Global Constrained Optimization Problems Research Articles

A collective neurodynamic approach to distributed resource allocation with event-triggered communication

To solve a distributed optimal resource allocation problem, a collective neurodynamic approach based on recurrent neural networks (RNNs) is proposed in this paper. Multiple RNNs cooperatively solve a global constrained optimization problem in which the objective function is a total of local non-smooth convex functions and is subject to local convex sets and a global equality constraint. Different from the projection dynamics to deal with local convex sets in the existing work, an internal dynamics with projection output is designed in the algorithm to relax the Slater’s condition satisfied by the optimal solution. To overcome continuous-time communication in a group of RNNs, an aperiodic communication scheme, called the event-triggered scheme, is presented to alleviate communication burden. It is analyzed that the convergence of the designed collective neurodynamic approach based on the event-triggered communication does not rely on global information. Furthermore, it is proved the freeness of the Zeno behavior in the event-triggered scheme. Two examples are presented to illustrate the obtained results

Theta-mechanism based cluster search algorithm for global constrained optimization

This study concerns constructing an evolutionary search system to solve the global constrained optimization problems. Firstly, we proposed a hybrid constraint-handling method, called theta-mechanism, which blends two types of constraint-handling functions and alternates use of them in the searching process to balance two competing objectives: seeking as much as possible feasible regions and quickly converging to the optimum point in the found feasible regions. Secondly, to enable the search system to cooperate well with the theta-mechanism, we designed the cluster search algorithm (CSA) and developed the search reachability analysis (SRA) method. Based on SRA, we evaluated the characteristics of several typical search operators in order to assemble them into different operator combinations in CSA to maximize its performance, which enables CSA with theta-mechanism to accomplish the two inconsistent search objectives effectively. We tested the proposed method on 18 benchmark functions from IEEE CEC2010 and 32 real-world constrained optimization problems collected in IEEE CEC2020. Our results show the CSA with theta-mechanism is more competitive than the existing state-of-the-art approaches.

Studying the Efficiency of Parallelization in Optimal Control of Multistage Chemical Reactions

In this paper, we investigate the problem of optimal control of complex multistage chemical reactions, which is considered a nonlinear global constrained optimization problem. This class of problems is computationally expensive due to the inclusion of multiple parameters and requires parallel computing systems and algorithms to obtain a solution within a reasonable time. However, the efficiency of parallel algorithms can differ depending on the architecture of the computing system. One available approach to deal with this is the development of specialized optimization algorithms that consider not only problem-specific features but also peculiarities of a computing system in which the algorithms are launched. In this work, we developed a novel parallel population algorithm based on the mind evolutionary computation method. This algorithm is designed for desktop girds and works in synchronous and asynchronous modes. The algorithm and its software implementation were used to solve the problem of the catalytic reforming of gasoline and to study the parallelization efficiency. Results of the numerical experiments are presented in this paper.

An additive algorithm for origami design

Inspired by the allure of additive fabrication, we pose the problem of origami design from a different perspective: How can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable fourfold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a complete marching, or additive, algorithm for the inverse design of the complete space of developable quad origami patterns that can be folded from flat sheets. We illustrate the flexibility of our approach by growing ordered, disordered, straight, and curved-folded origami and fitting surfaces of given curvature with folded approximants. Overall, our simple shift in perspective from a global search to a local rule has the potential to transform origami-based metastructure design.

Inverse kinematics for cooperative mobile manipulators based on self-adaptive differential evolution.

This article presents an approach to solve the inverse kinematics of cooperative mobile manipulators for coordinate manipulation tasks. A self-adaptive differential evolution algorithm is used to solve the inverse kinematics as a global constrained optimization problem. A kinematics model of the cooperative mobile manipulators system is proposed, considering a system with two omnidirectional platform manipulators with n DOF. An objective function is formulated based on the forward kinematics equations. Consequently, the proposed approach does not suffer from singularities because it does not require the inversion of any Jacobian matrix. The design of the objective function also contains penalty functions to handle the joint limits constraints. Simulation experiments are performed to test the proposed approach for solving coordinate path tracking tasks. The solutions of the inverse kinematics show precise and accurate results. The experimental setup considers two mobile manipulators based on the KUKA Youbot system to demonstrate the applicability of the proposed approach.

Minimum-Acceleration Trajectory Optimization for Humanoid Manipulator Based on Differential Evolution

A humanoid manipulator produces significantly reactive forces against a humanoid body when it operates in a rapid and continuous reaction environment (e.g., playing baseball, ping-pong etc.). This not only disturbs the balance and stability of the humanoid robot, but also influences its operation precision. To solve this problem, a novel approach, which is able to generate a minimum-acceleration and continuous acceleration trajectory for the humanoid manipulator, is presented in this paper. By this method, the whole trajectory of humanoid manipulation is divided into two processes, i.e., the operation process and the return process. Moreover, the target operation point is considered as a particular point that should be passed through. As such, the trajectory of each process is described through a quartic polynomial in the joint space, after which the trajectory planning problem for the humanoid manipulator can be formulated as a global constrained optimization problem. In order to alleviate the reactive force, a fitness function that aims to minimize the maximum acceleration of each joint of the manipulator is defined, while differential evolution is employed to determine the joint accelerations of the target operation point. Thus, a trajectory with a minimum-acceleration and continuous acceleration profile is obtained, which can reduce the effect on the body and be favourable for the balance and stability of the humanoid robot to a certain extent. Finally, a humanoid robot with a 7-DOF manipulator for ping-pong playing is employed as an example. Simulation experiment results show the effectiveness of this method for the trajectory planning problem being studied.

