Constrained Optimization Research Articles

Multi-Unmanned Aerial Vehicle Path Planning Based on Improved Nutcracker Optimization Algorithm

For the multi-UAV path planning problem, environmental modeling and an improved swarm intelligence-based optimization algorithm are discussed in this paper. Firstly, to align with reality, specific constraints of UAVs in motions, attitudes and altitudes, real-world threats such as radars and no-fly zones, and inter-UAV collisions are considered. Thus, multi-UAV path planning is transformed into a multi-objective constrained optimization problem. Accordingly, an improved nutcracker optimization algorithm is proposed to solve this problem. Through initializing with logistic chaotic mapping and the lens imaging inverse learning strategy, a more fit elite initialization population is produced to increase the efficiency of path planning. Furthermore, by adjusting adaptive parameters and integrating an improved sine-cosine search strategy, a balance between global exploration capability and local exploitation capability during path planning is achieved. Experimental results show that the improved nutcracker optimization algorithm surpasses other algorithms with respect to both convergence speed and convergence value, making it an effective method for multi-UAV path planning.

Self-adaptive differential evolution-based coati optimization algorithm for multi-robot path planning

Abstract The multi-robot path planning problem is an NP-hard problem. The coati optimization algorithm (COA) is a novel metaheuristic algorithm and has been successfully applied in many fields. To solve multi-robot path planning optimization problems, we embed two differential evolution (DE) strategies into COA, a self-adaptive differential evolution-based coati optimization algorithm (SDECOA) is proposed. Among these strategies, the proposed algorithm adaptively selects more suitable strategies for different problems, effectively balancing global and local search capabilities. To validate the algorithm’s effectiveness, we tested it on CEC2020 benchmark functions and 48 CEC2020 real-world constrained optimization problems. In the latter’s experiments, the algorithm proposed in this paper achieved the best overall results compared to the top five algorithms that won in the CEC2020 competition. Finally, we applied SDECOA to optimization multi-robot online path planning problem. Facing extreme environments with multiple static and dynamic obstacles of varying sizes, the SDECOA algorithm consistently outperformed some classical and state-of-the-art algorithms. Compared to DE and COA, the proposed algorithm achieved an average improvement of 46% and 50%, respectively. Through extensive experimental testing, it was confirmed that our proposed algorithm is highly competitive. The source code of the algorithm is accessible at: https://ww2.mathworks.cn/matlabcentral/fileexchange/164876-HDECOA.

Constrained Multiobjective Optimization With Escape and Expansion Forces

Constraints may scatter the Pareto optimal solutions of a constrained multiobjective optimization problem (CMOP) into multiple feasible regions. To avoid getting trapped in local optimal feasible regions or a part of the global optimal feasible regions, a constrained multiobjective evolutionary algorithm (CMOEA) should consider both the escape force and the expansion force carefully during the search process. However, most CMOEAs fail to provide these two forces effectively. As a remedy for this limitation, this article proposes a method called TPEA. TPEA maintains three populations, termed Pop1, Pop2, and Pop3. Pop1 is a regular population, updated with a constrained NSGA-II variant. Pop2 and Pop3 are two auxiliary populations, containing the innermost and outermost nondominated infeasible solutions, respectively. The analysis reveals that these two types of nondominated infeasible solutions can contribute to the generation of escape and expansion forces, respectively. Due to these two forces, TPEA is likely to identify more global optimal feasible regions, which is crucial for constrained multiobjective optimization. Also, a mating selection strategy is developed in TPEA to coordinate the interaction among these three populations. Extensive experiments on 58 benchmark CMOPs and 35 real-world ones demonstrate that TPEA is significantly superior or comparable to six state-of-the-art CMOEAs on most test instances.

