Dynamic nonlinear constrained optimization problems(DNCOP) is a class of complex dynamic optimization problems, the difficult to solve the DNCOP is how to do with the constraint and its time(environment) variance. In this paper, a new multi-objective evolutionary algorithm for solving a class of nonlinear constrained optimization problem which the time (environment) variance is defined in discrete space is given. First, a new dynamic entropy function based on the constraint conditions of dynamic nonlinear constrained optimization problem is given. Then using the new entropy function, the original dynamic nonlinear constrained optimization problem is transformed into a bi-objective dynamic optimization problem. Furthermore, a new crossover operator and a mutation operator with local search were designed. Based on these, a new multi objective evolutionary algorithm is proposed. The computer simulations are made on two dynamic nonlinear constrained optimization problems, and the results indicate the proposed algorithm is effective.

Operational indices optimization of beneficiation process is a dynamic optimization problem in nature. It is difficult to solve because the related dynamic models of operational indices cannot be achieved easily. Focusing on the operational indices optimization under uncertain environments in production process, this paper first formulates a constrained dynamic multi-objective optimization problem based on the collected data, which considers the changing factors in production and the constraints of operational and production indices, and takes the production indices as optimization objectives and the operational indices as decision variables. To solve the established constrained dynamic multi-objective problem, a prediction with modification mechanism based dynamic multi-objective evolutionary optimization algorithm is proposed. The algorithm first divides the population into several sub-populations and then predicts each sub-population center of new environment independently. New population is generated by Gaussian and uniform distribution based on the estimated centers to improve the convergence speed. At the same time, to ensure the population diversity, a modification strategy is adopted to detect which reference point has no individual associated and produces some individuals around it. The proposed algorithm is applied to solve the dynamic operational indices optimization problem and compared with a constrained and a modified unconstrained dynamic multi-objective optimization algorithm. The statistical results demonstrate the efficiency and effectiveness of the proposed algorithm to solve the real-world dynamic operational indices optimization problem.

There are many dynamic optimization problems in real-world applications. Although many variants of evolutionary algorithms and swarm intelligence have been proposed to solve such problems, little work has been conducted to address the dynamic constrained multimodal optimization problems (DCMMOPs). In DCMMOPs, there exist multiple optimal solutions corresponding to each environment that the algorithm is required to find. Sometimes, it is also necessary to identify the accepted local optima. Therefore, for each environment, the decision maker can select one from among multiple returned solutions according to his/her domain knowledge and/or preferences.The objective of this paper is to test the performance of various combinations of several population-based dynamic multimodal optimization algorithms and popular constraint handling techniques. First, the typical dynamic constrained optimization problems are slightly modified to be in the form of the dynamic constrained multimodal optimization problems. Second, four different population-based dynamic multimodal optimization algorithms, and five different constraint handling techniques, are pairwise tested in the experiments. Experimental results demonstrate that, among the candidates, DCMM-CSA-SR performs most successfully at all accuracy levels.

EvoDCMMO: Benchmarking and solving dynamic constrained multimodal optimization problems

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.

Evolutionary-Mean shift algorithm for dynamic multimodal function optimization

Optimization of a power supply system is one of the main directions in power engineering research. The reactive power compensation reduces active power losses in transmission lines. In general, researches devoted to allocation and control of the compensation units consider this issue as a static optimization problem. However, it is dynamic and stochastic optimization problem that requires a real-time solution. To solve the dynamic optimization NP-hard problem, it is advisable to use Swarm Intelligence. This research deals with the problem of the compensation units power control as a dynamic optimization problem, considering the possible stochastic failures of the compensation units. The Particle Swarm Optimization and the Bees Algorithm were applied to solve it to compare the effectiveness of these algorithms in the dynamic optimization of a power supply system.

In this paper, a new evolutionary algorithm based on a membrane system is proposed to solve the dynamic or uncertain optimization problems. The proposed algorithm employs objects, a dynamical membrane structure and several reaction rules of the membrane systems. The object represents a candidate solution of the optimization problems. The dynamical structure consists of the nested membranes where a skin membrane contains several membranes, which is useful for the proposed algorithm that finds optimal solutions. The reaction rules are designed to locate and track the optimal solutions of the dynamic optimization problems (DOPs), which are inspired by processing the chemical compounds in the region of cellular membranes. Experimental study is conducted based on the moving peaks benchmark to evaluate the performance of the proposed algorithm in comparison with three state-of-the-art dynamic optimization algorithms. The results indicate the proposed algorithm is effective to solve the DOPs.

