Solution Of Optimization Problem Research Articles

Solution existence for a class of nonsmooth robust optimization problems

AbstractThe main purpose of this paper is to investigate the existence of global optimal solutions for nonsmooth and nonconvex robust optimization problems. To do this, we first introduce a concept called extended tangency variety and show how a robust optimization problem can be transformed into a minimizing problem of the corresponding tangency variety. We utilize this concept together with a constraint qualification condition and the boundedness of the objective function to provide relationships among the concepts of robust properness, robust M-tamesness and robust Palais-Smale condition related to the considered problem. The obtained results are also employed to derive necessary and sufficient conditions for the existence of global optimal solutions to the underlying robust optimization problem.

An Innovative Hybrid Approach Producing Trial Solutions for Global Optimization

Global optimization is critical in engineering, computer science, and various industrial applications as it aims to find optimal solutions for complex problems. The development of efficient algorithms has emerged from the need for optimization, with each algorithm offering specific advantages and disadvantages. An effective approach to solving complex problems is the hybrid method, which combines established global optimization algorithms. This paper presents a hybrid global optimization method, which produces trial solutions for an objective problem utilizing a genetic algorithm’s genetic operators and solutions obtained through a linear search process. Then, the generated solutions are used to form new test solutions, by applying differential evolution techniques. These operations are based on samples derived either from internal line searches or genetically modified samples in specific subsets of Euclidean space. Additionally, other relevant approaches are explored to enhance the method’s efficiency. The new method was applied on a wide series of benchmark problems from recent studies and comparison was made against other established methods of global optimization.

Dynamic Supplier Selection and Its Optimal Strategy Considering Full Truck Load and Fuzzy Demand using Fuzzy Expected Value-Based Programming

This article proposes a linear integer optimization model incorporating fuzzy parameters to find the optimal solution for a dynamic supplier selection problem with uncertain demand. The uncertain demand value is represented using a fuzzy variable. A fuzzy expected value-based linear optimization solver is used to address the optimization problem, to minimize the total cost under fuzzy demand values. Several computational experiments were conducted to evaluate and analyze the model. The results show that the proposed model effectively identifies the optimal suppliers for each product. Additionally, the model determines the optimal purchase volumes for each product type from the selected suppliers, leading to the minimal total expected cost.

Multi-Objective Optimization of Three-Stage Turbomachine Rotor Based on Complex Transfer Matrix Method

This study presents the complex transfer matrix method (CTMM) as an advanced mathematical model, providing significant advantages over the finite element method (FEM) by yielding rapid solutions for complex optimization problems. In order to design a more efficient structure of a three-stage turbomachine rotor, we integrated this method with various optimization algorithms, including genetic algorithm (GA), differential evolution (DE), simulated annealing (SA), gravitational search algorithm (GSA), black hole (BH), particle swarm optimization (PSO), Harris hawk optimization (HHO), artificial bee colony (ABC), and non-metaheuristic pattern search (PS). Thus, the best rotor geometry can be obtained fast with minimum bearing forces and disk deflections within design limits. In the results, the efficiency of the CTMM for achieving optimized designs is demonstrated. The CTMM outperformed the FEM in both speed and applicability for complex rotordynamic problems. The CTMM was found to deliver results of comparable quality much faster than the FEM, especially with higher element quality. The use of the CTMM in the iterative optimization process is shown to be highly advantageous. Furthermore, it is noted that among the different optimization algorithms, ABC provided the best results for this multi-objective optimization problem.

Multitask scheduling on cloud additive manufacturing using NSGA-II

Purpose: Cloud manufacturing (CM) represents a new manufacturing paradigm that integrates distributed resources to provide on-demand services. The high consumer demand from various locations, coupled with the customizability and complexity of manufacturing, complicates task scheduling. In this context, 3D printers are crucial as innovative manufacturing technologies with significant potential in producing complex and custom products. Scheduling in CM falls under the non-deterministic polynomial time-hard category, where tasks must be scheduled and distributed rapidly. Considerations of distance, minimization of delays, and makespan become critical variables that must be considered. This research aims to schedule and distribute tasks in CM using the non-dominated sorting genetic algorithm II (NSGA-II) to minimize delays, reduce makespan, and decrease costs.Methodology: NSGA-II is employed to tackle the complexities of scheduling in CM. The strength of NSGA-II lies in its ability to determine optimal and efficient solutions for multiobjective problems. Tasks originating from requests at various locations are adjusted based on material parameters and dimensions and then distributed to providers while considering aspects such as makespan, delay minimization, and cost.Findings: The optimization results using NSGA-II demonstrate effective and efficient task distribution to providers. Across the four tested task distribution scenarios, the average computational time required was 5.59 seconds. Pareto analysis indicates a trade-off between various objective functions. Solutions with short distances tend to have increased maximum time and delays.Originality/value: NSGA-II is effective for task distribution with multiobjective considerations. Not all three objective functions can be optimized simultaneously, given the trade-offs between distance, maximum time, and lateness. The priority of the objective functions should be determined to achieve optimal results. If minimizing lateness is most important, the focus should be on points with low lateness values. Further development can be done by modifying the Pareto front to make data-driven decisions that consider these trade-offs.