Camera-LiDAR Extrinsic Calibration Using Constrained Optimization With Circle Placement

Camera-LiDAR Extrinsic Calibration Using Constrained Optimization With Circle Placement

Deep reinforcement learning assisted surrogate model management for expensive constrained multi-objective optimization

Deep reinforcement learning assisted surrogate model management for expensive constrained multi-objective optimization

Promising boundaries explore and resource allocation evolutionary algorithm for constrained multiobjective optimization

Promising boundaries explore and resource allocation evolutionary algorithm for constrained multiobjective optimization

A Surrogate-Assisted Constrained Optimization Evolutionary Algorithm by Searching Multiple Kinds of Global and Local Regions

A Surrogate-Assisted Constrained Optimization Evolutionary Algorithm by Searching Multiple Kinds of Global and Local Regions

A surrogate-assisted differential evolution for high-dimensional expensive constrained optimization problems with mixed-integer variables

A surrogate-assisted differential evolution for high-dimensional expensive constrained optimization problems with mixed-integer variables

Two-Stage Archive Evolutionary Algorithm for Constrained Multi-Objective Optimization

Two-Stage Archive Evolutionary Algorithm for Constrained Multi-Objective Optimization

Constrained optimization approach for magnetohydrostatic equilibria on the solar atmosphere

The magnetic field plays an essential role in the evolution of structures and the description of events in the solar atmosphere. Several models have been developed to reconstruct the magnetic field, due to the impossibility of its direct measurement in the solar corona. The model proposed here extrapolates the photospheric magnetogram data up to the corona using a constrained optimization method. In the upper photosphere and chromosphere, both the magnetic and nonmagnetic forces must be taken into account, and the magnetic field reconstruction must be done considering the plasma pressure and density. This is done by applying the Lagrange multiplier technique, as the constrained optimization method, to compute the magnetic field, plasma pressure, and density in magnetohydrostatic equilibria. This approach has previously been introduced to reconstruct a nonlinear force-free magnetic field. For this work we extended it to a more realistic issue to reconstruct the magnetic field and calculate the plasma pressure and density in a magnetohydrostatic environment. Our approach was to use the constrained optimization method, which is computationally more efficient and easy to implement. The Lagrange multiplier technique is a powerful mathematical tool that has been successfully applied to many areas of physics. We sought to minimize a Lagrangian, which minimizes the divergence term subject to the constraint magnetohydrostatic equilibrium equation. The plasma parameters and magnetic field were eventually computed following the iteration scheme along with appropriate boundary data. In our previous work, we applied Lagrange multiplier techniques to reconstruct a force-free magnetic field for the solar atmosphere. For this wok, we extended the same optimization technique to extrapolate magnetic field and plasma parameters in magnetohydrostatic equilibria. The results for the magnetic field and plasma parameters were calculated and compared with those obtained by other models in the magnetohydrostatic equilibrium environment as well as the semi-analytical solution as a reference model. A force-free magnetic field and a suitable distribution for pressure and density were used as the initial input for their corresponding evolution equations. After $20,000$ iterations, the convergence of the Lagrangian in our model was slightly better than that of the comparison model. The indicators such as the relative magnetic energy and magnetic field lines were investigated, which are in agreement with the reference model compared to the comparison model.

A low-carbon scheduling method based on improved ant colony algorithm for underground electric transportation vehicles

Improved scheduling of underground transportation vehicles in coal mines can significantly enhance work efficiency and contribute to safer production. However, the specific working conditions and limitations of electric vehicles pose significant challenges to effective vehicle scheduling. To address this issue, a constrained single-objective optimization model is developed to minimize transportation costs for low-carbon scheduling of underground electric transportation vehicles (ETVs). The model incorporates constraints related to load capacity, cruising range, and safety regulations. A specific energy consumption model for ETVs is formulated, considering factors such as road conditions, load, and driving state. To solve this problem, an improved ant colony optimization algorithm integrated with Q-learning (ACO-QL) is proposed. Specifically, ant colony optimization explores the global solution space and identifies promising regions, while the split strategy effectively distributes demand across multiple vehicles. Q-learning enhances local search by selecting the most appropriate operator, preventing premature convergence to local optima. Experimental results on four real-world instances demonstrate the superior performance of ACO-QL compared to state-of-the-art algorithms.

The Proximal Alternating Direction Method of Multipliers for a Class of Nonlinear Constrained Optimization Problems

This paper presents a class of proximal alternating direction multiplier methods for solving nonconvex, nonsmooth optimization problems with nonlinear coupled constraints. The key feature of the proposed algorithm is that we use a linearized proximal technique to update the primary variables, followed by updating the dual variables using a discounting approach. This approach eliminates the requirement for an additional proxy function and then simplifies the optimization process. In addition, the algorithm maintains fixed parameter selection throughout the update process, removing the requirement to adjust parameters to ensure the decreasing nature of the generated sequence. Building on this framework, we establish a Lyapunov function with sufficient decrease and a lower bound, which is essential for analyzing the convergence properties of the algorithm. We rigorously prove both the subsequence convergence and the global convergence of the algorithm and ensure its robustness and effectiveness in solving complex optimization problems. Our paper provides a solid theoretical foundation for the practical application of this method in solving nonconvex optimization problems with nonlinear coupled constraints.

