Optimizing fixed-size stochastic controllers for POMDPs and decentralized POMDPs

POMDPs and their decentralized multiagent counterparts, DEC-POMDPs, offer a rich framework for sequential decision making under uncertainty. Their high computational complexity, however, presents an important research challenge. One way to address the intractable memory requirements of current algorithms is based on representing agent policies as finite-state controllers. Using this representation, we propose a new approach that formulates the problem as a nonlinear program, which defines an optimal policy of a desired size for each agent. This new formulation allows a wide range of powerful nonlinear programming algorithms to be used to solve POMDPs and DEC-POMDPs. Although solving the NLP optimally is often intractable, the results we obtain using an off-the-shelf optimization method are competitive with state-of-the-art POMDP algorithms and outperform state-of-the-art DEC-POMDP algorithms. Our approach is easy to implement and it opens up promising research directions for solving POMDPs and DEC-POMDPs using nonlinear programming methods.     

一种求解混合整数非线性规划问题的模拟退火算法

通过适当处理离散变量，将求解无约束非凸ＮＬＰ问题的高效模拟退火全局优化算法推广到求解一般非凸混合整数非线性规划问题。数值计算结果表明，文中模拟退火算法在适用性、解的质量和计算效率等方面优于其它方法，是求解一般非凸ＭＩＮＬＰ问题的一种有效的全局优化算法。     

Adaptive air-fuel ratio control with MLP network

This paper presents an application of adaptive neural network model-based predictive control (MPC) to the air-fuel ratio of an engine simulation. A multi-layer perceptron (MLP) neural network is trained using two on-line training algorithms: a back propagation algorithm and a recursive least squares (RLS) algorithm. It is used to model parameter uncertainties in the nonlinear dynamics of internal combustion (IC) engines. Based on the adaptive model, an MPC strategy for controlling air-fuel ratio is realized, and its control performance compared with that of a traditional PI controller. A reduced Hessian method, a newly developed sequential quadratic programming (SQP) method for solving nonlinear programming (NLP) problems, is implemented to speed up nonlinear optimization in the MPC.     

Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect

The growing costs of fuel and operation of power generating units warrant improvement of optimization methodologies for economic dispatch (ED) problems. The practical ED problems have non-convex objective functions with equality and inequality constraints that make it much harder to find the global optimum using any mathematical algorithms. Modern optimization algorithms are often meta-heuristic, and they are very promising in solving nonlinear programming problems. This paper presents a novel approach to determining the feasible optimal solution of the ED problems using the recently developed Firefly Algorithm (FA). Many nonlinear characteristics of power generators, and their operational constraints, such as generation limitations, prohibited operating zones, ramp rate limits, transmission loss, and nonlinear cost functions, were all contemplated for practical operation. To demonstrate the efficiency and applicability of the proposed method, we study four ED test systems having non-convex solution spaces and compared with some of the most recently published ED solution methods. The results of this study show that the proposed FA is able to find more economical loads than those determined by other methods. This algorithm is considered to be a promising alternative algorithm for solving the ED problems in practical power systems.     

A new class of projection and contraction methods for solving variational inequality problems

This paper presents a new class of projection and contraction methods for solving monotone variational inequality problems. The methods can be viewed as combinations of some existing projection and contraction methods and the method of shortest residuals, a special case of conjugate gradient methods for solving unconstrained nonlinear programming problems. Under mild assumptions, we show the global convergence of the methods. Some preliminary computational results are reported to show the efficiency of the methods.     

一个通用的混合非线性规划问题的演化算法

提出了一种新的求解非线性规划问题的演化算法，它是在郭涛算法的基础上提出的，新算法的主要特点是引入了变维子空间，加入了子空间搜索过程和规范化约束条件以及增加了处理带等式约束的实数规划，整数规划，0－1规划和混合整数规划问题的功能，使之成为一种求解非线性规划（NLP）问题的通用算法，数值实验表明，新算法不仅是一种通用的算法，而且与已有算法的计算结果相比，其解的精确度也最好。     

A Hybrid Particle Swarm Branch-and-Bound (HPB) Optimizer for Mixed Discrete Nonlinear Programming

This paper proposes a new algorithm for solving mixed discrete nonlinear programming (MDNLP) problems, designed to efficiently combine particle swarm optimization (PSO), which is a well-known global optimization technique, and branch-and-bound (BB), which is a widely used systematic deterministic algorithm for solving discrete problems. The proposed algorithm combines the global but slow search of PSO with the rapid but local search capabilities of BB, to simultaneously achieve an improved optimization accuracy and a reduced requirement for computational resources. It is capable of handling arbitrary continuous and discrete constraints without the use of a penalty function, which is frequently cumbersome to parameterize. At the same time, it maintains a simple, generic, and easy-to-implement architecture, and it is based on the sequential quadratic programming for solving the NLP subproblems in the BB tree. The performance of the new hybrid PSO–BB architecture algorithm is evaluated against real-world MDNLP benchmark problems, and it is found to be highly competitive compared with existing algorithms.      