Digital-analog counterdiabatic quantum optimization with trapped ions

Abstract We introduce a hardware-specific, problem-dependent digital-analog quantum algorithm of a counterdiabatic quantum dynamics tailored for optimization problems. Specifically, we focus on trapped-ion architectures, taking advantage from global Mølmer–Sørensen gates as the analog interactions complemented by digital gates, both of which are available in the state-of-the-art technologies. We show an optimal configuration of analog blocks and digital steps leading to a substantial reduction in circuit depth compared to the purely digital approach. This implies that, using the proposed encoding, we can address larger optimization problem instances, requiring more qubits, while preserving the coherence time of current devices. Furthermore, we study the minimum gate fidelity required by the analog blocks to outperform the purely digital simulation, finding that it is below the best fidelity reported in the literature. To validate the performance of the digital-analog encoding, we tackle the maximum independent set problem, showing that it requires fewer resources compared to the digital case. This hybrid co-design approach paves the way towards quantum advantage for efficient solutions of quantum optimization problems.

Optimal performance design of bat algorithm: An adaptive multi‐stage structure

AbstractThe bat algorithm (BA) is a metaheuristic algorithm for global optimisation that simulates the echolocation behaviour of bats with varying pulse rates of emission and loudness, which can be used to find the globally optimal solutions for various optimisation problems. Knowing the recent criticises of the originality of equations, the principle of BA is concise and easy to implement, and its mathematical structure can be seen as a hybrid particle swarm with simulated annealing. In this research, the authors focus on the performance optimisation of BA as a solver rather than discussing its originality issues. In terms of operation effect, BA has an acceptable convergence speed. However, due to the low proportion of time used to explore the search space, it is easy to converge prematurely and fall into the local optima. The authors propose an adaptive multi‐stage bat algorithm (AMSBA). By tuning the algorithm's focus at three different stages of the search process, AMSBA can achieve a better balance between exploration and exploitation and improve its exploration ability by enhancing its performance in escaping local optima as well as maintaining a certain convergence speed. Therefore, AMSBA can achieve solutions with better quality. A convergence analysis was conducted to demonstrate the global convergence of AMSBA. The authors also perform simulation experiments on 30 benchmark functions from IEEE CEC 2017 as the objective functions and compare AMSBA with some original and improved swarm‐based algorithms. The results verify the effectiveness and superiority of AMSBA. AMSBA is also compared with eight representative optimisation algorithms on 10 benchmark functions derived from IEEE CEC 2020, while this experiment is carried out on five different dimensions of the objective functions respectively. A balance and diversity analysis was performed on AMSBA to demonstrate its improvement over the original BA in terms of balance. AMSBA was also applied to the multi‐threshold image segmentation of Citrus Macular disease, which is a bacterial infection that causes lesions on citrus trees. The segmentation results were analysed by comparing each comparative algorithm's peak signal‐to‐noise ratio, structural similarity index and feature similarity index. The results show that the proposed BA‐based algorithm has apparent advantages, and it can effectively segment the disease spots from citrus leaves when the segmentation threshold is at a low level. Based on a comprehensive study, the authors think the proposed optimiser has mitigated the main drawbacks of the BA, and it can be utilised as an effective optimisation tool.

Multi-objective optimization based robotic path planning for interpolation reconstruction model of CT data

Robotic path planning plays a pivotal role in computer-aided liver tumor thermal ablation surgery. However, traditional methods face challenges in terms of low reconstruction efficiency and planning safety. To address these issues, we propose a method for robotic path planning of liver tumor thermal ablation surgery. Firstly, an interlayer interpolation algorithm based on optical flow estimation is utilized to compensate for large interlayer spacing in computed tomography (CT) images by inserting predicted images between sequence images. Secondly, the voxel traversal strategy and patch intersection calculation strategy in the standard marching cube (MC) algorithm is optimized to improve the efficiency of abdominal tissues reconstruction. Finally, comprehensive clinical constraints are summarized to ensure the surgery safety and the strength pareto evolutionary algorithm II (SPEA-II) is leveraged to optimize surgery path, which can obtain even distribution of solutions in high-dimension optimization problems. Extensive experiments conducted on the 3Dircadb and SLIVER07 datasets revealed that our proposed method reduces reconstruction time by 21.5% compared to the standard MC algorithm, while achieving an average overlap rate of 88.25% and an average Hausdorff distance of 15.25 mm between Pareto front points and surgeon's recommended puncture points.

