Hybrid differential evolution including geometric mean mutation for optimization of biochemical systems

Inspired by the phenomenon of migration of monarch butterflies, Wang et al. developed a novel promising swarm intelligence algorithm, called monarch butterfly optimization (MBO), for addressing unconstrained low-dimensional optimization problems. In this paper, we firstly extend the application area of the basic MBO to solve the constrained optimization problems. At the same time, the crossover operator originally used in evolutionary algorithms (EAs) is incorporated into the butterfly adjusting operator in order to strengthen the exploitation of the basic MBO algorithm. Furthermore, the crossover rate is self-adaptively adjusted according to the fitness of the corresponding individual instead of the fixed crossover rate used in EAs. For migration operator, only individuals having better fitness are accepted and passed to the next generation instead of accepting all the individuals in the basic MBO algorithm. After incorporated all the modifications into the basic MBO algorithm, an improved MBO algorithm with self-adaptive crossover namely SACMBO, is proposed for unstrained and constrained optimization problems. Finally, the proposed SACMBO algorithm is further used to solve 22 unstrained optimization problems (with dimension of 100, 300, 500, 1000, and 1500) and 28 constrained real-parameter optimization functions from CEC 2017 competition (with dimension of 50 and 100), respectively. The experimental results indicate that the proposed SACMBO algorithm outperforms the basic MBO and other five state-of-the-art metaheuristic algorithms.

Symbolic functions, as an important class of nonsmooth functions, play a key role in many fields such as system control and optimization theory. In this study, the special case of nonlinear optimization problems with sign function constraints is discussed in depth. Based on the smooth approximation theory, the study first adopts an approximate substitution method to smooth the nonsmooth constraints and then transforms them into differentiable optimization problems, thus effectively avoiding the numerical computational difficulties caused by the sign function. Second, the constrained optimization problem is transformed into an unconstrained optimization problem by constructing an exact penalty function. Third, two forms of second-order dynamical systems are established to solve the problem, and a rigorous theoretical analysis of the stability of these systems is conducted. Finally, the convergence and computational efficiency of the proposed method are verified by numerical simulation experiments of the system, and the simulation results fully prove the effectiveness and practicality of the algorithm.

Generalized Nash equilibrium problems (GNEPs) allow, in contrast to standard Nash equilibrium problems, a dependence of the strategy space of one player from the decisions of the other players. In this paper, we consider jointly convex GNEPs which form an important subclass of the general GNEPs. Based on a regularized Nikaido-Isoda function, we present two (nonsmooth) reformulations of this class of GNEPs, one reformulation being a constrained optimization problem and the other one being an unconstrained optimization problem. While most approaches in the literature compute only a so-called normalized Nash equilibrium, which is a subset of all solutions, our two approaches have the property that their minima characterize the set of all solutions of a GNEP. We also investigate the smoothness properties of our two optimization problems and show that both problems are continuous under a Slater-type condition and, in fact, piecewise continuously differentiable under the constant rank constraint qualification. Finally, we present some numerical results based on our unconstrained optimization reformulation.

Informative path planning is an important and challenging problem in robotics that remains to be solved in a manner that allows for wide-spread implementation and real-world practical adoption. Among various reasons for this, one is the lack of approaches that allow for informative path planning in high-dimensional spaces and non-trivial sensor constraints. In this work we present a sampling-based approach that allows us to tackle the challenges of large and high-dimensional search spaces. This is done by performing informed sampling in the high-dimensional continuous space and incorporating potential information gain along edges in the reward estimation. This method rapidly generates a global path that maximizes information gain for the given path budget constraints. We discuss the details of our implementation for an example use case of searching for multiple objects of interest in a large search space using a fixed-wing UAV with a forward-facing camera. We compare our approach to a sampling-based planner baseline and demonstrate how our contributions allow our approach to consistently out-perform the baseline by 18.0%. With this we thus present a practical and generalizable informative path planning framework that can be used for very large environments, limited budgets, and high dimensional search spaces, such as robots with motion constraints or high-dimensional configuration spaces. [Code] <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> Codebase: https://github.com/castacks/tigris [Video] <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sup> Video: https://youtu.be/bMw5nUGL5GQ