Some algebraic methods for solving multiobjective polynomial integer programs

Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the past few years. However, the polynomial case has not been studied in detail due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem to the problem of solving one or more systems of polynomial equations and we use certain Gröbner bases to solve these systems. Different transformations give different methodologies that are theoretically stated and compared by some computational tests via the algorithms that they induce.     

一种高效的快速近似控制向量参数化方法

控制向量参数化(Control vector parameterization, CVP) 方法是目前求解流程工业中最优操作问题的主流数值方法,然而,该方法的主要缺点之一是 计算效率较低,这是因为在求解生成的非线性规划(Nonlinear programming, NLP) 问题时,需要随着控制参数的调整,反复不断地求解相关的微分方程组,这也是CVP 方法中最耗时的部分.为了提高CVP 方法的计算效率,本文提出一种新颖的快速近似方法,能够有效减少微分方程组、函数值以及 梯度的计算量.最后,两个经典的最优控制问题上的测试结果及与国外成熟的最优控制 软件的比较研究表明:本文提出的快速近似CVP 方法在精度和效率上兼有良好的表现.     

A Robust Algorithm for Solving Nonlinear Programming Problems

In this paper, we introduce a new algorithm for solving nonlinear programming (NLP) problems. It is an extension of Guo's algorithm [1] which possesses enhanced capabilities for solving NLP problems. These capabilities include: a) extending the variable subspace, b) adding a search process over subspaces and normalized constraints, c) using an adaptive penalty function, and d) adding the ability to deal with integer NLP problems, 0-1 NLP problems, and mixed-integer NLP problems which have equality constraints. These four enhancements increase the capabilities of the algorithm to solve nonlinear programming problems in a more robust and universal way. This paper will present results of numerical experiments which show that the new algorithm is not only more robust and universal than its competitors, but also its performance level is higher than any others in the literature.     

Interactive intuitionistic fuzzy methods for multilevel programming problems

Multilevel programming problems model a decision-making process with a hierarchy structure. Traditional solution methods including vertex enumeration algorithms and penalty function methods are not only inefficient to obtain the solution of the multilevel programming problems, but also lead to a paradox that the follower’s decision power dominates the leader’s. In this paper, both multilevel programming and intuitionistic fuzzy set are used to model problems in hierarchy expert and intelligent systems. We first present a score function to objectively depict the satisfactory degrees of decision makers by virtue of the intuitionistic fuzzy set for solving multilevel programming problems. Then we develop three optimization models and three interactive intuitionistic fuzzy methods to consider different satisfactory solutions for the requirements of expert decision makers. Furthermore, a new distance function is proposed to measure the merits of a satisfactory solution. Finally, a case study for cloud computing pricing problems and several numerical examples are given to verify the applicability and the effectiveness of the proposed models and methods.     

Neutrino-like particle for particle swarm optimization

The real-world optimal problems frequently encountered by various industries are the nonlinear constrained optimization problems (NCOPs), where the constraints represent the limitations of practical resources. Many researchers have attempted to improve particle swarm optimization (PSO) in the past decades; however, in solving the NCOPs, the PSO-based approaches often cause premature convergences. The problem-specific constraints frequently generate many infeasible regions that block the movements of particles. The particles' behavior causes the exploration abilities of particles that tend to weaken along with time. The decreasing of exploration ability often comes from the particle becoming stagnant or moving unusefully. This study proposes a neutrino-like particle (NLP) with adaptive NLP hyperparameters that simulate the natural neutrino behavior. The proposed NLPs can be embedded in the PSO-based approaches for overcoming premature convergence. The experiment results demonstrate that all referenced PSO-based methods with the NLPs improved significantly compared with those without the NLPs to solve the NCOPs. All referenced PSO-based methods that embedded the NLPs also significantly outperform four recent strong algorithms in most IEEE CEC 2020 benchmark problems. Therefore, the proposed NLPs with adaptive NLP hyperparameters can effectively solve the premature convergences, reinforce the exploration ability, and maintain the exploitation capability for solving the NCOPs over the whole evolution process.     

Numerical and computational efficiency of solvers for two-phase problems

We consider two-phase flow problems, modelled by the Cahn–Hilliard equation. In this work, the nonlinear fourth-order equation is decomposed into a system of two coupled second-order equations for the concentration and the chemical potential.We analyse solution methods based on an approximate two-by-two block factorization of the Jacobian of the nonlinear discrete problem. We propose a preconditioning technique that reduces the problem of solving the non-symmetric discrete Cahn–Hilliard system to a problem of solving systems with symmetric positive definite matrices where off-the-shelf multilevel and multigrid algorithms are directly applicable. The resulting solution methods exhibit optimal convergence and computational complexity properties and are suitable for parallel implementation.We illustrate the efficiency of the proposed methods by various numerical experiments, including parallel results for large scale three dimensional problems.     

