Memory Design for Constrained Dynamic Optimization Problems

Pareto-domination was adopted to handle not only trade-off between objective and constraints but also trade-off between convergence and diversity on solving a constrained optimisation problem (COP) in this paper like many other researchers. But there are some differences. This paper converts a COP into an equivalent dynamic constrained multi-objective optimisation problem (DCMOP) first, then dynamic version of non-dominated sorting genetic algorithm with decomposition (NSGA/D) is designed to solve the equivalent DCMOP, consequently solve the COP. A key issue for the NSGA/D working effectively is that the environmental change should not destroy the feasibility of the population. With a feasible population, the NSGA/D could solve well the DCMOP just as a MOEA usually can solve well an unconstrained MOP. Experimental results show that the NSGA/D outperforms or performs similarly to other state-of-the-art algorithms referred to in this paper, especially in global search.

Dynamic constrained optimization problems (DCOPs) are difficult to solve because both objective function and constraints can vary with time. Although DCOPs have drawn attention in recent years, little work has been performed to solve DCOPs with multiple dynamic feasible regions from the perspective of locating and tracking multiple feasible regions in parallel. Moreover, few benchmarks have been proposed to simulate the dynamics of multiple disconnected feasible regions. In this paper, first, the idea of tracking multiple feasible regions, originally proposed by Nguyen and Yao, is enhanced by specifically adopting multiple subpopulations. To this end, the dynamic species-based particle swam optimization (DSPSO), a representative multipopulation algorithm, is adopted. Second, an ensemble of locating and tracking feasible regions strategies is proposed to handle different types of dynamics in constraints. Third, two benchmarks are designed to simulate the DCOPs with dynamic constraints. The first benchmark, including two variants of G24 (called G24v and G24w), could control the size of feasible regions. The second benchmark, named moving feasible regions benchmark (MFRB), is highly configurable. The global optimum of MFRB is calculated mathematically for experimental comparisons. Experimental results on G24, G24v, G24w, and MFRB show that the DSPSO with the ensemble of strategies performs significantly better than the original DSPSO and other typical algorithms.

An empirical study of the algorithm dynamic differential evolution with combined variants with a repair method (DDECV $$+$$+ Repair) in the solution of dynamic constrained optimization problems is presented. Unexplored aspects of the algorithm are of particular interest in this work: (1) the role of each one of its elements, (2) its sensitivity to different change frequencies and change severities in the objective function and the constraints, (3) its ability to detect a change and recover after it, besides its diversity handling (percentage of feasible and infeasible solutions) during the search, and (4) its performance with dynamism present in different parts of the problem. Seven performance measures, eighteen recently proposed test problems and eight algorithms found in the specialized literature are considered in four experiments. The statistically validated results indicate that DDECV $$+$$+ Repair is robust to change frequency and severity variations, and that it is particularly fast to recover after a change in the environment, but highly depends on its repair method and its memory population to provide competitive results. DDECV $$+$$+ Repair shows evidence on the convenience of keeping a proportion of infeasible solutions in the population when solving dynamic constrained optimization problems. Finally, DDECV $$+$$+ Repair is highly competitive particularly when dynamism is present in both, objective function and constraints.

Cooperative perception constitutes a critical technology to enhance situational awareness of vehicular users (VUs) by fusing multi-source observation data. Existing approaches employ either vehicles or road infrastructure as fusion platforms. However, vehicle-based approaches suffer from severe occlusions that compromise perception reliability, while infrastructure-based approaches are constrained by fixed coverage ranges that restrict spatial perception, thereby failing to achieve both reliable and comprehensive perception simultaneously. To overcome these limitations, we propose an uncrewed aerial vehicle (UAV)-enabled cooperative perception system where a UAV operates in a cyclic process: it adjusts its position to respond to VU requests, collects observation data, and returns the compressed fusion results to the VUs. In each cycle, we jointly optimize decisions regarding UAV trajectory, request response, data collection, compression degree of the fusion results, and resource allocation to balance fusion reliability and service latency, subject to UAV kinematics, task assignment, resource allocation, and latency constraints. We formulate this optimization problem as a dynamic constrained multi-objective optimization problem featuring cascaded dependencies where the request response, data collection, and resource allocation should be determined sequentially due to the inherent logic of cooperative perception. To solve this problem, we design an evolutionary algorithm based on a cascaded dependency generation strategy in which decision variables are generated according to their dependency order. Experimental results demonstrate the superior solution performance of our algorithm over four baseline algorithms. This study advances cooperative perception for vehicular networks by providing a UAV-enabled solution ensuring reliable fusion and timely service under dynamic traffic conditions.

