Sample Complexity of Chance Constrained Optimization in Dynamic Environment

This paper introduces the optimization of a quantum control application, the so-called molecular alignment problem, subject to a dynamic environment. Given the relative simplicity of optimized pulse-shapes in the low-intensity variant of the problem, versus the high complexity of the optimized pulse-shapes in the high-intensity case, a dynamic-intensity environment is simulated in a noise-free calculation. Specific evolution strategies, natural candidates for optimization in dynamic environments, are applied to this task. The calculations reveal the evolution of the pulse-shapes and their underlying evolving structures, that allow a complete physical interpretation. The combination of an optimization in a dynamic environment with the examination of the intermediate optimized solutions offers a sharper physics view of the problem, and accomplishes a fruitful interdisciplinary study.

A prediction mechanism for Memetic Algorithm is presented in this paper. The Predictive Memetic Algorithm (PMA) uses a nonlinear regression method to estimate the parameters used by the algorithm to obtain good solutions in a dynamic and stochastic environment. The algorithm is applied to nonlinear data sets and performance is compared with genetic and simulated annealing algorithms. When compared with the existing methods, the proposed method generates a relatively small error difference after prediction thereby proving its superior performance. A dynamic stochastic environment is used for experimentation, so as to determine the efficacy of the algorithm on non-stationary problem environments.

In the real world, many optimization problems are dynamic. This requires an optimization algorithm to not only find the global optimal solution under a specific environment but also to track the trajectory of the changing optima over dynamic environments. To address this requirement, this paper investigates a clustering particle swarm optimizer (PSO) for dynamic optimization problems. This algorithm employs a hierarchical clustering method to locate and track multiple peaks. A fast local search method is also introduced to search optimal solutions in a promising subregion found by the clustering method. Experimental study is conducted based on the moving peaks benchmark to test the performance of the clustering PSO in comparison with several state-of-the-art algorithms from the literature. The experimental results show the efficiency of the clustering PSO for locating and tracking multiple optima in dynamic environments in comparison with other particle swarm optimization models based on the multiswarm method.

Based on the polar coordination particle swarm optimization (PPSO), this paper presents a novel method for the robot path planning in dynamic environment. It decomposes the task into a global planning stage and a local planning stage. PPSO algorithm can search for the global optimal path based on static obstacles information. When the robot moves along the optimal global path, an on-line real-time path planning strategy is adopted to avoid dynamic obstacles by means of predicting the future positions of moving obstacles. Simulation experiment shows that the method is more efficient than traditional particle swarm optimization (TPSO) and genetic algorithm (GA) for solving path planning problem. The feasibility and high stability of real-time obstacle avoidance strategy are demonstrated in dynamic environment.

In recent years, optimization in dynamic environments has attracted a growing interest from the genetic algorithm community due to the importance and practicability in real world applications. This paper proposes a new genetic algorithm, based on the inspiration from biological immune systems, to address dynamic traveling salesman problems. Within the proposed algorithm, a permutation-based dualism is introduced in the course of clone process to promote the population diversity. In addition, a memory-based vaccination scheme is presented to further improve its tracking ability in dynamic environments. The experimental results show that the proposed diversification and memory enhancement methods can greatly improve the adaptability of genetic algorithms for dynamic traveling salesman problems.

A novel immune algorithm suitable for dynamic environments (GIDE) is proposed based on a biological immune mechanism. GIDE models the dynamic process of artificial immune response with gradient-based diversity operators. Unlike traditional artificial immune algorithms, which require that randomly generated cells be added to the current population to explore its fitness landscape, GIDE uses a gradient-based diversity operator to speed up optimization in dynamic environments. Other immune algorithms are compared to GIDE by using Moving Peaks Benchmarks. Preliminary experiments showed that GIDE can maintain high population diversity during the search process, while simultaneously speeding up optimization. Thus, GIDE is useful for optimization of dynamic environments.

The insertion of atypical solutions (immigrants) in Evolutionary Algorithms populations is a well studied and successful strategy to cope with the difficulties of tracking optima in dynamic environments in single-objective optimization. This paper studies a probabilistic model, suggesting that centroid-based diversity measures can mislead the search towards optima, and presents an extended taxonomy of immigration schemes, from which three immigrants strategies are generalized and integrated into NSGA2 for Dynamic Multiobjective Optimization (DMO). The correlation between two diversity indicators and hypervolume is analyzed in order to assess the influence of the diversity generated by the immigration schemes in the evolution of non-dominated solutions sets on distinct continuous DMO problems under different levels of severity and periodicity of change. Furthermore, the proposed immigration schemes are ranked in terms of the observed offline hypervolume indicator.

