Optimization of feed rate profile for the monoclonal antibody production

The optimal control algorithm to calculate the optimal feed rate profile of nutrient solution containing two limiting nutrients was proposed. Different from other conventional optimization methods, the proposed algorithm calculated the optimal control profiles for different initial and feed conditions. The singular optimal control algorithm, dynamic programming, and nonsingular transformation algorithm were used for the optimization of simple problems of the 4th order and the performances were compared. With the proposed transformation algorithm, the final MAb concentration increased and the CPU time decreased. For the different initial glucose and glutamine conditions, the optimal control profiles were calculated with the proposed transformation algorithm. As the initial glutamine concentration increased, the final MAb concentration also increased due to the cell viability increase. This was also applied to the different feed compositions. When the glutamine concentration was increased in the feed stream, the final MAb concentration also increased.     

Local versus global optimal sports techniques in a group of athletes

Various optimization algorithms have been used to achieve optimal control of sports movements. Nevertheless, no local or global optimization algorithm could be the most effective for solving all optimal control problems. This study aims at comparing local and global optimal solutions in a multistart gradient-based optimization by considering actual repetitive performances of a group of athletes performing a transition move on the uneven bars. Twenty-four trials by eight national-level female gymnasts were recorded using a motion capture system, and then multistart sequential quadratic programming optimizations were performed to obtain global optimal, local optimal and suboptimal solutions. The multistart approach combined with a gradient-based algorithm did not often find the local solution to be the best and proposed several other solutions including global optimal and suboptimal techniques. The qualitative change between actual and optimal techniques provided three directions for training: to increase hip flexion–abduction, to transfer leg and arm angular momentum to the trunk and to straighten hand path to the bar.     

On the optimal control of fed-batch reactors with substrate-inhibited kinetics

The optimal feed rate profiles, for fed-batch fermentation that maximizes the biomass production and accounts for time, are analyzed. The solution can be found only if the final arc of the optimal control is a batch arc, since in this case the final concentrations of substrate and biomass can be determined by ulterior conditions on the mass balance and on the final growth rate of biomass and thus it is possible to solve the resulting time optimal problem by using Green's theorem. This evidences the "turnpike property" of the solution, which tries to spend the maximum time on or at least near the singular arc along which the substrate concentration is maintained constant. The optimality of the final batch arc is related to the time operational cost in the performance index. The sequence of the control depends on the initial conditions for which six different regions, with the respective patterns, have been identified, in case the performance index allows the control sequence to have a final batch.     

Optimal coordination and control of posture and locomotion.

This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory, and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and stance model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses.     

Optimal coordination and control of posture and movements

This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton–Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and movement model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses. Validation examples with experimental data are provided.     

Random Search Algorithm for Solving the Nonlinear Fredholm Integral Equations of the Second Kind

In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods and solution of this discretized form converges to the exact solution of the integral equation by considering some conditions on the kernel of the integral equation. And then we convert the problem to an optimal control problem by introducing an artificial control function. Following that, in the next step, solution of the discretized form is approximated by a kind of Monte Carlo (MC) random search algorithm. Finally, some examples are given to show the efficiency of the proposed approach.     

The Model Identification for Small Unmanned Aerial Rotorcraft Based on Adaptive Ant Colony Algorithm

This paper proposes a model identification method to get high performance dynamic model of a small unmanned aerial rotorcraft.With the analysis of flight characteristics,a linear dynamic model is constructed by the small perturbation theory.Using the micro guidance navigation and control module,the system can record the control signals of servos,the state information of attitude and velocity information in sequence.After the data preprocessing,an adaptive ant colony algorithm is proposed to get optimal parameters of the dynamic model.With the adaptive adjustment of the pheromone in the selection process,the proposed model identification method can escape from local minima traps and get the optimal solution quickly.Performance analysis and experiments are conducted to validate the effectiveness of the identified dynamic model.Compared with real flight data,the identified model generated by the proposed method has a better performance than the model generated by the adaptive genetic algorithm.Based on the identified dynamic model,the small unmanned aerial rotorcraft can generate suitable control parameters to realize stable hovering,turning,and straight flight.     

AN IMPROVEMENT OF MYERS──MILLER'S ALGORITHM FOR SEQUENCE ALIGNMENT

1.IntroductionWhenabiomacromolecule(nucleicacidorprotein)issequenced,molecularbiologistswillpaymoreattentiontotheproblemofanalyzingtherelationbetweenitsstructureandfunctions.Itisoneoftheeffectivewaysacquiringinformationrelatedthisproblemtocomparesuchamole…     

Algorithms and Complexity Analyses for Control of Singleton Attractors in Boolean Networks

A Boolean network (BN) is a mathematical model of genetic networks. We propose several algorithms for control of singleton attractors in BN. We theoretically estimate the average-case time complexities of the proposed algorithms, and confirm them by computer experiments. The results suggest the importance of gene ordering. Especially, setting internal nodes ahead yields shorter computational time than setting external nodes ahead in various types of algorithms. We also present a heuristic algorithm which does not look for the optimal solution but for the solution whose computational time is shorter than that of the exact algorithms.     