Anti-cancer drug administration in cancer treatment under stochastic disturbances: modeling and numerical optimization algorithms

Actual cancer treatment is typically a dynamic process with stochastic disturbances. Uncertain constraints (UCs) are suitable for modeling of dynamic processes under stochastic disturbance conditions, in which constraints are not fully met. Therefore, uncertain constrained dynamic optimization (UCDO) models can be utilized for addressing anti-cancer drug administration (ACDA) in cancer treatment. Due to the dynamics, randomness, and complexity of decision functions, the UCDO problem arising from ACDA in cancer treatment is difficult to deal with. To tackle this issue, a relaxation technique (RT) and an improved smooth approximation strategy (ISAS) are proposed for formulating the UCDO problem as a deterministic approximation problem, where a vector parameterization strategy and equality/inequality constraint dealing with method are integrated. Following that, to attain a global optimal solution (GOS) to the deterministic approximation problem, a hybrid optimization method (HOM) is proposed based on limited memory BFGS (L-BFGS) and a novel stochastic search method (NSSM) and its global convergence results are established. Simulation results show that the proposed HOM can achieve a higher quality solution with a lower calculating cost and lower conservativeness than existing approaches for solving the ACDA problem in cancer treatment under stochastic disturbances.

Object Detection and Multiple Objective Optimization Manipulation Planning for Underwater Autonomous Capture in Oceanic Natural Aquatic Farm

ABSTRACTUnderwater autonomous capture operations offer significant potential for reducing labor and health risks in sea organism industries. This study presents a comprehensive solution for cross‐domain underwater object detection and autonomous capture. A novel unsupervised domain adaptive learning method is proposed, integrating multiscale domain adaptive modules and attention mechanisms into a Faster Region‐Convolutional Neural Network framework. This approach enhances feature alignment across diverse aquatic domains without parameter tuning. Additionally, an efficient, parameterless constrained multiobjective optimization algorithm is introduced for underwater autonomous mobile capture, integrating parameterized trajectory planning with innovative features, such as adaptive mutation strategies and constraint violation tolerance. The proposed approaches are extensively validated through simulations, tank experiments, and real‐world oceanic trials in the Natural Aquatic Farm of Zhangzidao Island. Results demonstrate the system's robustness in complex underwater environments with varying currents, with experimental outcomes validating the accuracy and reliability of detection and capture capabilities. This research significantly advances autonomous underwater systems' capabilities in object detection and capture tasks, addressing complex challenges in realistic organism capture applications across diverse aquatic environments.

A spherical vector-based adaptive evolutionary particle swarm optimization for UAV path planning under threat conditions

Unmanned aerial vehicle (UAV) path planning is a constrained multi-objective optimization problem. With the increasing scale of UAV applications, finding an efficient and safe path in complex real-world environments is crucial. However, existing particle swarm optimization (PSO) algorithms struggle with these problems as they fail to consider UAV dynamics, resulting in many infeasible solutions and poor convergence to optimal solutions. To address these challenges, we propose a spherical vector-based adaptive evolutionary particle swarm optimization (SAEPSO) algorithm. This algorithm, based on spherical vectors, directly incorporates UAV dynamic constraints and introduces improved tent map and reverse learning to enhance the diversity and distribution of initial solutions. Additionally, dynamic nonlinear and adaptive factors are integrated to balance exploration and exploitation capabilities. To avoid local optima in highly complex environments, we propose an adaptive acceleration strategy for poor particles, and an evolutionary programming strategy is incorporated to further improve the optimization capability. Finally, we conducted comparative studies and in six benchmark scenarios with varying threat levels, and the results demonstrated that the proposed algorithm outperforms others in the initial solution effectiveness, the final solution accuracy, convergence stability, and scalability.