In parallel to optimizing energy consumption within houses, users' comfort is increasingly considered as an essential success criterion for automated smart home solutions. From the user perspective, balancing trade-offs between energy consumption and users' comfort when scheduling home appliances is a challenging task mainly within dynamic context (energy price, budget, user preferences, energy source, etc). To address this challenge, this paper has modeled appliances scheduling as a dynamic constrained multi-objective optimization problem and have leveraged a recently introduced dynamic evolutionary algorithm for the problem resolution. Moreover, there are typically multiple inhabitants in the same home who often share context-aware applications with various individual preferences which are likely to be conflicting. We propose a new comfort function to support multi-user conflictual preferences. Our experimental results have shown that our approach has a confirmed advantage on the user comfort while coping dynamically with the context changes.

We study in this paper, a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk management. The linear constraint on both the control and state variables considered in our model destroys the elegant structure of the conventional LQ formulation and has blocked the derivation of an explicit control policy so far in the literature. We successfully derive in this paper, the analytical control policy for such a class of problems by utilizing the state separation property induced from its structure. We reveal that the optimal control policy is a piecewise affine function of the state and can be computed offline efficiently by solving two coupled Riccati equations. Under some mild conditions, we also obtain the stationary control policy for an infinite time horizon. We demonstrate the implementation of our method via some illustrative examples and show how to calibrate our model to solve dynamic constrained portfolio optimization problems.

As indicated in Chap. 2, the VCIM production scheduling, an important issue in operation of any VCIM system, is a dynamic constrained optimisation problem.

Optimization issues are often defined statically, assuming constant environmental conditions.However, in many real-world scenarios, problem environments are dynamic and continuously changing.Thus we need optimization algorithms that could solves those issues in dynamic environments as well.Dynamic optimization problems are change(s) that may occur through the time.Such environments are characterized by uncertainty, temporal changes, and structural complexities, which makes the optimization process a significant challenge.In addressing these challenges, evolutionary algorithms have emerged as one of the most effective approaches for solving dynamic optimization problems (DOPs).Among these algorithms, the Imperialist Competitive Algorithm (ICA), designed based on swarm intelligence and competition among imperialist countries, has garnered considerable attention due to its capability in solving static optimization issues.In this research, Imperialist Competitive Algorithms, inspired by the historical and political processes of colonization and assimilation, have been known as one of the efficient evolutionary algorithms.These algorithms face numerous challenges when dealing with dynamic problems , including reduced population diversity, performance degradation in conditions of rapid environmental changes, and limitations in optimal convergence.These cases indicate the need to develop improved and more adaptable versions of these algorithms.Using concepts such as memory, population clustering, and repulsion mechanisms, this algorithm has been able to maintain population diversity at all stages while increasing the speed of convergence in the face of environmental changes.The key feature of the proposed algorithm is the use of memory to store previous optimal solutions, a clustering mechanism to manage population diversity, and repulsion to prevent unnecessary accumulation of solutions in specific regions.Nevertheless, ICA exhibits poor performance in dynamic environments because it lacks mechanisms to maintain diversity, quick adaptation to environmental changes, and new optima track.This study presents an improved version of ICA aimed at overcoming these limitations.The proposed algorithm incorporates a combination of a memory mechanism and a clustering strategy to enhance its adaptability to environmental changes and preserve diversity within the population.The memory mechanism stores information about previous optima and utilizes it under appropriate conditions to accelerate the optimization process.forclustering method is used for clustering.Clustering in the proposed method ensures that diversity is maintained for the population during the execution of the algorithm.In this study, our goal is to solve problems that change the environment in a global way.That means, the fitness of all points in the environment changes.By testing just one point in the environment and comparing the fitness obtained with its previously stored value, we can detect a change in the environment.On the other hand, the clustering strategy, particularly the k-means technique, to maintain maintain population diversity and prevents the convergence of solutions to specific regions.Together, these two components create a balance between exploration and exploitation, thereby improving the algorithm's performance in dynamic environments.To evaluate the performance of the proposed algorithm, the Moving Peaks Benchmark (MPB) was used as a standard metric.Due to its capability to simulate complex and diverse changes in dynamic environmentsparticularly in Branke's second scenario-MPB is one of the most recognized tools for assessing the performance of dynamic optimization algorithms.The proposed algorithm was evaluated alongside advanced algorithms such as FTmPSO (TMO), RAmQSO-s4, RmNAFSA-s4, TFTmPSO, RFTmPSO, mQSO10 (5+5q), FMSO, CellularPSO, Multi-SwarmPSO, mCPSO, AmQSO*, FTMPSO, almPSO, and CDEPSA.Experimental results demonstrated that the proposed algorithm outperformed other methods in areas such as convergence speed, adaptability to environmental changes, and population diversity preservation.A key feature of the proposed algorithm is its ability to retain identified optima even after environmental changes.Additionally, the use of the k-means clustering technique has ensured that the algorithm effectively avoids excessive focus on specific regions and maintains population diversity while facing complex environmental changes.Another advantage of this algorithm is its scalability in handling dynamic optimization issues with high dimensions and complexities.These findings indicate that the proposed algorithm is not only effective in laboratory settings but also suitable for real-world applications with fast and dynamic changes.