This paper presents a general class of dynamic stochastic optimization problems we refer to as stochastic depletion problems. A number of challenging dynamic optimization problems of practical interest are stochastic depletion problems. Optimal solutions for such problems are difficult to obtain, both from a pragmatic computational perspective as well as from a theoretical perspective. As such, simple heuristics are desirable. We isolate two simple properties that, if satisfied by a problem within this class, guarantee that a myopic policy incurs a performance loss of at most 50% relative to the optimal adaptive control policy for that problem. We are able to verify that these two properties are satisfied for several interesting families of stochastic depletion problems and, as a consequence, we identify computationally efficient approximations to optimal control policies for a number of interesting dynamic stochastic optimization problems.

A clonal selection algorithm for dynamic multimodal function optimization

The ant colony optimization (ACO) meta-heuristic was inspired from the foraging behaviour of real ant colonies. In particular, real ants communicate indirectly via pheromone trails and find the shortest path. Although real ants proved that they can find the shortest path when the available paths are known a prior, they may face serious challenges when some paths are made available after the colony has converged to a path. This is because the colony may continue to follow the current path rather than exploring the new paths in case a shorter path is available. For the ACO meta-heuristic, the challenges are similar when applied to dynamic optimization problems (DOPs). Once the algorithm converges, it loses its adaptation capabilities and may have poor performance in DOPs. Several strategies have been integrated with ACO to address difficult combinatorial DOPs. Their performance proved that ACO is a powerful computational technique for combinatorial DOPs once enhanced. This chapter investigates the applications of ACO for combinatorial DOPs.

Dynamic time-linkage optimization problems (DTPs) are special dynamic optimization problems (DOPs) where the current solutions chosen by the solver can influence how the problems might change in the future. Although DTPs are very common in real-world applications (e.g. online scheduling, online vehicle routing, and online optimal control problems), they have received very little attention from the evolutionary dynamic optimization (EDO) research community. Due to this lack of research there are still many characteristics that we do not fully know about DTPs. For example, how should we define and classify DTPs in detail; are there any characteristics of DTPs that we do not know; with these characteristics are DTPs still solvable; and what is the appropriate strategy to solve them. In this chapter these issues will be partially addressed. First, we will propose a detailed definition framework to help characterising DOPs and DTPs. Second, we will identify a new and challenging class of DTPs where it might not be possible to solve the problems using traditional methods. Third, an approach to solve this class of problems under certain circumstances will be suggested and experiments to verify the hypothesis will be carried out. Two test problems will be proposed to simulate the property of this new class of DTPs, and discussions of real-world applications will be introduced.

Dynamic nonlinear constrained optimization problems (DNCOP) have been arisen in a diverse range of sciences, such as agriculture, economics, airspace engineering, chemistry, mechanics, management etc.. In order to solve DNCOP, we are interested in the designed algorithm not only to find the optimal solutions or the quasi-optimum solutions, but recover and track the trajectory of the optimal solutions changing with the time. In this paper, the considering DNCOP is transformed into a dynamic unconstrained optimization problem by adding the slack variables to the inequations constraint of the original problem firstly. Secondly, an improved imperialist competitive optimization algorithm for solving the DNCOP is proposed. At last, the computation simulations show that the proposed algorithm is more effective and can find the better optimal solutions or the quasi-optimum solutions in environment-varying than the compared algorithms for dynamic nonlinear constrained optimization problem.

Many engineering tasks can be formulated as dynamic optimization or open-loop optimal control problems, where we search a priori for the input profiles to a dynamic system that optimize a given performance measure over a certain time period. Further, many systems of interest in the chemical processing industries experience significant discontinuities during transients of interest in process design and operation. This paper discusses three classes of dynamic optimization problems with discontinuities: path-constrained problems, hybrid discrete/continuous problems, and mixed-integer dynamic optimization problems. In particular, progress toward a general numerical technology for the solution of large-scale discontinuous dynamic optimization problems is discussed.

Dynamic optimization of 1,3-propanediol fermentation process: A switched dynamical system approach