The term, "Waveform inversion" (WFI), refers to a collection of techniques that use the information from seismic data to derive high-fidelity earth models for seismic imaging. The attractiveness of WFI lies mainly in its lack of approximations, at least in a theoretical sense, in contrast to other model determination techniques such as semblance or tomography. However, a whole raft of approximations must be made to make the technique viable with today'scomputing technology and restrictions of seismic acquisition. These are collectively referred to as "waveform inversion strategies" and in this paper we mainly discuss regularization and preconditioning strategies. Because the wavefields need to be accurately modeled to represent the kinematics of all the waves during WFI iterations, the effects of anisotropy often help to improve WFI results. In this paper, forward modeling and its adjoint computation are based on acoustic wave equations in vertical transversely isotropic (VTI)media. We introduce a multi-parameter inversion for P-wave velocity and anisotropy parameters. WFI is a highly nonlinear, ill-posed problem. We introduce additional information and turn the unconstrained optimization problem into a constrained optimization problem in order to reduce the ill-posedness. The geophysics of the problem leads to appropriate constraints, such as restriction of model parameters, or information from well logs. In this paper, we use well logs as constraints and solve the problem using the augmented Lagrangian method (ALM), a mathematical method that replaces a constrained optimization problem by a series of unconstrained problems. The ALM with well constraints aims at preserving velocity characteristics from welllogs and providing us with more reliable velocity updates. This paper presents the acoustic anisotropic WFI implementation using ALM with well constraints. It also discusses practical strategies for regularization and preconditioning and their influences on the models that are obtained from WFI. We illustrate these approaches on a 2D synthetic Marmousi example and another application to 3D VSOOBC data from the Green Canyon area of the Gulf of Mexico. From the results, we show that multi-parameter VTI WFI with ALM provides us with more useful and reliable model updates. To further evaluate our WFI results, we also compare offset gathers and RTM images and illustrate their significant improvement susing updated models generated from WFI.

The Meta heuristic algorithms are the higher level technique which helps to find the best feasible solution out of all possible solution of an optimization problem. There are various different types of meta heuristic algorithms like Ant Colony Optimization (ACO), Genetic Algorithm, Simulated Annealing, Particle Swarm Optimization, etc. Genetic Algorithm is a search-based optimization technique based on the biological principle of Genetics and adaptation. It is a meta-heuristic approach which is used to solve complex combinatorial problem. The integration of Genetic algorithm with machine learning will be helpful in solving unconstrained and constrained optimization problem. The various genetic operator like selection operator, mutation and cross-over are discussed which will be helpful in knowing how these operators significantly improves State Space search. In this paper the various applications of Genetic algorithms which can be used in machine learning has been discussed. In this paper the author discussed how the significance of Genetic algorithm will be improved while solving complex optimization problem in machine learning. In this paper, flow diagram of Genetic Algorithms has been discussed which will ease the understanding of complex optimization problem like 0–1 Knapsack, Traveling Salesman Problem, etc. In this paper a comparative analysis between traditional algorithm and genetic algorithm has been done on the basis of parameters like flow of control, state space search, Complication, Preconditions, CPU utilization etc. The various limitations of Genetic Algorithms in solving problems with optimal solutions has also been discussed.

This paper presents a genetic algorithm (GA) approach to solve the redundancy allocation problem (RAP) with imprecise parameters. The impreciseness has been considered here to tackle the unpredictable environment in real-life affairs which is directly striking the design parameters. Imprecise parameters are represented by several types of representations, viz. fuzzy, stochastic, and deterministic interval-valued. In the case of fuzzy and stochastic representations, the corresponding problems have been transformed into a deterministic interval optimization problem. Hence, to solve the problem, a GA based penalty function technique is proposed. The constraint(s) of the same are handled by constraints satisfaction rule which has been proposed in this paper. In the proposed approach, the constrained optimization problem has been converted into an unconstrained optimization problem by use of Big-M penalty technique. To solve the RAP with imprecise parameters, GA has been implemented. Finally, numerical experiments have been done for illustration purpose.

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. In terms of the objective function, most existing research has been focused on the makespan criterion. However, in contemporary manufacturing systems, due‐date‐related performances are more important because they are essential for maintaining a high service reputation. Therefore, in this study we aim at minimizing the total weighted tardiness in JSSP. Considering the high complexity, a hybrid differential evolution (DE) algorithm is proposed for the problem. To enhance the overall search efficiency, a neighborhood property of the problem is discovered, and then a tree search procedure is designed and embedded into the DE framework. According to the extensive computational experiments, the proposed approach is efficient in solving the job shop scheduling problem with total weighted tardiness objective.