Dual-path differential perturbation sand cat swarm optimization algorithm integrated with escape mechanism

In this paper, based on the sand cat swarm optimization (SCSO) algorithm, a dual-path differential perturbation sand cat swarm optimization algorithm integrated with escape mechanism (EDSCSO) is proposed. EDSCSO aims to solve the problems of the original SCSO, such as the limited diversity of the population, low efficiency of solving complex functions, and ease of falling into a local optimal solution. First, an escape mechanism was proposed to balance the exploration and exploitation of the algorithm. Second, a random elite cooperative guidance strategy was used to utilize the elite population to guide the general population to improve the convergence speed of the algorithm. Finally, the dual-path differential perturbation strategy is used to continuously perturb the population using two differential variational operators to enrich population diversity. EDSCSO obtained the best average fitness for 27 of 39 test functions in the IEEE CEC2017 and IEEE CEC2019 test suites, indicating that the algorithm is an efficient and feasible solution for complex optimization problems. In addition, EDSCSO is applied to optimize the three-dimensional wireless sensor network coverage as well as the unmanned aerial vehicle path planning problem, and it provides optimal solutions for both problems. The applicability of EDSCSO in real-world optimization scenarios was verified.

HSMAOA: An enhanced arithmetic optimization algorithm with an adaptive hierarchical structure for its solution analysis and application in optimization problems

The Arithmetic Optimization Algorithm (AOA) has recently gained significant attention as a novel meta-heuristic algorithm. However, it faces challenges such as premature convergence and entrapment in local optima when addressing complex optimization problems. To overcome these limitations, this paper proposes an enhanced AOA, termed the Self-Adaptive Hierarchical Arithmetic Optimization Algorithm (HSMAOA). The proposed method integrates three key strategies: Firstly, a spiral-guided random walk mechanism is introduced to improve global search ability. Secondly, a novel adaptive hierarchy leader and follower mechanism is proposed, which establishes a complete multi-branch tree hierarchy with decreasing branching degrees within the population, thereby increasing information exchange among population individuals to escape local optima. Finally, a differential mutation strategy based on ranked selection is introduced to enhance candidate solution quality. HSMAOAʼs performance was evaluated on the CEC2022 test suite against some state-of-the-art algorithms. Results, including optimization accuracy analysis, convergence curves, and various statistical tests, demonstrate HSMAOAʼs superior optimization capability and robustness. In addition, tests on eight engineering structure optimization problems, including the pressure vessel design problem, the multiple disk clutch brake design problem, and the step-cone pulley problem, and so forth, further validate its effectiveness. Thus, HSMAOA shows strong competitiveness in complex optimization tasks and potential for a wide range of applications, and is an advantageous and promising alternative solution for optimization problems.

Experimental Study on Direct Shear Behavior of New-to-Old Interface for Recycled Aggregate Concrete with Different Replacement Ratios

The large amount of construction waste produced by the construction industry brings severe natural resource consumption and environmental pollution, elevating the awareness of sustainable development. Recycled aggregate concrete, crushed from construction waste, is recognized as an eco-friendly material and the current optimal solution for the environmental problem. The interface shear failure between substrate recycled coarse aggregate concrete (RAC) and overlay natural aggregate concrete becomes vital for structural safety. In order to study the direct shear performance, a total of 19 specimens were designed to carry out the direct shear test with different replacement ratios, interface types and curing ages. The whole process and failure mode were recorded. The relationships between the shear capacity and deformation, ductility, damage evolution, and energy dissipation were evaluated and discussed. The results demonstrate that the RAC component in the interface was the weak line in the shear plane, accelerating the damage evolution. In the early curing stage, the replacement ratio had a slight influence on the shear properties. Increasing the recycled aggregate replacement ratio from 0 to 100% improved the normalized strength ratio by 8.94% and 14.62%, respectively, for curing ages of 3 days and 7 days. A regression equation was proposed to predict the shear strength, accounting for the curing ages. With the increase in the replacement ratio, the ductility and energy dissipation gradually enhanced.

