Solution Of Optimization Problem Research Articles

Allocation of Starting Points in Global Optimization Problems

We propose new multistart techniques for finding good local solutions in global optimization problems. The objective function is assumed to be differentiable, and the feasible set is a convex compact set. The techniques are based on finding maximum distant points on the feasible set. A special global optimization problem is used to determine the maximum distant points. Preliminary computational results are given.

Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems

We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical system in the multiobjective setting, which trajectories converge weakly to Pareto optimal solutions. Discretization of this system yields an inertial multiobjective algorithm which generates sequences that converge weakly to Pareto optimal solutions. We employ Nesterov acceleration to define an algorithm with an improved convergence rate compared to the plain multiobjective steepest descent method (Algorithm 1). A further improvement in terms of efficiency is achieved by avoiding the solution of a quadratic subproblem to compute a common step direction for all objective functions, which is usually required in first-order methods. Using a different discretization of our inertial gradient-like dynamical system, we obtain an accelerated multiobjective gradient method that does not require the solution of a subproblem in each step (Algorithm 2). While this algorithm does not converge in general, it yields good results on test problems while being faster than standard steepest descent.

Novel hybrid kepler optimization algorithm for parameter estimation of photovoltaic modules

The parameter identification problem of photovoltaic (PV) models is classified as a complex nonlinear optimization problem that cannot be accurately solved by traditional techniques. Therefore, metaheuristic algorithms have been recently used to solve this problem due to their potential to approximate the optimal solution for several complicated optimization problems. Despite that, the existing metaheuristic algorithms still suffer from sluggish convergence rates and stagnation in local optima when applied to tackle this problem. Therefore, this study presents a new parameter estimation technique, namely HKOA, based on integrating the recently published Kepler optimization algorithm (KOA) with the ranking-based update and exploitation improvement mechanisms to accurately estimate the unknown parameters of the third-, single-, and double-diode models. The former mechanism aims at promoting the KOA’s exploration operator to diminish getting stuck in local optima, while the latter mechanism is used to strengthen its exploitation operator to faster converge to the approximate solution. Both KOA and HKOA are validated using the RTC France solar cell and five PV modules, including Photowatt-PWP201, Ultra 85-P, Ultra 85-P, STP6-120/36, and STM6-40/36, to show their efficiency and stability. In addition, they are extensively compared to several optimization techniques to show their effectiveness. According to the experimental findings, HKOA is a strong alternative method for estimating the unknown parameters of PV models because it can yield substantially different and superior findings for the third-, single-, and double-diode models.

A fresh look at nonsmooth Levenberg–Marquardt methods with applications to bilevel optimization

In this paper, we revisit the classical problem of solving over-determined systems of nonsmooth equations numerically. We suggest a nonsmooth Levenberg–Marquardt method for its solution which, in contrast to the existing literature, does not require local Lipschitzness of the data functions. This is possible when using Newton-differentiability instead of semismoothness as the underlying tool of generalized differentiation. Conditions for local fast convergence of the method are given. Afterwards, in the context of over-determined mixed nonlinear complementarity systems, our findings are applied, and globalized solution methods, based on a residual induced by the maximum and the Fischer–Burmeister function, respectively, are constructed. The assumptions for local fast convergence are worked out and compared. Finally, these methods are applied for the numerical solution of bilevel optimization problems. We recall the derivation of a stationarity condition taking the shape of an over-determined mixed nonlinear complementarity system involving a penalty parameter, formulate assumptions for local fast convergence of our solution methods explicitly, and present results of numerical experiments. Particularly, we investigate whether the treatment of the appearing penalty parameter as an additional variable is beneficial or not.

Integrated Q-Learning with Firefly Algorithm for Transportation Problems

The study addresses the optimization of land transportation in the context of vehicle routing, a critical aspect of transportation logistics. The specific objectives are to employ various meta-heuristic optimization techniques, including Genetic Algorithms (GA), Ant Colony Optimization (ACO), Firefly Algorithm (FA), Particle Swarm Optimization (PSO), and Q-Learning reinforcement algorithm, to find the optimal solutions for vehicle routing problems. The primary aim is to enhance the efficiency and effectiveness of land transportation systems by minimizing factors such as travel distance or time while adhering to constraints. The study evaluates the advantages and limitations of each algorithm and introduces a novel-based approach that integrates Q-learning with the FA. The results demonstrate that these meta-heuristic optimization techniques offer promising solutions for complex vehicle routing challenges. The integrated Q-learning with Firefly Algorithm (iQLFA) emerges as the most successful approach among them, showcasing its potential to significantly improve transportation optimization outcomes.

