Constrained Optimization Research Articles

Energy management strategy for low hydrogen consumption in hybrid power systems consisting of dual fuel cells and a single lithium battery

ABSTRACT Low hydrogen consumption is an important objective for fuel cell power systems as it impacts both economic efficiency and continuous power supply. This paper addresses the optimization problem of minimizing hydrogen consumption in a hybrid power system comprising dual fuel cells and a single lithium battery. We introduce an energy management method for the multi-period synchronous optimization, incorporating a data processing module and power allocation module. The quasi-periodic loads are predicted using a modified gray-Markov chain model, while the optimization problem is solved using an adaptive constrained particle swarm optimization (ACPSO) algorithm. An initial swarm generation algorithm is introduced to enhance the effectiveness of ACPSO, and a power correction algorithm is integrated to address deviations between predicted and actual loads. The effectiveness and advantages in optimizing hydrogen consumption of the proposed strategy have been demonstrated through simulations and experiments.

A novel state transition algorithm with adaptive fuzzy penalty for multi-constraint UAV path planning

Unmanned aerial vehicles (UAVs) require pre-planned flight paths that are energy-efficient, safe and smooth across their wide range of application scenarios. In this study, a novel UAV path planning method is proposed. Firstly, the UAV path planning under numerous obstacles is modeled as a continuous constrained optimization problem. The cost function is formulated as a linear combination of length, height variation, and smoothness, while the constraints include obstacle avoidance, height limitation, and the maneuverability of UAV. Subsequently, a novel constrained state transition algorithm with adaptive fuzzy penalty (AFSTA) is proposed to solve the optimization problem. In AFSTA, a novel adaptive fuzzy penalty function is designed to leverage expert knowledge to establish a reasonable mapping relationship from the fitness value and the degree of constraint violation to the penalty factor for a candidate solution. Meanwhile, the state transition algorithm (STA) is used as the search engine for both global and local search. Experimental results illustrate that the proposed method can find energy-efficient, safe, and maneuverable flight paths successfully with the superiority over other state-of-the-art metaheuristic algorithms.

Rationing in an Era of Multiple Tight Constraints: Is Cost-Utility Analysis Still Fit for Purpose?

Cost-utility analysis may not be sufficient to support reimbursement decisions when the assessed health intervention requires a large proportion of the healthcare budget or when the monetary healthcare budget is not the only resource constraint. Such cases include joint replacement, coronavirus disease 2019 (COVID-19) interventions and settings where all resources are constrained (e.g. post-COVID-19 or in low/middle-income countries). Using literature on health technology assessment, rationing and reimbursement in healthcare, we identified seven alternative frameworks for simultaneous decisions about (dis)investment and proposed modifications to deal with multiple resource constraints. These frameworks comprised constrained optimisation; cost-effectiveness league table; 'step-in-the-right-direction' approach; heuristics based on effective gradients; weighted cost-effectiveness ratios; multicriteria decision analysis (MCDA); and programme budgeting and marginal analysis (PBMA). We used numerical examples to demonstrate how five of these alternative frameworks would operate. The modified frameworks we propose could be used in local commissioning and/or health technology assessment to supplement standard cost-utility analysis for interventions that have large budget impact and/or are subject to additional constraints.

Constrained multi-objective optimization with dual-swarm assisted competitive swarm optimizer

Many metaheuristic methods have been proposed and have shown promising performance in solving multi-objective optimization problems (MOPs). As a representative example, the competitive swarm optimizer (CSO) exhibits excellent performance in solving large-scale MOPs. However, CSO performs poorly when used straightforwardly for constrained MOPs with complex constraints or objective spaces. In this paper, we propose a dual-swarm-based CSO framework that co-evolves two swarms with different orientations: (i) CSO is improved using genetic algorithms, namely CSO-GA to form a convergence-directed swarm without considering constraints to accelerate the convergence. (ii) CSO is further improved by differential evolution, namely CSO-DE to form a search-directed swarm by considering constraints to enhance diversity and improving the search for the constrained Pareto front. Moreover, a new constraint relaxation method is proposed that combines the particle swarm feasible rate and current evolutionary generation to dynamically adjust the factor for decreasing or increasing constraint relaxation. Extensive experiments with 37 benchmark instances and nineteen real-world constrained MOPs demonstrate that our proposed algorithm yields significantly better or at least more competitive results than ten state-of-the-art methods.