Constrained optimal control problem of oncolytic viruses in cancer treatment

Oncolytic viruses are genetically modified viruses that selectively infect and destroy cancer cells while leaving normal and healthy cells intact. Most previous studies did not consider realistic constraints such as daily or total injection amount of oncolytic viruses; consequently, a gap exists between the research results and the real-world setting. This study aimed to investigate a constrained optimal control problem in tumor treatment utilizing oncolytic viruses, based on a mathematical model. This constraint reflects the practical scenario where the total dosage of oncolytic viruses that can be administered is limited. We introduced auxiliary state variables to address these limitations and employed the penalty function method. Furthermore, we established the existence of an optimal solution for the optimal control problem and derived the corresponding optimality system. Numerical simulations demonstrate the effectiveness of an approach that involves initiating treatment with a high dosage and gradually reducing it over time. Additionally, we confirmed that applying the optimal control strategy leads to a significant reduction in the number of cancer cells compared with uniform dosing, even when the same quantity of virus is administered.

Improved krill swarm algorithm and its application in structural optimization

This paper improves and perfects the standard Krill herd algorithm (KH), which has the defects of slow convergence speed, insufficient calculation accuracy and easy to fall into local optimal solution for complex problems. An improved Krill herd algorithm (SDEKH) integrating improved differential evolution operator and S-type adaptive inertia weight is proposed. SDEKH, KH and other intelligent algorithms are compared and tested through a variety of standard test functions to verify the excellent performance of SDEKH; SDEKH is used to optimize the design of truss structure. By comparing the optimization results with other methods, it is verified that the optimization efficiency and accuracy of SDEKH are improved, which provides a more efficient and accurate method for the optimization design of engineering structures.

Knapsack Balancing via Multiobjectivization

In this paper, we address the aspect of knapsack balancing in the classic knapsack problem. Recognizing that excessive dispersion in the objective function or constraint coefficients of the optimal solution can be undesirable, we propose, when appropriate, to control this effect through problem multiobjectivization. By multiobjectivization, we mean the addition of one or more objective functions that aim to shift the original problem’s optimal solutions towards Pareto optimal solutions of the multiobjectivized problem, reducing the dispersion of the respective coefficients. We detail how the knapsack balance aspect can be incorporated into the standard knapsack problem model and demonstrate the functionality of this enriched model through illustrative examples.

Comparative view of the modified Vogel’s approximation methods in transportation problem

Recently, the whole world is experiencing economic hardship and one fast road to ply is to cut out some expenses. Xlife group is equally affected and so the study proposes a means to minimize its transportation cost if effected. A comparative surgery on Vogel’s approximation with its modified versions were conducted on minimizing the cost of transporting manufactured goods from (Xlife group’s) points of supply to certain destinations was undertaken. The Vogel's Approximation Method (VAM) and the Modified Vogel's Approximation Method based on standard deviation, distribution indicators and average cost were applied to determine an initial basic feasible solution and optimal solution for certain transportation problems. All methods yield identical minimum transportation cost except at an instance.

Recursive utility optimization problem described by forward–backward stochastic differential inclusions

The main result of the paper deals with the existence of a solution of a recursive utility optimization problem described by systems of the forward–backward stochastic differential inclusion of the form: X t − X s ∈ ∫ s t F ( τ , X τ ) d τ + ∫ s t ( G ∘ X ) d B τ and Y t ∈ E [ H ( X T ) + ∫ t T Φ ( τ , X τ , Y τ ) d τ | F t ] , considered in the author paper [Kisielewicz. Weak compactness of weak solutions to forward–backward stochastic differential inclusions. Stoch Anal Appl. 2024;42(2):306–326], where the existence of weak solutions and weak compactness in distribution of the set W ( F , H , Φ , G , μ ) of all its weak solutions have been proved.

Population-based algorithm for discrete facility location with ranking of candidate locations

Facility location problems are mathematical optimization problems that involve finding the best locations for facilities (e.g., factories, warehouses, stores) to serve customers within a given geographic area. The goal is typically to minimize costs, maximize efficiency, or optimize other objectives. Facility location problems can vary in several ways, including customer behavior rules, the type of search space, and constraints on locations for new facilities being located. These variations directly impact the complexity of the problem and the appropriate solution methods that can be used to tackle the problem. This research is focused on the discrete competitive facility location problem for an entering firm, which is a crucial scenario for new firms entering the existing market. The goal is to strategically locate new facilities to maximize their profit, while considering existing competitors. A new random search heuristic algorithm to approximate the optimal solution for discrete competitive facility location problems for firm expansion has been developed. The algorithm extends its precursor that ranks potential locations for the new facilities depending on their usefulness and uselessness in creating new solutions in the past. The new algorithm uses a population to handle and reuse the best solutions found so far and new strategies for ranking potential locations, considering features of the solutions in the population. The designed algorithm has been investigated by solving competitive facility location problems actual for an entering firms using real geographical data.