A new MPPT controller based on a modified multiswarm PSO algorithm using an adaptive factor selection strategy for partially shaded PV systems

Maximum power point tracking (MPPT) controller is the main element in photovoltaic (PV) systems, which is used to ensure maximum power extraction under different meteorological conditions. A MPPT controller can guarantee good performance criteria even in the presence of climatic changes. To achieve this goal, several techniques have been proposed in the literature to improve robustness of the PV system control, such as artificial intelligence and multiswarm particle swarm optimization (MSPSO) algorithm. Previous research on classical MSPSO has shown that the algorithm search behavior cannot find the optimal solution for certain problems. In this context, we investigate the design of a new MPPT controller based on a modified version of heterogeneous multiswarm particle swarm optimization algorithm using an adaptive factor selection strategy (FMSPSO) for PV systems. The proposed FMSPSO can improve the tracking capability with high accuracy, less oscillations, and high robustness. To validate the proposed solution, a simulation and experimental benchmarking of a PV system are presented and analyzed. The obtained results show the effectiveness of the proposed solution compared with the classical MSPSO, fuzzy logic, and perturb and observe (P&O) control presented in other recent works.

A Surrogate-Assisted Evolutionary Algorithm for Seeking Multiple Solutions of Expensive Multimodal Optimization Problems

A Surrogate-Assisted Evolutionary Algorithm for Seeking Multiple Solutions of Expensive Multimodal Optimization Problems

Exploiting sparsity for localisation of large‐scale wireless sensor networks

AbstractWireless Sensor Network (WSN) localisation refers to the problem of determining the position of each of the agents in a WSN using noisy measurement information. In many cases, such as in distance and bearing‐based localisation, the measurement model is a non‐linear function of the agents' positions, leading to pairwise interconnections between the agents. As the optimal solution for the WSN localisation problem is known to be computationally expensive in these cases, an efficient approximation is desired. The authors show that the inherent sparsity in this problem can be exploited to greatly reduce the computational effort of using an Extended Kalman Filter (EKF) for large‐scale WSN localisation. In the proposed method, which the authors call the L‐Banded Extended Kalman Filter (LB‐EKF), the measurement information matrix is converted into a banded matrix by relabelling (permuting the order of) the vertices of the graph. Using a combination of theoretical analysis and numerical simulations, it is shown that typical WSN configurations (which can be modelled as random geometric graphs) can be localised in a scalable manner using the proposed LB‐EKF approach.

A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems

AbstractWater distribution systems (WDSs) are critical infrastructure used to convey water from sources to consumers. The mathematical framework governing the distribution of flows and heads in extended period simulations of WDSs lends itself to application in a wide range of optimization problems. Applying the classical mixed integer linear programming (MILP) approach to model WDSs hydraulics within an optimization framework can contribute to higher solution accuracy with lower computational effort. However, adapting WDSs models to conform to a MILP formulation has proven challenging because of the intrinsic non‐linearity of system hydraulics and the complexity associated with modeling hydraulic devices that influence the state of the WDS. This paper introduces MILPNet, an adjustable framework for WDSs that can be used to build and solve an extensive array of MILP optimization problems. MILPNet includes constraints that represent the mass balance and energy conservation equations, hydraulic devices, control rules, and status checks. To conform to MILP structure, MILPNet employs piece‐wise linear approximation and integer programming. MILPNet was implemented and tested using Gurobi Python API. Modeling accuracy was shown to be comparable to EPANET, a public domain software for hydraulic modeling, and sensitivity analyses were conducted to examine the impacts of the modeling assumptions on the performance of MILPNet. Additionally, application of the framework was demonstrated using pump scheduling optimization examples in single and rolling horizon scenarios. Our results show that MILPNet can facilitate the construction and solution of optimization problems for a range of applications in WDSs operations.

