Solution Of Optimization Problem Research Articles

Automatic Docking Trajectory Design-Based Time-Varying-Radius Dubins for Unmanned Surface Vessel

Facing the demand of efficient automatic docking for USV, this paper proposes a new kind of iterative varying-radius Dubins curve design. Due to the special mobility of dockyards, one novel trajectory optimization problem considering time optimum is modeled first. Then, we use the ant colony optimization (ACO) algorithm to solve such a complex problem. In addition to the global exhaustive search algorithm and ACO-based solution, a novel distributed local path planning algorithm named ADTA-TRD is proposed to obtain the solution of the above optimization problem restricted by the local perception of the USV. In essence, this paper draws lessons from the idea of the circular arc segment and straight line segment in the traditional Dubins curve, and consequently, the smoothness of the derived automatic docking trajectory can be guaranteed. Finally, the performance of proposed automatic docking path planning method is verified through simulation results and an actual sea trial.

A reinforcement learning-based metaheuristic algorithm for solving global optimization problems

The purpose of this study is to utilize reinforcement learning in order to improve the performance of the Sand Cat Swarm Optimization algorithm (SCSO). In this paper, we propose a novel algorithm for the solution of global optimization problems that is called RLSCSO. In this method, metaheuristic algorithm is combined with reinforcement learning techniques to form a hybrid metaheuristic algorithm. This study aims to provide search agents with the opportunity to perform efficient exploration of the search space in order to find a global optimal solution by using efficient exploration and exploitation to find optimal solutions within a given search space. A comprehensive evaluation of the RLSCSO has been conducted on 20 benchmark functions and 100-digit challenge basic test functions. Additionally, the proposed algorithm is applied to the problem of localizing mobile sensor nodes, which is NP-hard (nondeterministic polynomial time). Several extensive analyses have been conducted in order to determine the effectiveness and efficiency of the proposed algorithm in solving global optimization problems. In terms of cost values, the RLSCSO algorithm provides the optimal solution, along with tradeoffs between exploration and exploitation.

S-Iteration inertial subgradient extragradient method for variational inequality and fixed point problems

In developing iterative methods for approximating solutions of optimization problems, one of the major goals of researchers is to construct efficient iterative schemes. Over the years, different techniques have been devised by authors to achieve this goal. In this paper, we study a non-Lipschitz pseudomonotone variational inequality problem with common fixed points constraint of Bregman quasi-nonexpansive mappings. We introduce a new iterative method for approximating the solution of this problem in a more general framework of reflexive Banach spaces. Our method employs several techniques to achieve high level of efficiency. One of the techniques employed is the S-iteration process, a method known to be highly efficient in comparison with several of the well-known methods. Moreover, our proposed algorithm utilizes the inertial technique and a non-monotonic self-adaptive step size to guarantee high rate of convergence and easy implementation. Unlike several of the existing results on variational inequality problem with non-Lipschitz operator, the design of our method does not involve any linesearch technique. We obtain strong convergence result for the proposed algorithm without the sequentially weakly continuity condition often assumed by authors to guarantee convergence when solving pseudomonotone variational inequality problems. Furthermore, we apply our result to study utility-based bandwidth allocation problem and image restoration problem. Finally, we present several numerical experiments to demonstrate the efficiency of our proposed method in comparison with existing state-of-the-art methods. Our result extends and improves several of the recently announced results in this direction in the literature.

Solving a multi-objective chance constrained hierarchical optimization problem under intuitionistic fuzzy environment with its application

Various optimization approaches have been developed and used for generating optimal solutions for different industry related optimization problems. The semantic representation of imprecise coefficients and various types of uncertainties arising in real life optimization problems are still a challenging task and require attention of academicians as well as professionals. Decision makers (DMs) often face problems in presenting the linguistically expressed constraints. The impreciseness of information also plays a key role in modelling and thus in decision making. The impreciseness of coefficients is usually handled by using various elements of fuzzy set theory. The uncertainty associated with constraints in optimization problem is handled by using stochastic programming approaches. These coefficients are usually revealed by a logical DM, who takes into account the scope of hesitation along with the imprecise nature of data. Such coefficients can be very well represented by using Intuitionistic fuzzy numbers. In this work, an approach for solving multi-objective bi-level chance constrained optimization problem in an intuitionistic fuzzy environment has been presented. The technological coefficients and the coefficients of objective functions are represented by Triangular Intuitionistic fuzzy numbers whereas normal random variables are used to represent the coefficient of resources. The concept of component wise optimization is used for the reduction of intuitionistic fuzzy objective into their equivalent deterministic form. The concept of alpha-beta cut, chance constrained programming and interval programming are then used to convert the problem into a deterministic multi-objective bi-level linear programming problem. The resultant deterministic optimization problem is then solved by using TOPSIS method. The production planning problem of a firm has been modelled and solved by using the proposed approach.