In this paper, we formulate human motion tracking as a high dimensional constrained dynamic optimization problem. A novel generative method, called Sequential Immune Genetic Algorithm, is proposed for human motion tracking. The main contribution is that we introduce immune genetic algorithm (IGA) for pose optimization in latent space of human motion. As the latent space is low-dimensional and contains the prior knowledge of human motion, it makes pose analysis more efficient and accurate. We apply IGA for pose optimization. Compared with GA and other evolutionary methods, its main advantage is the ability to use the prior knowledge of human motion. As motion tracking is a dynamic optimization problem, we incorporate the temporal continuity information into the traditional IGA and propose a sequential IGA (S-IGA) algorithm. We demonstrate our methods on different videos of different motion types. Experimental results show that the S-IGA motion tracking method can achieve accurate and stable tracking of 3D human motion.

When facing dynamic optimization problems the goal is no longer to find the extrema, but to track their progression through the space as closely as possible. Over these kind of over changing, complex and ubiquitous real-world problems, the explorative-exploitive subtle counterbalance character of our current state-of-the-art search algorithms should be biased towards an increased explorative behavior. While counterproductive in classic problems, the main and obvious reason of using it in severe dynamic problems is simple: while we engage ourselves in exploiting the extrema, the extrema moves elsewhere. In order to tackle this subtle compromise, we propose a novel algorithm for optimization in dynamic binary landscapes, stressing the role of negative feedback mechanisms. The Binary Ant Algorithm (BAA) mimics some aspects of social insects' behavior. Like Ant Colony Optimization (ACO), BAA acts by building pheromone maps over a graph of possible trails representing pseudo-solutions of increasing quality to a specific optimization problem. Main differences rely on the way this search space is represented and provided to the colony in order to explore/exploit it, while and more important, we enrol in providing strong evaporation to the problem-habitat. By a process of pheromone reinforcement and evaporation the artificial insect's trails over the graph converge to regions near the ideal solution of the optimization problem. Over each generation, positive feedbacks made available by pheromone reinforcement consolidate the best solutions found so far, while enhanced negative feedbacks given by the evaporation mechanism provided the system with population diversity and fast self-adaptive characteristics, allowing BAA to be particularly suitable for severe complex dynamic optimization problems. Experiments made with some well known test functions frequently used in the Evolutionary Algorithms' research field illustrate the efficiency of the proposed method. BAA was also compared with other algorithms, proving to be more able to track fast moving extrema on several test problems.