A heuristic approach to optimization of complex physicochemical processes in the form of a genetic algorithm for solving problems is presented. In comparison with other evolutionary methods, the genetic algorithm allows working with large search spaces and complex evaluation functions, which is especially important in the study of multifactor physicochemical systems. Due to the relatively high need for computing resources when working with large and complex search spaces, optimization of existing calculation organization schemes has a positive effect on the accuracy of the calculated results. The paper presents a modified genetic algorithm that minimizes the number of iterations to achieve a given accuracy when solving the problem of finding the optimal composition of the initial reaction mixture. For a complex physicochemical process, an optimization problem is formulated which consists in finding the composition of the initial reaction mixture that promotes maximization (or minimization) of a given target parameter. The optimality criterion is determined by the type of the problem being solved and, when organizing calculations, is focused on the maximum yield of the target product. The main steps of implementing the genetic algorithm include creating an initial set of solutions and subsequent iterative evaluation of their quality for subsequent combination and modification until optimal values are achieved using mechanisms similar to biological evolution. To improve the efficiency of the method and reduce the number of iterations, a modification of the genetic algorithm is proposed which boils down to a dynamic estimate of the “mutation” parameter, depending on the diversity of individuals in the formed population of solutions. In a series of computational experiments, an analysis was made of the influence of the genetic algorithm parameters on the accuracy and efficiency of solving the problem using the example of studying the kinetics of the Michaelis-Menten enzymatic reaction. The results of calculations to determine the optimal composition of the reaction mixture showed that the dynamic determination of the “mutation” parameter contributes to an increase in the accuracy of the problem solution and a multiple decrease in the relative error value reaching 0.77 % when performing 200 iterations and 0.21 % when performing 400 iterations. The presented modified approach to solving the optimization problem is not limited by the type and content of the studied physicochemical process. The calculations performed showed a high degree of influence of the “mutation” parameter on the accuracy and efficiency of the problem solution, and dynamic control of the value of this parameter allowed increasing the speed of the genetic algorithm and reduce the number of iterations to achieve an optimal solution of a given accuracy. This is especially relevant in the study of multifactorial systems when the influence of parameters is non-trivial.

Evolutionary optimized Padé approximation scheme for analysis of covid-19 model with crowding effect

A piecewise linear chaotic map and sequential quadratic programming based robust hybrid particle swarm optimization

An important and challenging data mining application in marketing is to learn models for predicting potential customers who contribute large profit to a company under resource constraints. In this paper, we first formulate this learning problem as a constrained optimization problem and then converse it to an unconstrained Multi-objective Optimization Problem (MOP). A parallel Multi-Objective Evolutionary Algorithm (MOEA) on consumer-level graphics hardware is used to handle the MOP. We perform experiments on a real-life direct marketing problem to compare the proposed method with the parallel Hybrid Genetic Algorithm, the DMAX approach, and a sequential MOEA. It is observed that the proposed method is much more effective and efficient than the other approaches.

Immunity-based hybrid evolutionary algorithm for multi-objective optimization in global container repositioning

In this paper, energy efficient power control for small cells underlaying a macro cellular network is investigated. We formulate the power control problem in self-organizing small cell networks as a non-cooperative game, and propose a distributed energy efficient power control scheme, which allows the small base stations (SBSs) to take individual decisions for attaining the Nash equilibrium (NE) with minimum information exchange. Specially, in the non-cooperative power control game, a non-convex optimization problem is formulated for each SBS to maximize their energy efficiency (EE). By exploiting the properties of parameter-free fractional programming and the concept of perspective function, the non-convex optimization problem for each SBS is transformed into an equivalent constrained convex optimization problem. Then, the constrained convex optimization problem is converted into an unconstrained convex optimization problem by exploiting the mixed penalty function method. The inequality constraints are eliminated by introducing the logarithmic barrier functions and the equality constraint is eliminated by introducing the quadratic penalty function. We also theoretically show the existence and the uniqueness of the NE in the non-cooperative power control game. Simulation results show remarkable improvements in terms of EE by using the proposed scheme.

Spacecraft safe proximity, as a critical component of on-orbit servicing missions, primarily encounters the following two challenges: the partial observability of the environment surrounding the service spacecraft and the necessity to evade uncertain obstacles. A safe reinforcement learning algorithm based on a graph neural network is proposed to address the constrained Markov decision problem in partially observable scenarios for spacecraft safe proximity missions. A graph neural network mechanism is introduced to solve the problem of dynamic variations in the quantity and location of obstacles in the observation area of the service spacecraft. The graph attention network is used to facilitate the extraction of feature information from the graph structure, which is then utilized as input for the subsequent reinforcement learning algorithm. The Soft Actor–Critic–Lagrangian algorithm is adopted to deal with the problems of tuning reward function parameters and balancing safety and optimality. By introducing Lagrange multipliers, the constrained optimization problem is transformed into an unconstrained optimization problem. In order to verify the effectiveness of the algorithm proposed in this paper, a spacecraft safe proximity environment model with dynamic obstacles is constructed, and the GAT-SACL algorithm proposed in this paper is validated by the Monte Carlo shooting method. The results show that the GAT-SACL algorithm possess excellent exploratory characteristics and delivers significant advantages in balancing optimality and safety.