Calibration of Watershed Conceptual Models Using Local and Global ptimization

Many issues related to water resources require the solution of optimization problems. Optimization problems can be quite difficult such as the calibration of many conceptual watershed models. Conceptual watershed models are formulated using empirical relationships between hydrological variables observed in nature or field experiments .The success of automatic calibration depends mainly on the choice of optimization method. Most early attempts to calibrate watershed models have been based on local-search optimization methods. Local optimization methods are not designed to handle the presence of multiple regions of attraction, multi-local optima, insensitivities and parameter interdependencies, and other problems encountered in the calibration of watersheds models. It is therefore imperative that global optimization procedures that are capable of dealing with these various difficulties be employed. In this study, one local search optimization method and one global search method are used to calibrate the parameters a simple tenparameter rainfall-runoff model. The local search method is the well-known Rosenbrock's direct search method; the global search method is the newly developed Shuffled Complex Evolution (SCE) method . The results revealed that Shuffle Complex Evolution optimization method is more superior to Rosenbrok’s direct search method. The results confirmed the finding of many watershed modellers about the dependency of Rosenbrock’s method on the choice of initial search points. It further adds that Rosenbrock’s method is only effective when the initial search points are taken within 5 % or less from the true optimum parameter set. The results indicate that a proper choice of optimization methods can enhance the possibility of obtaining unique and conceptually realistic parameter estimate.

An Improved MOEA/D Algorithm for the Solution of the Multi-Objective Optimal Power Flow Problem

The optimal power flow (OPF) is an important tool for the secure and economic operation of the power system. It attracts many researchers to pay close attention. Many algorithms are used to solve the OPF problem. The decomposition-based multi-objective algorithm (MOEA/D) is one of them. However, the effectiveness of the algorithm decreases as the size of the power system increases. Therefore, an improved MOEA/D (IMOEA/D) is proposed in this paper to solve the OPF problem. The main goal of IMOEA/D is to speed up the convergence of the algorithm and increase species diversity. To achieve this goal, three improvement strategies are introduced. Firstly, the competition strategy between the barnacle optimization algorithm and differential evolution algorithm is adopted to overcome the reduced species diversity. Secondly, an adaptive mutation strategy is employed to enhance species diversity at the latter stage of iteration. Finally, the selective candidate with similarity selection is used to balance the exploration and exploitation capabilities of the proposed algorithm. Simulation experiments are performed on IEEE 30-bus and IEEE 57-bus test systems. The obtained results show that the above three measures can effectively improve the diversity of the population, and also demonstrate the competitiveness and effectiveness of the proposed algorithm for the OPF problem.

Stability of solutions for fuzzy set optimization problems with applications

In this paper, we introduce a new parametric fuzzy set optimization problem based on the ordering relations of fuzzy sets, where a parametric function and an objective function both take values on fuzzy sets. We show the continuity of solution mappings for such a problem under some mild conditions. Moreover, we give the Painlevé-Kuratowski upper convergence and lower convergence of solution sets for fuzzy set optimization problems. As applications, the stability results are applied to obtain the continuity of a minimal solution mapping and the Painlevé-Kuratowski convergence of minimal solution sets for continuous-time fuzzy set optimization problems.