In applications of the evolutionary algorithms (EAs) to problems of adaptation to changing environments, maintenance of the diversity of the population is an essential requirement. This paper proposes an evolutionary algorithm combined with a chaotic sequence (CEA) which provides a good technique for population diversity in dynamic optimization problems. Many numerical experiments are reported in order to compare the performance of the CEA with the self-adaptive approach by other authors, and the numerical results show that the performance of CEA algorithm is superior to that of other published algorithms for two dynamic benchmark problems.

In this paper, online convex optimization (OCO) problems with time-varying objective and constraint functions are studied from the perspective of an agent who takes actions in real time. Information about the current objective and constraint functions is revealed only after the corresponding action is already chosen. Inspired by a fast converging algorithm for time-invariant optimization in the very recent work [1], we develop a novel online algorithm based on virtual queues for constrained OCO. Optimal points of the dynamic optimization problems with full knowledge of the current objective and constraint functions are used as a dynamic benchmark sequence. Upper bounds on the regrets with respect to the dynamic benchmark and the constraint violations are derived for the presented algorithm in terms of the temporal variations of the underlying dynamic optimization problems. It is observed that the proposed algorithm possesses sublinear regret and sublinear constraint violations, as long as the temporal variations of the optimization problems are sublinear, i.e., the objective and constraint functions do not vary too drastically across time. The performance bounds of the proposed algorithm are superior to those of the state-of-the-art OCO method in most scenarios. Besides, different from the saddle point methods widely used in constrained OCO, the stepsize of the proposed algorithm does not rely on the total time horizon, which may be unknown in practice. Finally, the algorithm is applied to a dynamic resource allocation problem in data center networks. Numerical experiments are conducted to corroborate the merit of the developed algorithm and its advantage over the state-of-the-art.

Surrogate-assisted evolutionary computation: Recent advances and future challenges

Constrained optimization problems are common in theoretical study and engineering practice. The constraint functions can be equality or inequality, convex or non-convex, which makes it difficult to find a constrained optimal solution. Evolutionary algorithms are powerful tools for constrained optimization problems. The balance between constraints and objective functions is always a difficult task and hotspot in EA-community. Many EA-based constraint handling methods have been proposed, but this problem is far to be completely solved.This paper presents a new view of constraint handling: A bi-level differential evolutionary algorithm (BLDE). BLDE has a bi-level structure, which deals with the constraints and searches optimal solutions separately. In the lower level, the objective is to find a population of candidate feasible solutions, and in the upper level, the objective is to search the global optimal solution. The proposed BLDE gets competitive results in 13 benchmark functions, with a comparison of two state-of-the-art constraint handling algorithms. BLDE shows the following advantages: 1) it is efficient in search constrained optimal solutions; 2) it is easy to implement and requires few hyper-parameters; 3) it can guarantee the obtained solutions are feasible or close to feasible.

Dynamic optimization problems have gained significant attention in evolutionary computation as evolutionary algorithms (EAs) can easily adapt to changing environments. We show that EAs can solve the graph coloring problem for bipartite graphs more efficiently by using dynamic optimization. In our approach the graph instance is given incrementally such that the EA can reoptimize its coloring when a new edge introduces a conflict. We show that, when edges are inserted in a way that preserves graph connectivity, Randomized Local Search (RLS) efficiently finds a proper 2-coloring for all bipartite graphs. This includes graphs for which RLS and other EAs need exponential expected time in a static optimization scenario. We investigate different ways of building up the graph by popular graph traversals such as breadth-first-search and depth-first-search and analyse the resulting runtime behavior. We further show that offspring populations (e. g. a (1+$\lambda$) RLS) lead to an exponential speedup in $\lambda$. Finally, an island model using 3 islands succeeds in an optimal time of $\Theta(m)$ on every $m$-edge bipartite graph, outperforming offspring populations. This is the first example where an island model guarantees a speedup that is not bounded in the number of islands.