Particle Swarm Optimization (PSO) is the global optimization technique that inspires many researchers to solve large scale of non-linear optimization problems. For certain complex scenarios, the premature convergence problem of PSO algorithm cannot find global optimum in dynamic environments. In this paper, a new variant motility factor based Cellular Particle Swarm Optimization (m-CPSO) algorithm is proposed which is developed by the migration behavior observed from fibroblast cellular organism to overcome this problem. The proposed m-CPSO algorithm is modeled in two different social best and individual best models. The performance of m-CPSO is tested in the benchmark and real-time data instances and compared with classical PSO. The outcome of experimental results has demonstrated that m-CPSO algorithm produces promising results than classical PSO on all evaluated environments.

A novel culture-based multiswarm artificial bee colony (CMABC) algorithm was proposed to address dynamic optimization problems. The historical experience of sub-swarms is preserved as cultural knowledge to guide the subsequent evolutionary process. Experiments were conducted on the moving peaks benchmark function. The results show that the CMABC algorithm was better than, or at least comparable to, the basic ABC algorithm, and other state-of-the-art algorithms.

Methods of sequential test optimization in dynamic environment

Formulating the solution as an optimisation problem has proven to be effective in developing solutions to many real world problems. We generally obtain the best possible solution using these methods. In this work, the traffic scheduling problem has been formulated as a waiting time minimisation problem, and appropriate cost functions have been developed, in pursuit of finding the optimal solution. A first-in, first-out queuing model is used, with the vehicles arriving in a Poisson process, and the service time being exponentially distributed. The key feature of this model is that it adapts to varying service and arrival rates of the lanes. These rates are forecast using a neural network model, and appear in the objective function. It was observed that the use of the neural network greatly improved the robustness of the model. Although the model has been developed for a four lane, two way architecture, it can be generalised to any architecture. Results have been analysed by comparing the proposed method to a proportional time distribution. It is shown that the proposed model performs relatively well, when there is rapid variation in the arrival and service rates.

This paper investigates optimization in dynamic environments where the numbers of optima are unknown or fluctuating. The authors present a novel algorithm, Dynamic Population Differential Evolution (DynPopDE), which is specifically designed for these problems. DynPopDE is a Differential Evolution based multi-population algorithm that dynamically spawns and removes populations as required. The new algorithm is evaluated on an extension of the Moving Peaks Benchmark. Comparisons with other state-of-the-art algorithms indicate that DynPopDE is an effective approach to use when the number of optima in a dynamic problem space is unknown or changing over time.

With the rapid development of renewable energy, power systems face increased flexibility and dispatch requirements, particularly in response to grid load fluctuations and energy reserve security. Pumped hydro storage, a mature energy storage technology, is widely used in power regulation and reserve capacity provision, but its dispatching still presents significant optimization challenges. Traditional dispatching methods struggle to simultaneously meet multi-objective optimization requirements. Therefore, this study proposes a dispatching optimization method based on Proximal Policy Optimization (PPO) combined with Multi-Objective Optimization (MOO) to maximize profit, ensure sufficient reserve capacity, and safeguard grid stability. We construct a multi-objective optimization model for pumped hydro storage and combine it with the Proximal Policy Optimization (PPO) algorithm for dynamic dispatch optimization. A multi-objective reward function is used to weightedly optimize profit, reserve capacity, and grid stability. Experimental results demonstrate that the PPO + MOO method significantly outperforms traditional methods (such as piecewise linear approximation, genetic algorithm, and particle swarm optimization) across multiple evaluation metrics. It effectively improves dispatching accuracy and system stability, particularly in complex power markets and under conditions of large load fluctuations. Furthermore, the PPO algorithm demonstrates excellent convergence and stability during training, ensuring continuous model optimization in dynamic environments. Although computational time is relatively long, optimization techniques such as weight pruning have significantly improved computational efficiency. Ultimately, this study provides a new solution for the scheduling optimization of pumped hydro energy storage systems and provides an important reference for scheduling problems in smart grids and renewable energy systems.

Optimisation in dynamic environments is a very active and important area which tackles problems that change with time (as most real-world problems do). The possibility to use a new centralised cooperative strategy based on trajectory methods (tabu search) for solving Dynamic Optimisation Problems (DOPs) was previously introduced showing good results against state of the art methods like the Particle Swarm Optimisation (PSO) variant with multiple swarms and different types of particles. The analysis of this previous work are further extended here by exploring more possibilities for the cooperation rules used in the strategy. The results show that different classes of cooperation can lead to quite different results, some of them greatly outperforming the previous ones.

Particle Swarm Optimization in Dynamic Environments