The geometry of adversarial training in binary classification

AbstractWe establish an equivalence between a family of adversarial training problems for non-parametric binary classification and a family of regularized risk minimization problems where the regularizer is a nonlocal perimeter functional. The resulting regularized risk minimization problems admit exact convex relaxations of the type $L^1+\text{(nonlocal)}\operatorname{TV}$, a form frequently studied in image analysis and graph-based learning. A rich geometric structure is revealed by this reformulation which in turn allows us to establish a series of properties of optimal solutions of the original problem, including the existence of minimal and maximal solutions (interpreted in a suitable sense) and the existence of regular solutions (also interpreted in a suitable sense). In addition, we highlight how the connection between adversarial training and perimeter minimization problems provides a novel, directly interpretable, statistical motivation for a family of regularized risk minimization problems involving perimeter/total variation. The majority of our theoretical results are independent of the distance used to define adversarial attacks.

Slime Mould Algorithm: A Comprehensive Survey of Its Variants and Applications.

Meta-heuristic algorithms have a high position among academic researchers in various fields, such as science and engineering, in solving optimization problems. These algorithms can provide the most optimal solutions for optimization problems. This paper investigates a new meta-heuristic algorithm called Slime Mould algorithm (SMA) from different optimization aspects. The SMA algorithm was invented due to the fluctuating behavior of slime mold in nature. It has several new features with a unique mathematical model that uses adaptive weights to simulate the biological wave. It provides an optimal pathway for connecting food with high exploration and exploitation ability. As of 2020, many types of research based on SMA have been published in various scientific databases, including IEEE, Elsevier, Springer, Wiley, Tandfonline, MDPI, etc. In this paper, based on SMA, four areas of hybridization, progress, changes, and optimization are covered. The rate of using SMA in the mentioned areas is 15, 36, 7, and 42%, respectively. According to the findings, it can be claimed that SMA has been repeatedly used in solving optimization problems. As a result, it is anticipated that this paper will be beneficial for engineers, professionals, and academic scientists.

Grammatical-Evolution-based parameterized Model Predictive Control for urban traffic networks

While Model Predictive Control (MPC) is a promising approach for network-wide control of urban traffic, the computational complexity of the, often nonlinear, online optimization procedure is too high for real-time implementations. In order to make MPC computationally efficient, this paper introduces a parameterized MPC (PMPC) approach for urban traffic networks that uses Grammatical Evolution to construct continuous parameterized control laws using an effective simulation-based training framework. Furthermore, a projection-based method is proposed to remove the nonlinear constraints that are imposed on the parameters of the parameterized control laws and to guarantee the feasibility of the solution of the MPC optimization problem. The performance and computational efficiency of the constructed parameterized control laws are compared to those of a conventional MPC controller in an extensive simulation-based case study. The results show that the parameterized control laws, which are automatically constructed using Grammatical Evolution, decrease the computational complexity of the online optimization problem by more than 80% with a decrease in performance by less than 10%.

Robust duality for robust efficient solutions in uncertain vector optimization problems

Robust duality for robust efficient solutions in uncertain vector optimization problems

A New Approach of Evaluating the Security Against Differential and Linear Cryptanalysis and Its Applications to Serpent, NOEKEON and ASCON

Abstract In recent years, Mixed-Integer Linear Programming (MILP)-based automatic tools have played a significant role in providing security evaluations of symmetric-key primitives. Differential and linear cryptanalysis are the two most important cryptographic techniques. Although some methods have conducted a great effort in exploiting MILP-aided tools in searching for differential (linear) characteristics, traditional methods still suffer from primitives with strong diffusion layers and large sizes, such as NOEKEON. Typically, searching for differential (linear) characteristics of such primitives is difficult, and the corresponding MILP models are too heavy to be solved efficiently. To this end, we propose a simple yet efficient approach to employ MILP to evaluate the security against differential and linear cryptanalysis of such primitives. The core of our approach is to reduce the complex problem to a set of simpler subproblems and obtain the optimal solution of the complex problem by combining all the subproblems. A subproblem is equivalent to searching for all differential (linear) characteristics with a fixed number of active S-boxes in each round. Furthermore, we design an elaborate algorithm consisting of three MILP-aided methods to solve various subproblems and adopt some techniques to improve efficiency further. Applying our new algorithm to three SPN primitives Serpent, NOEKEON and ASCON, we obtain the tightest security bounds against differential and linear cryptanalysis for all three primitives so far and find improved differential and linear characteristics for Serpent and NOEKEON. For Serpent, we improve the upper bound of the maximum probability of 7-round differential characteristics from $2^{-71}$ to $2^{-76}$ and find for the first time 7-round differential characteristics. For NOEKEON, our results show that there is no 9-round (10-round) differential (linear) characteristic with a probability (correlation) higher than $2^{-128}$ ($2^{-64}$), whereas it needs 10 rounds (11 rounds) according to the previous results. In addition, we find an 8-round (9-round) differential (linear) characteristic with a probability (correlation) of $2^{-127}$ ($2^{-60}$). For ASCON permutation, we provide for the first time an upper bound of the maximum probability (correlation) of 5-round differential (linear) characteristics as $2^{-70}$ ($2^{-33}$).