A Neural Separation Algorithm for the Rounded Capacity Inequalities

The cutting plane method is a key technique for successful branch-and-cut and branch-price-and-cut algorithms that find the exact optimal solutions for various vehicle routing problems (VRPs). Among various cuts, the rounded capacity inequalities (RCIs) are the most fundamental. To generate RCIs, we need to solve the separation problem, whose exact solution takes a long time to obtain; therefore, heuristic methods are widely used. We design a learning-based separation heuristic algorithm with graph coarsening that learns the solutions of the exact separation problem with a graph neural network (GNN), which is trained with small instances of 50 to 100 customers. We embed our separation algorithm within the cutting plane method to find a lower bound for the capacitated VRP (CVRP) with up to 1,000 customers. We compare the performance of our approach with CVRPSEP, a popular separation software package for various cuts used in solving VRPs. Our computational results show that our approach finds better lower bounds than CVRPSEP for large-scale problems with 400 or more customers, whereas CVRPSEP shows strong competency for problems with less than 400 customers. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) [RS-2023-00259550] and the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) [2022-0-01032, Development of Collective Collaboration Intelligence Framework for Internet of Autonomous Things]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0310 .

SCOP: Schrödinger Control Optimal Planning for Goal-based Wealth Management

We consider the problem of optimization of contributions of a financial planner such as a working individual towards a financial goal such as retirement. The objective of the planner is to find an optimal and feasible schedule of periodic installments to an investment portfolio set up towards the goal. Because portfolio returns are random, the practical version of the problem amounts to finding an optimal contribution scheme such that the goal is satisfied at a given confidence level. This paper suggests a semi-analytical approach to a continuous-time version of this problem based on a controlled backward Kolmogorov equation (BKE) which describes the tail probability of the terminal wealth given a contribution policy. The controlled BKE is solved semi-analytically by reducing it to a controlled Schrödinger equation and solving the latter using an algebraic method. Numerically, our approach amounts to finding semi-analytical solutions simultaneously for all values of control parameters on a small grid, and then using the standard two-dimensional spline interpolation to simultaneously represent all satisficing solutions of the original plan optimization problem. Rather than being a point in the space of control variables, satisficing solutions form continuous contour lines (efficient frontiers) in this space.

Group contribution method for rapid estimation of crystal growth rates

The morphological evolution of organic crystals during crystallization depends on the face-specific growth rates. Classical growth rate models relate the face-specific growth rates to the crystal lattice, energy of stable facets, growth mechanism, and supersaturation. The complexities of these models have increased over time to account accurately for solution conditions, the structure of growth units, and their attachment rates. Such advanced growth rate models require several layers of computations to obtain attachment energies of facets, nucleation rates, kink density, and attachment rates. Among these, the most intensive and time-consuming computation is for attachment rates, which require molecular dynamic simulations. This substantially increases the overall computation time to predict the absolute growth rate for even one crystallization condition. Since it is nearly impossible to iterate such a growth rate model, optimization schemes cannot be implemented to identify solution conditions that favor specific crystal growth. To reduce the computational time for attachment rate calculations, we implement a group contribution method (GCM) that relates the properties of functional groups in a molecule to their attachment rates to the crystal lattice, thereby rapidly estimating the growth rates of organic crystals. The process of molecular attachment involves partial desolvation of a solvated molecule, referred to as a transition state, followed by total desolvation via spontaneous attachment to a crystal facet. The first step in GCM is to identify the equilibrium states of fully solvated and partially desolvated solute molecules. The degree of supersaturation dictates the extent of this equilibrium and, thereby, the activation barrier for the growth of crystals, according to transition state theory. Identifying this equilibrium phenomenon allows for capturing the functional-group-specific interactions that depend on molecular motion, which could be related to operating conditions such as temperature and pressure. The stochastic optimization technique with Monte-Carlo sampling allows an efficient optimization problem solution to obtain the group interaction parameters. The GCM approach is first validated for the estimation of growth rates of glutamic acid and L-histidine, and then extended to predict growth rates of alanine and glycine rapidly. The optimized parameters and GCM scheme can be used to estimate growth rates in other crystallization systems.

Страхование капитального ремонта в Российской Федерации: актуальные проблемы и перспективы

Issues of provision of housing to citizens, dilapidation of the housing stock of the country and the importance of its renovation are named among the acute problems in Addresses of the President of the Russian Federation . A wisely developed system of major renovations of apartment blocks is the most optimal problem solution. However, although the adopted measures have been advanced and timely, they could not alleviate the emerging destructive tendencies, so the legislator has brought forward an initiative to introduce a mechanism of insurance of major renovations in the Russian Federation. This idea is not new in the world’s practice and is quite efficiently implemented in foreign laws and orders, primarily in form of an insurance coverage or performance bond. Its practical implementation in Russia and prospects of successful functioning present a relevant civil task. Following the results of the study, the authors conclude that the efficiency of this novelty will depend on the level of development of its implementation, establishment of the optimal legal framework and organizational mechanism.