A Nonconvex Proximal Bundle Method for Nonsmooth Constrained Optimization

An implementable algorithm for solving nonsmooth nonconvex constrained optimization is proposed by combining bundle ideas, proximity control, and the exact penalty function. We construct two kinds of approximations to nonconvex objective function; these two approximations correspond to the convex and concave behaviors of the objective function at the current point, which captures precisely the characteristic of the objective function. The penalty coefficients are increased only a finite number of times under the conditions of Slater constraint qualification and the boundedness of the constrained set, which limit the unnecessary penalty growth. The given algorithm converges to an approximate stationary point of the exact penalty function for constrained nonconvex optimization with weakly semismooth objective function. We also provide the results of some preliminary numerical testing to show the validity and efficiency of the proposed method.

Two-Stage Multiobjective Evolution Strategy for Constrained Multiobjective Optimization

For the past many years, several constrained multiobjective evolutionary algorithms (CMOEAs) have been designed for solving constrained multi-objective optimization problems (CMOPs). In these CMOEAs, some constraint-handling techniques (CHTs) were proposed to balance the convergence and constrained satisfaction, however, they still face some serious challenges, such as premature convergence to the local optimal region and labor-intensive tuning of parameters for a specific CMOP. Furthermore, most of the existing CHTs are derived by solving constrained single-objective optimization. The information hidden from the feasible non-dominated set (FNDS) has not been fully utilized. This study proposed a novel parameter-less constraint handling technique, which divides the entire population into three mutually exclusive subsets dynamically: FNDS, the subset dominated by FNDS, and the subset not dominated by FNDS. According to the proposed division of labor, it is not necessary to balance the convergence and constrained satisfaction in each subset. To avoid being entrapped in local optima, the proposed algorithm adopts a two-stage strategy to solve CMOPs. In the first stage, the proposed algorithm focuses solely on converging toward the unconstrained Pareto front without considering the constrained satisfaction. In the second stage, the FNDS constraint handling technique is adopted to guide the population converging toward constrained Pareto front effectively. The performance of the proposed algorithm was compared to that of nine state-of-the-art CMOEAs, and the comparison results show that the proposed algorithm performs significantly better on the CF, MW, and LIRCMOP test suites.

Process Knowledge-Guided Autonomous Evolutionary Optimization for Constrained Multiobjective Problems

Various real-world problems can be attributed to constrained multi-objective optimization problems. Although there are various solution methods, it is still very challenging to automatically select efficient solving strategies for constrained multi-objective optimization problems. Given this, a process knowledge-guided constrained multi-objective autonomous evolutionary optimization method is proposed. Firstly, the effects of different solving strategies on population states are evaluated in the early evolutionary stage. Then, the mapping model of population states and solving strategies is established. Finally, the model recommends subsequent solving strategies based on the current population state. This method can be embedded into existing evolutionary algorithms, which can improve their performances to different degrees. The proposed method is applied to 41 benchmarks and 30 dispatch optimization problems of the integrated coal mine energy system. Experimental results verify the effectiveness and superiority of the proposed method in solving constrained multi-objective optimization problems.

A Constrained Competitive Swarm Optimizer With an SVM-Based Surrogate Model for Feature Selection

Feature selection (FS) is an important data preprocessing technique that selects a small subset of relevant features to improve learning performance. However, it is also challenging due to its large search space. Recently, competitive swarm optimiser (CSO) has shown promising results in FS because of its potential global search ability. The main idea of CSO is to select two solutions randomly and then let the loser (worse fitness) learn from the winner (better fitness). Although such a search mechanism provides a high population diversity, it is at risk of generating unqualified solutions since the winner’s quality is not guaranteed. In this work, we propose a constrained evolutionary mechanism for CSO, which verifies the quality of all the particles and lets the infeasible (unqualified) solutions learn from the feasible (qualified) ones. We also propose a novel local search and a size-change operator that guide the population to search for smaller feature subsets with similar or better classification performance. A surrogate model, based on support vector machines, is proposed to assist both local search and the size-change operator to explore a massive number of potential feature subsets without requiring excessive computational resource. Results on 24 real-world datasets show that the proposed algorithm can select smaller feature subsets with higher classification performance than state-of-the-art evolutionary computation (EC) and non-EC benchmark algorithms.