Computation of the phase and gain margins of MIMO control systems

This paper solves the problem of exact computation of the phase and gain margins of multivariable control systems. These stability margins are studied using the concept of the Davis–Wielandt shell of complex matrices. Calculation of the phase and gain margins requires solving a quadratically constrained quadratic program (QCQP) and a parametrized quadratically constrained problem, respectively, which are known to be difficult in general. The semidefinite relaxation (SDR) technique is often used as a computationally efficient approximation technique to solve QCQPs. It turns out that the QCQPs formulated from the phase and gain margin problems in this paper fall under the class of quadratic optimization problem, for which the SDR is exact. This is so in the sense that optimal values of the QCQP and its SDR are equal, and an optimal solution for the original QCQP problem can be obtained from an optimal solution of its SDR. Thus, we are able to propose computationally efficient algorithms to compute the phase and gain margins with an arbitrarily high precision. Numerical examples are given to illustrate the effectiveness of the proposed algorithms.

A Stackelberg game scheme for pricing and task offloading based on idle node-assisted edge computational model

Mobile edge server (MES) can meet the low latency requirements of End user (EU) tasks, but the MES computing resources are limited. This paper proposes an IDs-assisted MES (MES-IDs) computing model to expand MES. However, how to find a task offload strategy to minimize EU calculation costs and improve MES and ID benefits on a task completion basis. This paper proposes a three-way optimization calculation method based on the Stackelberg game to reduce the problem complexity, which decomposes into EUs-BS and BS-IDs problems. The EUs-BS problem design pricing scheme obtains the EU task optimal offload rate. The BS-IDs problem uses nonlinear pricing methods to find the optimal task offload problem between MES and ID on the resource unit price, a multi-constrained nonlinear convex optimization problem. We propose an immune Metropolis-based particle swarm loss optimization algorithm (PIMA) to obtain an approximate optimal solution for the nonlinear convex optimization problem by adjusting the resource price. Numerical simulation results show that compared with GSP and PSI algorithms, the PIMA algorithm shows more robust stability and can effectively reduce task completion delay and computational cost.

Trihedral Lattice Towers Optimization with a Limitation on the Resonant Vortex Excitation Occurrence

Trihedral lattice towers are widely used as transmission line supports, wind turbine supports, cell towers, and floodlight towers. The aim of this work is to develop a technique for optimizing trihedral lattice supports to reduce their weight, taking into account the limitation on resonant vortex excitation. At the same time, restrictions are also introduced on the maximum stress, as well as the ultimate slenderness of the elements. Thus, with a minimum weight, the tower must meet all the requirements of the design codes. A lattice tower used as a floodlight mast is considered. The tower consists of two sections, the upper of which is of constant width, and the width of the lower section varies according to a linear law. The elements of the tower are made from pipes with an annular cross section. The sections’ widths and heights, the dimensions of elements’ cross-sections, and the number of panels are the variable parameters. The solution of the nonlinear optimization problem is implemented in MATLAB software. Internal forces in the tower and natural frequencies are calculated by the finite element method. The tower is subjected to the action of ice and wind loads, dead weight and the weight of the equipment. The wind load is considered as the sum of the average and pulsation components. To solve the problem of nonlinear optimization, the surrogate optimization method and the genetic algorithm are used. One of the serially used designs was chosen as the initial approximation. The design obtained as a result of optimization compared to the initial approximation has a mass more than two times less and at the same time satisfies all design requirements.