An arc-search interior-point algorithm for nonlinear constrained optimization

An arc-search interior-point algorithm for nonlinear constrained optimization

A novel Kriging-assisted multi-objective optimisation method considering infeasibility ratio under input uncertainty

Many real-life engineering applications come with various sources of uncertainty. Uncertainty can also impact the feasibility of solutions in constrained optimisation. Classic robust optimisation approaches often significantly increase the computational burden and might overlook different tolerable risks, resulting in conservative sub-optimal solutions. We reformulate the classic constrained problem as a multi-objective optimisation problem and propose a Kriging-assisted multi-objective optimisation method that trades off Infeasibility Ratio (IR) with robust performance: (1) a formulation to approximate IR is developed and introduced as an additional objective and (2) an acquisition function balancing exploration (refining feasible boundaries) and exploitation of promising areas with multiple designs is proposed. Furthermore, a new quality metric has been developed to effectively measure the convergence and diversity of the obtained Pareto solution set. The proposed framework is tested on five numerical problems and applied to an engineering case: the design of a honeycomb vibration isolator. A comparison study with other optimisation methods is conducted to verify its effectiveness and performance with promising results.

Surrogate-assisted global and distributed local collaborative optimization algorithm for expensive constrained optimization problems

This paper presents a surrogate-assisted global and distributed local collaborative optimization (SGDLCO) algorithm for expensive constrained optimization problems where two surrogate optimization phases are executed collaboratively at each generation. As the complexity of optimization problems and the cost of solutions increase in practical applications, how to efficiently solve expensive constrained optimization problems with limited computational resources has become an important area of research. Traditional optimization algorithms often struggle to balance the efficiency of global and local searches, especially when dealing with high-dimensional and complex constraint conditions. For global surrogate-assisted collaborative evolution phase, the global candidate set is generated through classification collaborative mutation operations to alleviate the pre-screening pressure of the surrogate model. For local surrogate-assisted phase, a distributed central region local exploration is designed to achieve intensively search for promising distributed local areas which are located by affinity propagation clustering and mathematical modeling. More importantly, a three-layer adaptive selection strategy where the feasibility, diversity and convergence are balanced effectively is designed to identify promising solutions in global and local candidate sets. Therefore, the SGDLCO efficiently balances global and local search during the whole optimization process. Experimental studies on five classical test suites demonstrate that the SGDLCO provides excellent performance in solving expensive constrained optimization problems.

Inter-DS: a cost saving algorithm for expensive constrained multi-fidelity blackbox optimization

Inter-DS: a cost saving algorithm for expensive constrained multi-fidelity blackbox optimization

Floorplanning with I/O Assignment via Feasibility-Seeking and Superiorization Methods.

The feasibility-seeking approach offers a systematic framework for managing and resolving intricate constraints in continuous problems, making it a promising avenue to explore in the context of floorplanning problems with increasingly heterogeneous constraints. The classic legality constraints can be expressed as the union of convex sets. However, conventional projection-based algorithms for feasibility-seeking do not guarantee convergence in such situations, which are also heavily influenced by the initialization. We present a quantitative property about the choice of the initial point that helps good initialization and analyze the occurrence of the oscillation phenomena for bad initialization. In implementation, we introduce a resetting strategy aimed at effectively reducing the problem of algorithmic divergence in the projection-based method used for the feasibility-seeking formulation. Furthermore, we introduce the novel application of the superiorization method (SM) to floorplanning, which bridges the gap between feasibility-seeking and constrained optimization. The SM employs perturbations to steer the iterations of the feasibility-seeking algorithm towards feasible solutions with reduced (not necessarily minimal) total wirelength. Notably, the proposed algorithmic flow is adaptable to handle various constraints and variations of floorplanning problems, such as those involving I/O assignment. To evaluate the performance of Per-RMAP, we conduct comprehensive experiments on the MCNC benchmarks and GSRC benchmarks. The results demonstrate that we can obtain legal floorplanning results 166× faster than the branch-and-bound (B&B) method while incurring only a 5% wirelength increase compared to the optimal results. Furthermore, we evaluate the effectiveness of the algorithmic flow that considers the I/O assignment constraints, which achieves an 6% improvement in wirelength. Besides, considering the soft modules with a larger feasible solution space, we obtain 15% improved runtime compared with PeF, the state-of-the-art analytical method. Moreover, we compared our method with Parquet-4 and Fast-SA on GSRC benchmarks which include larger-scale instances. The results highlight the ability of our approach to maintain a balance between floorplanning quality and efficiency.