Design optimization of automotive carbon fiber composite material floor laminate based on PSO-BFO algorithm

In response to the current challenges of low precision and efficiency in the optimization of composite material layups, the insufficient lightweight of automotive body floors, and the high cost of carbon fiber composites, this study introduces an optimized design method for carbon fiber composite flooring layups. Based on implicit parametric technology, a hybrid PSO-BFO (Particle Swarm Optimization-Bacterial Foraging Optimization) algorithm is employed. This approach achieves an integrated optimization of materials, processes, and structures, thereby balancing and reducing costs. The SFE-CONCEPT is utilized to establish an implicit parameterization model for the body floor, which is validated through experiments and finite element simulation analysis. Concept design and modeling of the carbon fiber composite material floor laminate are performed. Continuous variable optimization is employed to determine the thickness, tile shape, and number of layers for the front, middle, and rear floors. A continuous variable discretization rounding strategy is used to obtain the discrete layer numbers for each laminate orientation of the composite material floor. The continuous fiber lamination strategy is applied to create different shared lamination regions. The PSO-BFO hybrid optimization method is proposed to optimize the lamination sequence as a multi-objective optimization, addressing the challenges of discrete lamination sequence, explosive combinations, and multiple variables in the optimization design of carbon fiber composite material floor laminates. The optimization results demonstrate improvements of 34.4% in floor quality M, 6.0% in static bending stiffness BS, and 5.3% in lightweight coefficient QLX using the proposed PSO-BFO method. PSO-BFO and PSO-GA (Particle Swarm Optimization-Genetic Algorithm) methods are more capable of obtaining global optimal solutions for complex optimization problems than single optimization algorithms. Still, the results obtained by the PSO-BFO method are more balanced.

Inverse demand tracking in transportation networks

AbstractThis paper deals with the reconstruction of the desired demand in an optimal control problem, stated over a tree-shaped transportation network which is governed by a linear hyperbolic conservation law. As desired demands typically undergo fluctuations due to seasonality or unexpected events making short-term adjustments necessary, such an approach can exemplary be used for forecasting from past data. We suggest to model this problem as a so-called inverse optimal control problem, i.e., a hierarchical optimization problem whose inner problem is the optimal control problem and whose outer problem is the reconstruction problem. In order to guarantee the existence of solutions in the function space framework, the hyperbolic conservation law is interpreted in weak sense allowing for control functions in Lebesgue spaces. For the computational treatment of the model, we transfer the hierarchical problem into a nonsmooth single-level one by plugging the uniquely determined solution of the inner optimal control problem into the outer reconstruction problem before applying techniques from nonsmooth optimization. Some numerical experiments are presented to visualize various features of the model including different types of noise in the demand and strategies of how to observe the network in order to obtain good reconstructions of the desired demand.

Q-Learning-Based Dumbo Octopus Algorithm for Parameter Tuning of Fractional-Order PID Controller for AVR Systems

The tuning of fractional-order proportional-integral-derivative (FOPID) controllers for automatic voltage regulator (AVR) systems presents a complex challenge, necessitating the solution of real-order integral and differential equations. This study introduces the Dumbo Octopus Algorithm (DOA), a novel metaheuristic inspired by machine learning with animal behaviors, as an innovative approach to address this issue. For the first time, the DOA is invented and employed to optimize FOPID parameters, and its performance is rigorously evaluated against 11 existing metaheuristic algorithms using 23 classical benchmark functions and CEC2019 test sets. The evaluation includes a comprehensive quantitative analysis and qualitative analysis. Statistical significance was assessed using the Friedman’s test, highlighting the superior performance of the DOA compared to competing algorithms. To further validate its effectiveness, the DOA was applied to the FOPID parameter tuning of an AVR system, demonstrating exceptional performance in practical engineering applications. The results indicate that the DOA outperforms other algorithms in terms of convergence accuracy, robustness, and practical problem-solving capability. This establishes the DOA as a superior and promising solution for complex optimization problems, offering significant advancements in the tuning of FOPID for AVR systems.