Serial advanced-multi-step nonlinear model predictive control using an extended sensitivity method

Nonlinear model predictive control (NMPC) can directly handle multi-input multi-output nonlinear systems and explicitly consider input and state constraints. However, the computational load for nonlinear programming (NLP) of large-scale systems limits the range of possible applications and degrades NMPC performance. An NLP sensitivity based approach, advanced-step NMPC, has been developed to address the online computational load. In addition, for cases where the NLP solving time exceeds one sampling time, two types of advanced-multi-step NMPC (amsNMPC), parallel and serial, have been proposed. However, in previous studies, a serial amsNMPC could not be applied to large-scale problems because of the size of extended Karush–Kuhn–Tucker matrix and its Schur complement decomposition, and the robustness was analyzed under a conservative assumption for memory effects. In this paper, we propose a serial amsNMPC using an extended sensitivity method to increase the online computation speed further. We successfully apply it to a large-scale air separation unit using the sparse matrix handling packages of Python, Pyomo, and k_aug tools. Furthermore, an auxiliary NLP formulation is defined to analyze the robustness. Using this with the key properties of an extended sensitivity matrix, we can prove robustness while avoiding the memory effects term.     

Adaptive neural network model based predictive control for air–fuel ratio of SI engines

The dynamics of air manifold and fuel injection of the spark ignition engines are severely nonlinear. This is reflected in nonlinearities of the model parameters in different regions of the operating space. Control of the engines has been investigated using observer-based methods or sliding-mode methods. In this paper, the model predictive control (MPC) based on a neural network model is attempted for air–fuel ratio, in which the model is adapted on-line to cope with nonlinear dynamics and parameter uncertainties. A radial basis function (RBF) network is employed and the recursive least-squares (RLS) algorithm is used for weight updating. Based on the adaptive model, a MPC strategy for controlling air–fuel ratio is realised to a nonlinear simulation of the engines, and its control performance is compared with that of a conventional PI controller. A reduced Hessian method, a new developed sequential quadratic programming (SQP) method for solving nonlinear programming (NLP) problems, is implemented to speed up the nonlinear optimisation in MPC.     

Optimal control problems treated with algorithms of linear and nonlinear programming

Algorithms solving optimal control problems for linear discrete systems and linear continuous systems (without discretization) are discussed. The algorithms are based on a new approach to solving linear programming problems worked out in Minsk (USSR). A new method for solving nonlinear programming problems is justified. It uses the network interpretation of nonlinear functions and special network operations. Results of numerical experiment (on geometric programming problems) are given. In conclusion an algorithm of solving optimal control problem for the system with nonlinear input is described.     

Efficient DC programming approaches for the asymmetric eigenvalue complementarity problem

In this paper, we propose nonlinear programming (NLP) formulations and difference of convex functions (DC) programming approaches for the asymmetric eigenvalue complementarity problem (EiCP). The EiCP has a solution if and only if these NLP formulations have zero global optimal value. We reformulate the NLP formulations as DC programs which can be efficiently solved by a DC algorithm. Some preliminary numerical results illustrate the good performance of the proposed methods.     

Advanced-multi-step nonlinear model predictive control

Nonlinear model predictive control (NMPC) has gained widespread attention due to its ability to handle variable bounds and deal with multi-input, multi-output systems. However, it is susceptible to computational delay, especially when the solution time of the nonlinear programming (NLP) problem exceeds the sampling time. In this paper we propose a fast NMPC method based on NLP sensitivity, called advanced-multi-step NMPC (amsNMPC). Two variants of this method are developed, the parallel approach and the serial approach. For the amsNMPC method, NLP problems are solved in background multiple sampling times in advance, and manipulated variables are updated on-line when the actual states are available. We present case studies about a continuous stirred tank reactor (CSTR) and a distillation column to show the performance of amsNMPC. Nominal stability properties are also analyzed.     

Two aggregate-function-based algorithms for analysis of 3D frictional contact by linear complementarity problem formulation

Three dimensional frictional contact is formulated as linear complementarity problem (LCP) by using the parametric variational principle and quadratic programming method. Two aggregate-function-based algorithms, called respectively as self-adjusting interior point algorithm and aggregate function smoothing algorithm, are proposed for the solution of the LCP derived from the contact problems. A nonlinear finite element code is developed for numerical analysis of 3D multi-body contact problems. Four numerical examples are computed to demonstrate the applicability and computational efficiency of the methods proposed.     

Non-linear integer programming

An exact method for solving all-integer non-linear programming problems with a separable non-decreasing objective function is presented. Dynamic programming methodology is used to efficiently search candidate hypersurfaces for the optimal feasible integer solution. An efficient computational and storage scheme exists and initial calculations give very promising results.