A Snowmelt Optimization Algorithm Applied to Green Low Carbon Logistics Pathways Optimization Problems

INTRODUCTION: Efficient and accurate optimization of green and low-carbon logistics paths, as one of the key technologies of green and low-carbon logistics, can not only promote the high-quality development of the economy, but also reduce the negative impacts of logistics on the environment and increase the cost of logistics delivery.
 OBJECTIVES: To address the problems of slow convergence and easy to fall into local optimization in the current performance prediction research on talent team building.
 METHODS: This paper proposes a snowmelt heuristic optimization algorithm to solve the green low-carbon logistics path optimization problem. Firstly, the objective function of green low-carbon logistics path optimization is designed by analyzing the optimization cost and conditional constraints of the green low-carbon logistics path optimization problem; then, a method based on intelligent optimization algorithm is proposed by designing the position-order array coding and fitness function, combined with the snow-melting optimization algorithm; finally, the validity and superiority of the proposed method are verified by simulation experiments.
 RESULTS: The results show that the proposed method not only improves the convergence speed but also increases the optimization fitness value.
 Conclusion: The problem of slow convergence and easy to fall into local optimum in the solution of green low-carbon logistics path optimization problem is solved.

Optimal Robust Control of Nonlinear Systems with Unknown Dynamics via NN Learning with Relaxed Excitation.

This paper presents an adaptive learning structure based on neural networks (NNs) to solve the optimal robust control problem for nonlinear continuous-time systems with unknown dynamics and disturbances. First, a system identifier is introduced to approximate the unknown system matrices and disturbances with the help of NNs and parameter estimation techniques. To obtain the optimal solution of the optimal robust control problem, a critic learning control structure is proposed to compute the approximate controller. Unlike existing identifier-critic NNs learning control methods, novel adaptive tuning laws based on Kreisselmeier's regressor extension and mixing technique are designed to estimate the unknown parameters of the two NNs under relaxed persistence of excitation conditions. Furthermore, theoretical analysis is also given to prove the significant relaxation of the proposed convergence conditions. Finally, effectiveness of the proposed learning approach is demonstrated via a simulation study.

Koopman-based surrogate models for multi-objective optimization of agent-based systems

Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend potentially nonlinearly on control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.

Comparison of a Hybrid Firefly–Particle Swarm Optimization Algorithm with Six Hybrid Firefly–Differential Evolution Algorithms and an Effective Cost-Saving Allocation Method for Ridesharing Recommendation Systems

The optimization and allocation of transport cost savings among stakeholders are two important issues that influence the satisfaction of information providers, drivers and passengers in ridesharing recommendation systems. For optimization issues, finding optimal solutions for nonconvex constrained discrete ridesharing optimization problems poses a challenge due to computational complexity. For the allocation of transport cost savings issues, the development of an effective method to allocate cost savings in ridesharing recommendation systems is an urgent need to improve the acceptability of ridesharing. The hybridization of different metaheuristic approaches has demonstrated its advantages in tackling the complexity of optimization problems. The principle of the hybridization of metaheuristic approaches is similar to a marriage of two people with the goal of having a happy ending. However, the effectiveness of hybrid metaheuristic algorithms is unknown a priori and depends on the problem to be solved. This is similar to a situation where no one knows whether a marriage will have a happy ending a priori. Whether the hybridization of the Firefly Algorithm (FA) with Particle Swarm Optimization (PSO) or Differential Evolution (DE) can work effectively in solving ridesharing optimization problems needs further study. Motivated by deficiencies in existing studies, this paper focuses on the effectiveness of hybrid metaheuristic algorithms for solving ridesharing problems based on the hybridization of FA with PSO or the hybridization of FA with DE. Another focus of this paper is to propose and study the effectiveness of a new method to allocate ridesharing cost savings to the stakeholders in ridesharing systems. The developed hybrid metaheuristic algorithms and the allocation method have been compared with examples of several application scenarios to illustrate their effectiveness. The results indicate that hybridizing FA with PSO creates a more efficient algorithm, whereas hybridizing FA with DE does not lead to a more efficient algorithm for the ridesharing recommendation problem. An interesting finding of this study is very similar to what happens in the real world: “Not all marriages have happy endings”.