A deep reinforcement learning approach for solving the Traveling Salesman Problem with Drone

Reinforcement learning has recently shown promise in learning quality solutions in many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems, including the Traveling Salesman Problem (TSP). Unfortunately, they perform poorly for the TSP with Drone (TSP-D), requiring routing a heterogeneous fleet of vehicles in coordination—a truck and a drone. In TSP-D, the two vehicles are moving in tandem and may need to wait at a node for the other vehicle to join. State-less attention-based decoder fails to make such coordination between vehicles. We propose a hybrid model that uses an attention encoder and a Long Short-Term Memory (LSTM) network decoder, in which the decoder’s hidden state can represent the sequence of actions made. We empirically demonstrate that such a hybrid model improves upon a purely attention-based model for both solution quality and computational efficiency. Our experiments on the min-max Capacitated Vehicle Routing Problem (mmCVRP) also confirm that the hybrid model is more suitable for the coordinated routing of multiple vehicles than the attention-based model. The proposed model demonstrates comparable results as the operations research baseline methods.

A new method to determine the Fermatean fuzzy optimal solution of transportation problems

Transportation Problems (TP) have multiple applications in supply chain management to reduce costs. Efficient methods have been developed to address TP when all factors, including supply, demand, and unit transportation costs, are precisely known. However, due to uncertainty in practical applications, it is necessary to study TP in an uncertain environment. In this paper, we define the Trapezoidal Fermatean Fuzzy Number (TrFFN) and its arithmetic operations. Then we introduce a new approach to solve TP, where transportation cost, supply, and demand are treated as TrFFN, and we call it Fermatean Fuzzy TP (FFTP). We illustrate the feasibility and superiority of this method with two application examples, and compare the performance of this method with existing methods. Furthermore, the advantages of the proposed method over existing methods are described to address TP in uncertain environments.

Noncooperative Distributed Model Predictive Control: A Multiparametric Programming Approach

The distributed control system architecture strikes a balance between the decentralized control system architecture, where subsystem interactions are unaccounted for, and the computationally expensive centralized control system architecture. Subsystem interactions can be significant in chemical process systems, especially when energy or material recycle loops are present. A drawback of the distributed control system is that it is computationally expensive as it requires intermediate iterations involving the solution of multiple optimization problems to be performed. To address this drawback, we develop a noncooperative, iterative, multiparametric distributed model predictive control (mpDiMPC) technique with an aim to decrease the computational costs of conventional, online distributed controllers by avoiding the need to solve an optimization problem at each intermediate iteration. We apply the developed control algorithm on an interacting reactor–separator process and study its control and computational performance. For the case study presented in this paper, mpDiMPC resulted in a reduction in computational costs by approximately 95% compared to its online counterpart.

Enhancing grasshopper optimization algorithm (GOA) with levy flight for engineering applications

The grasshopper optimization algorithm (GOA) is a meta-heuristic algorithm proposed in 2017 mimics the biological behavior of grasshopper swarms seeking food sources in nature for solving optimization problems. Nonetheless, some shortcomings exist in the origin GOA, and GOA global search ability is more or less insufficient and precision also needs to be further improved. Although there are many different GOA variants in the literature, the problem of inefficient and rough precision has still emerged in GOA variants. Aiming at these deficiencies, this paper develops an improved version of GOA with Levy Flight mechanism called LFGOA to alleviate the shortcomings of the origin GOA. The LFGOA algorithm achieved a more suitable balance between exploitation and exploration during searching for the most promising region. The performance of LFGOA is tested using 23 mathematical benchmark functions in comparison with the eight well-known meta-heuristic algorithms and seven real-world engineering problems. The statistical analysis and experimental results show the efficiency of LFGOA. According to obtained results, it is possible to say that the LFGOA algorithm can be a potential alternative in the solution of meta-heuristic optimization problems as it has high exploration and exploitation capabilities.

Solving distributed-order fractional optimal control problems via the Fibonacci wavelet method

A new approach to finding the approximate solution of distributed-order fractional optimal control problems (D-O FOCPs) is proposed. This method is based on Fibonacci wavelets (FWs). We present a new Riemann–Liouville operational matrix for FWs using the hypergeometric function. Using this, an operational matrix of the distributed-order fractional derivative is presented. Implementing the mentioned operational matrix with the help of the Gauss–Legendre numerical integration, the problem converts to a system of algebraic equations. Error analysis is proposed. Finally, the validation of the present technique is checked by solving some numerical examples.