Constrained efficient global multidisciplinary design optimization using adaptive disciplinary surrogate enrichment

Constrained efficient global multidisciplinary design optimization using adaptive disciplinary surrogate enrichment

An initial value insensitive method for phase equilibrium calculation: Constrained backtracking search optimization algorithm

Phase equilibrium calculations are frequently encountered in various industrial processes and many methods, including direct solution methods based on Newton's method and indirect solution methods based on thermodynamic principles sprang out. They all can calculate the satisfactory solutions of phase equilibria problem under given volume, temperature, and moles (NVT-flash), but there still exist problems of initial value sensitivity and solving complex derivatives. Thus, a constrained backtracking search optimization algorithm (CBSA), which added constraints handling of the NVT-flash problem to the original operation of BSA, is presented in this paper. The proposed algorithm takes the total Helmholtz free energy as the objective function, and the moles vector and volume of a certain phase as the decision variables. The direct search method and exterior point method were used to handle the constraints of NVT-flash problem. The numerical test results are 100% consistent with the published data, which verify the effectiveness and energy decay property of the proposed algorithm. The proposed scheme is the first successful attempt to apply meta-heuristic algorithm to the field of phase equilibrium calculation. This hints the wide application prospect of meta-heuristic algorithms in this field as well as broadens the application range of meta-heuristic optimization algorithms.

Growing Neural Gas Network for Offspring Generation in Evolutionary Constrained Multi-Objective Optimization

Growing Neural Gas Network for Offspring Generation in Evolutionary Constrained Multi-Objective Optimization

Constrained Multiobjective Optimization via Multitasking and Knowledge Transfer

Solving constrained multi-objective optimization problems (CMOPs) with various features and challenges via evolutionary algorithms is very popular. Existing methods usually adopt an additional helper problem to simplify and solve them by divide-and-conquer. This paper proposes a new multitasking framework for CMOPs, borrowing the idea of evolutionary multitasking optimization. The main contributions are i) a multitasking framework is proposed, where a CMOP is modeled as a multitasking optimization problem with three tasks. Then, it is solved by constraint-first, constraint-ignored, and constraint-relaxed multi-objective evolutionary algorithms; ii) a knowledge expression and a transfer strategy are devised to transfer the knowledge among the tasks; and iii) based on the proposed framework, a new two-stage algorithm is presented to solve CMOPs. The effectiveness of our approach is validated through experiments on four CMOP benchmark suites and 19 real-world CMOPs.

Even Search in a Promising Region for Constrained Multi-Objective Optimization

Even Search in a Promising Region for Constrained Multi-Objective Optimization

Fully Distributed Algorithms for Constrained Nonsmooth Optimization Problems of General Linear Multiagent Systems and Their Application

Fully Distributed Algorithms for Constrained Nonsmooth Optimization Problems of General Linear Multiagent Systems and Their Application

Improved nonlinear model predictive control with inequality constraints using particle filtering for nonlinear and highly coupled dynamical systems

Abstract Motion planning and controller design are challenging tasks for highly coupled and nonlinear dynamical systems such as autonomous vehicles and robotic applications. Nonlinear model predictive control (NMPC) is an emerging technique in which sampling-based methods are used to synthesize the control and trajectories for complex systems. In this study, we have developed the sampling-based motion planning algorithm with NMPC through Bayesian estimation to solve the online nonlinear constrained optimization problem. In the literature, different filtration techniques have been applied to extract knowledge of states in the presence of noise. Due to the detrimental effects of linearization, the Kalman filter with NMPC only achieves modest effectiveness. Moving horizon estimation (MHE), on the other hand, frequently relies on simplifying assumptions and lacks an effective recursive construction. Additionally, it adds another optimization challenge to the regulation problem that has to be solved online. To address this problem, particle filtering is implemented for Bayesian filtering in nonlinear and highly coupled dynamical systems. It is a sequential Monte Carlo method that involves representing the posterior distribution of the state of the system using a set of weighted particles that are propagated through time using a recursive algorithm. For nonlinear and strongly coupled dynamical systems, the novel sampling-based NMPC technique is effective and simple to use. The efficiency of the suggested method has been assessed using simulated studies.

Distributed Online Constrained Optimization With Feedback Delays.