Inexact Exponential Penalty Function with the Augmented Lagrangian for Multiobjective Optimization Algorithms

This paper uses an augmented Lagrangian method based on an inexact exponential penalty function to solve constrained multiobjective optimization problems. Two algorithms have been proposed in this study. The first algorithm uses a projected gradient, while the second uses the steepest descent method. By these algorithms, we have been able to generate a set of nondominated points that approximate the Pareto optimal solutions of the initial problem. Some proofs of theoretical convergence are also proposed for two different criteria for the set of generated stationary Pareto points. In addition, we compared our method with the NSGA-II and augmented the Lagrangian cone method on some test problems from the literature. A numerical analysis of the obtained solutions indicates that our method is competitive with regard to the test problems used for the comparison.

A safety-guaranteed game-theoretical velocity planning for autonomous vehicles on sharp curve roads

In this paper, a safety-guaranteed game-theoretical velocity planning framework in a hierarchical manner is proposed to generate safe, ride comfort, and travel efficiency-balanced velocity for autonomous vehicles (AVs). In the upper layer, a bang-bang decision-making method is utilized to determine which planning mode to be implemented based on acceleration and jerk constraints, including a comfort mode, an efficiency mode, and a game mode. In the lower layer, asymmetric jerk limits based on comfort characteristics sensibility analysis and safe velocity simultaneously considering longitudinal and lateral stability are firstly developed to maintain ride comfort and driving safety, respectively on curve roads, especially sharp curves where vehicle stability may be not fully considered in most researches. Based on these, a non-cooperative game-theoretical velocity planning method is presented to solve the conflict between comfort mode and efficiency mode by optimizing his own objective based on the other’s action. Finally, for the sake of solving efficiency and accuracy, a chaos optimization-based algorithm (COA) is designed to solve for the Stackelberg equilibrium solution of the bilevel game optimization problem. Three experimental tests are carried out to comprehensively demonstrate the effectiveness, robustness, and real time of the proposed framework. The results show that the proposed method can provide the great performance of ride comfort, travel efficiency, and longitudinal-lateral stability in real time in the velocity planning process.

Method for prediction and control by uncertain microsatellite magnetic cleanliness based on calculation and compensation magnetic field spatial harmonics

Aim. Development of method for prediction and control the microsatellite magnetic cleanliness taking into account the uncertainties of the magnetic characteristics of the microsatellite, based on calculation the magnetic field spatial spherical harmonics in the area of the onboard magnetometer installation and using compensating multipoles. Methodology. Spatial spherical harmonics of microsatellite magnetic field in the area of the onboard magnetometer installation calculated as solution of nonlinear minimax optimization problem based on near field measurements for prediction far spacecraft magnetic field magnitude. Nonlinear objective function calculated as the weighted sum of squared residuals between the measured and predicted magnetic field. Values of the compensating dipoles, quadrupoles and octupoles and coordinates of them placement inside the spaceship for compensation of the dipoles, quadrupoles and octupoles components of the microsatellite initial magnetic field also calculated as solution of nonlinear minimax optimization problem. Both solutions of this nonlinear minimax optimization problems calculated based on particle swarm nonlinear optimization algorithms. Results. Results of prediction spacecraft far magnetic field magnitude based on spacecraft spatial spherical harmonics of the magnetic field using near field measurements and compensation of the dipoles, quadrupoles and octupoles components of the initial magnetic field with consideration of spacecraft magnetic characteristics uncertainty for ensuring the microsatellite magnetic cleanliness. Originality. The method for prediction and control by spacecraft magnetic cleanliness based on calculation spatial spherical harmonics of the magnetic field in the area of the onboard magnetometer installation using compensation of the dipoles, quadrupoles and octupoles components of the initial magnetic field with consideration of magnetic characteristics uncertainty is developed. Practical value. The important practical problem of ensuring the magnetic cleanliness of the «Sich-2» microsatellite family based on the spatial spherical harmonics of the magnetic field model using the compensation of the dipole, quadrupole and octupole components of the output magnetic field of the sensor for the kinetic parameters of the neutral component of the space plasma at the point of installation of the on-board magnetometer LEMI-016 by setting the compensating dipole, quadrupole and octupole with consideration of spacecraft magnetic characteristics uncertainty solved.