Interval-based global optimization in engineering using model reformulation and constraint propagation

This paper deals with the preliminary design problem when the product is modeled as an analytic model. The analytic models based method aims to use mathematical equations to address both multi-physic and economic characteristics of a product. The proposed approach is to convert the preliminary design problem into a global constrained optimization problem. The objective is to develop powerful optimization methods enough to handle complex analytical models. We propose to adapt an approach to solve this problem based on interval analysis, constraint propagation and model reformulation. In order to understand the optimization algorithm used for engineering design problems, some basic definitions and properties of interval analysis are introduced. Then, the basic optimization algorithms for both unconstrained and constrained problems are introduced and illustrated. The next section introduces the reformulation technique as main accelerating device. An application of the reformulation device and its global optimization algorithm on the optimal design of electrical actuators is presented.

SOLVING CONSTRAINED GLOBAL OPTIMIZATION VIA ARTIFICIAL IMMUNE SYSTEM

Artificial immune systems (AISs) are computational intelligence (CI) oriented methods using information based on biological immune systems. In this study, an AIS, which combines the metaphor of clonal selection with idiotypic network theories, is developed. Although they are contradictory approaches, clonal selection and idiotypic network may prove useful in designing a stochastic global optimization tool. The AIS method consists of idiotypic network selection, somatic hypermuation, receptor editing and bone marrow operators. The idiotypic network selection operator determines the number of good solutions. The somatic hypermutation and receptor editing operators comprise the searching mechanisms for the exploration of the solution space. Diversity on the population of solutions is ensured by the bone marrow operator. The performance of the proposed AIS method is tested on a set of global constrained optimization problems (GCO), comprising of four benchmark nonlinear programming problems and four generalized polynomial programming (GPP) problems, where GPP problems are nonconvex optimization problems. The best solution found by the AIS algorithm is compared with the known global optimum. Numerical results show that the proposed method converged to the global optimal solution to each tested CGO problem. Moreover, this study compares the numerical results obtained by the AIS approach with those taken from published CI approaches, such as alternative AIS methods and genetic algorithms.

A heuristic-based framework to solve a complex aircraft sizing problem

Aircraft sizing studies consist in determining the main characteristics of an aircraft starting from a set of requirements. These studies can be summarized as global constrained optimization problems. The constraints express physical feasibility and the requirements to be satisfied; the objectives are market-driven performances of the aircraft. These optimizations are currently manually conducted as many input data frequently evolve during the study. This work introduced mathematical methods that are useful in a sizing tool to ease, fasten and enhance the aircraft configuration optimization problem. Using genetic algorithms, large amounts of design points satisfying the requirements were rapidly produced, despite some issues inherent to the aircraft model: numerical noise or physically meaningless design points due to the vast design space. Then, multicriteria optimization methods were introduced, as several criteria were considered concurrently. As calculation times became important, the aircraft model was substituted by a surrogate model. Radial basis functions approximated the constraint and the objective functions. Finally, a possible outcome of the integration of these different techniques was proposed in order to yield the engineers a global and operational perception of the design space.

Achieving developability of a polygonal surface by minimum deformation: a study of global and local optimization approaches

Surface developability is required in a variety of applications in product design, such as clothing, ship hulls, automobile parts, etc. However, most current geometric modeling systems using polygonal surfaces ignore this important intrinsic geometric property. This paper investigates the problem of how to minimally deform a polygonal surface to attain developability, or the so-called developability-by-deformation problem. In our study, this problem is first formulated as a global constrained optimization problem and a penalty-function-based numerical solution is proposed for solving this global optimization problem. Next, as an alternative to the global optimization approach, which usually requires lengthy computing time, we present an iterative solution based on a local optimization criterion that achieves near real-time computing speed.

Quasiconvex relaxations based on interval arithmetic

Interval analysis provides a tool for (i) forward error analysis, (ii) estimating and controlling rounding and approximation errors automatically, and (iii) proving existence and uniqueness of solutions. In this context the terms self-validating methods, inclusion methods orverification methods are in use. In this paper, we present a new self-validating method for solving global constrained optimization problems. This method is based on the construction of quasiconvex lower bound and quasiconcave upper bound functions of a given function, the latter defined by an arithmetical expression. No further assumptions about the nonlinearities of the given function are necessary. These lower and upper bound functions are rigorous by using the tools of interval arithmetic. In its easiest form they are constructed by taking appropriate linear and/or quadratical estimators which yield quasiconvex/quasiconcave bound functions. We show how these bound functions can be used to define rigorous quasiconvex relaxations for constrained global optimization problems and nonlinear systems. These relaxations can be incorporated in a branch and bound framework yielding a self-validating method.

A genetic algorithm for global constrained optimization problem

For many manufacturing processes the determination of an optimal control is stated as a constrained optimization problem involving nonconvex objective functions. In practical industrial situations, nonlinear models and nonconvexity lead to hard difficulties in the modelization and the control of the process, since, on the one hand, approximations can lead to unrealistic models and, on the other hand, the classical deterministic optimization methods can be inefficient. In such a framework the emergence of evolutive strategies offers new perspectives which have to be investigated. However, these algorithms are mainly proposed for unconstrained optimisation and appropriated development must he constructed for the case where restrictions must be taken into account. In this paper, we consider evolutionnary algorithms for constrained continuous problem. Convergence results are staled and numerical behaviour of the algorithms is compared.

Pattern Programming: A Method for Solving Global Constrained Optimization Problems

A method to find a global constrained optimum is described. The proposed method named "Pattern Programming" consists of the following three phases: pattern measurement, pattern representation and heuristic search method. In each phase, new concepts and algorithms are introduced. A procedure of this method is illustrated with some examples.