We investigate multiagent distributed online constrained convex optimization problems with feedback delays, where agents make sequential decisions before being aware of the cost and constraint functions. The main purpose of the distributed online constrained convex optimization problem is to cooperatively minimize the sum of time-varying local cost functions subject to time-varying coupled inequality constraints. The feedback information of the distributed online optimization problem is revealed to agents with time delays, which is common in practice. Every node in the system can interact with neighbors through a time-varying sequence of directed communication topologies, which is uniformly strongly connected. The distributed online primal-dual bandit push-sum algorithm that generates primal and dual variables with delayed feedback is used for the presented problem. Expected regret and expected constraint violation are proposed for measuring the performance of the algorithm, and both of them are shown to be sublinear with respect to the total iteration span T in this article. In the end, the optimization problem for the power grid is simulated to justify the proposed theoretical results.

Fuzzy Evolutionary Algorithm in Construction Project for Valuation

Clustering algorithms has emerged as an important data mining technique for pattern recognition, data analysis and dimensionality reduction. Clustering is usually used in all fields to merge the same feature objects into a single group. The clustering method is incorporated with search algorithms to search the dataset from the databases. For large databases, there is a need of good clustering algorithm with high accuracy. Despite its high performance, the existing methods show some limitations. This paper focused on optimize the clustering method with a search structure for large multidimensional databases with dynamic indexes for the effective validation of construction projects. In the construction project validation to improve the clustering methods using Evolutionary Constrained Differential Optimization (ECDO) and Distributed Weighted Fuzzy C-Means algorithm to improve clustering performance than the centralized clustering approaches. The proposed methodology includes ECDO which presents new cluster tree indexing approach with cluster speed improvement in the validation of the construction projects. Distributed Fuzzy Possibilistic C-Means algorithm is proposed in improvement of cluster centre to overcome coincidence cluster problems. The comparative analysis stated that proposed ECDO model exhibits ~6% reduced memory utilization ~11% reduced scalability and ~8% minimized selectivity than the conventional WPCM model.

Multi-objective constrained robust design of a metamaterial vibration isolator with a limited budget

Many real-world engineering design optimisation problems encounter input uncertainties, which may introduce undesired fluctuations in design performance or even make the design solution infeasible. Robust design optimisation (RDO) is widely studied due to its ability to deal with uncertainties. RDO methods require many evaluations generally, which is prohibitive when relying on expensive simulations. Surrogate-assisted optimisation can help to reduce the number of simulation calls. An improved constrained multi-objective efficient robust global optimisation method (CMO-ERGO) is proposed in this work, which combines the robust expected improvement of ERGO with the probability of feasibility. CMO-ERGO improves the ERGO framework and quantifies the robustness of the objective and the constraint functions using an analytical uncertainty quantification based on the Kriging surrogate. The proposed method is tested on three numerical benchmark functions and applied to the robust design of a metamaterial vibration isolator with a honeycomb structure to explore its performance in solving engineering applications. The robustness of optimal solutions is demonstrated using the Monte Carlo Method. Moreover, comparisons between CMO-ERGO and several existing RDO methods illustrate the effectiveness and efficiency of CMO-ERGO.

Parallel cooperative multiobjective coevolutionary algorithm for constrained multiobjective optimization problems

The existing parallel multiobjective evolutionary computation does not perform well for constrained multiobjective optimization problems with discontinuous Pareto fronts or narrow feasible regions. This study parallelizes the state-of-the-art cooperative multiobjective coevolutionary algorithm and proposes an effective parallel evolutionary algorithm for constrained multiobjective optimization problems that are difficult to optimize. Two parallelization methods are compared: a global parallel model in which solution evaluations are performed in parallel, and a hybrid model that treats the cooperative populations in a distributed manner while performing each solution evaluation in parallel. The first model is a straightforward parallelization, while the second one capitalizes on the characteristics of the coevolutionary framework. To investigate the efficacy of the proposed models, experiments are conducted on constrained multiobjective optimization problems, including complex characteristics, while varying the number of parallel cores up to 64. The experiments compare the two proposed methods from the viewpoint of search performance and execution time. The experimental results reveal that the latter hybrid model shows better computational efficiency and scalability against an increasing number of cores without adversely affecting the search performance compared to the former straightforward parallelization.

Constrained optimization of rank-one functions with indicator variables

Constrained optimization of rank-one functions with indicator variables