Multi-objective optimization in Aspergillus niger fermentation for selective product enhancement

A multi-objective optimization formulation that reflects the multi-substrate optimization in a multi-product fermentation is proposed in this work. This formulation includes the application of ε-constraint to generate the trade-off solution for the enhancement of one selective product in a multi-product fermentation, with simultaneous minimization of the other product within a threshold limit. The formulation has been applied to the fed-batch fermentation of Aspergillus niger that produces a number of enzymes during the course of fermentation, and of these, catalase and protease enzyme expression have been chosen as the enzymes of interest. Also, this proposed formulation has been applied in the environment of three control variables, i.e. the feed rates of sucrose, nitrogen source and oxygen and a set of trade-off solutions have been generated to develop the pareto-optimal curve. We have developed and experimentally evaluated the optimal control profiles for multiple substrate feed additions in the fed-batch fermentation of A. niger to maximize catalase expression along with protease expression within a threshold limit and vice versa. An increase of about 70% final catalase and 31% final protease compared to conventional fed-batch cultivation were obtained. Novel methods of oxygen supply through liquid-phase H₂O₂ addition have been used with a view to overcome limitations of aeration due to high gas–liquid transport resistance. The multi-objective optimization problem involved linearly appearing control variables and the decision space is constrained by state and end point constraints. The proposed multi-objective optimization is solved by differential evolution algorithm, a relatively superior population-based stochastic optimization strategy.     

The numerical method for the optimal supporting position and related optimal control for the catalytic reaction system

This paper considers the numerical approximation for the optimal supporting position and related optimal control of a catalytic reaction system with some control and state constraints, which is governed by a nonlinear partial differential equations with given initial and boundary conditions. By the Galerkin finite element method, the original problem is projected into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then the control parameterization method is applied to approximate the control and reduce the original system to an optimal parameter selection problem, in which both the position and related control are taken as decision variables to be optimized. This problem can be solved as a nonlinear optimization problem by a particle swarm optimization algorithm. The numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method.     

演化极端结合分支分类方法

从生物演化的逆方向考虑,提出一种聚合的分支分类运算方法,称为演化极端结合分支分类法。文章阐明其设计思路、演算步骤,并以实例具体说明其演算过程。最后以演化长度系数、合理解与合理方法等概念,对演化极端结合法进行评价。     

A novel comprehensive learning artificial bee colony optimizer for dynamic optimization biological problems

There are many dynamic optimization problems in the real world, whose convergence and searching ability is cautiously desired, obviously different from static optimization cases. This requires an optimization algorithm adaptively seek the changing optima over dynamic environments, instead of only finding the global optimal solution in the static environment. This paper proposes a novel comprehensive learning artificial bee colony optimizer (CLABC) for optimization in dynamic environments problems, which employs a pool of optimal foraging strategies to balance the exploration and exploitation tradeoff. The main motive of CLABC is to enrich artificial bee foraging behaviors in the ABC model by combining Powell’s pattern search method, life-cycle, and crossover-based social learning strategy. The proposed CLABC is a more bee-colony-realistic model that the bee can reproduce and die dynamically throughout the foraging process and population size varies as the algorithm runs. The experiments for evaluating CLABC are conducted on the dynamic moving peak benchmarks. Furthermore, the proposed algorithm is applied to a real-world application of dynamic RFID network optimization. Statistical analysis of all these cases highlights the significant performance improvement due to the beneficial combination and demonstrates the performance superiority of the proposed algorithm.     

Modelling and optimization of environmental conditions for kefiran production by Lactobacillus kefiranofaciens

A mathematical model for kefiran production by Lactobacillus kefiranofaciens was established, in which the effects of pH, substrate and product on cell growth, exopolysaccharide formation and substrate assimilation were considered. The model gave a good representation both of the formation of exopolysaccharides (which are not only attached to cells but also released into the medium) and of the time courses of the production of galactose and glucose in the medium (which are produced and consumed by the cells). Since pH and both lactose and lactic acid concentrations differently affected production and growth activity, the model included the effects of pH and the concentrations of lactose and lactic acid. Based on the mathematical model, an optimal pH profile for the maximum production of kefiran in batch culture was obtained. In this study, a simplified optimization method was developed, in which the optimal pH profile was determined at a particular final fermentation time. This was based on the principle that, at a certain time, switching from the maximum specific growth rate to the critical one (which yields the maximum specific production rate) results in maximum production. Maximum kefiran production was obtained, which was 20% higher than that obtained in the constant-pH control fermentation. A genetic algorithm (GA) was also applied to obtain the optimal pH profile; and it was found that practically the same solution was obtained using the GA.     

Parameter Estimation of Fractional-Order Chaotic Systems by Using Quantum Parallel Particle Swarm Optimization Algorithm

Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm.     

The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting . It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting , in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions.     

An evolutionary strategy for fed-batch bioreactor optimization; concepts and performance

An evolutionary program, based on a real-code genetic algorithm (GA), is applied to calculate optimal control policies for bioreactors. The GA is used as a nonlinear optimizer in combination with simulation software and constraint handling procedures. A new class of GA-operators is introduced to obtain smooth control trajectories, which leads also to a drastic reduction in computational load. The proposed method is easy to understand and has no restrictions on the model type and structure. The performance and optimal trajectories obtained by the extended GA are compared with those calculated with two common methods: (i) dynamic programming, and (ii) a Hamiltonian based gradient algorithm. The GA proved to be a good and often superior alternative for solving optimal control problems.     

Faster algorithms for optimal multiple sequence alignment based on pairwise comparisons

Multiple sequence alignment (MSA) is one of the most fundamental problems in computational molecular biology. The running time of the best known scheme for finding an optimal alignment, based on dynamic programming, increases exponentially with the number of input sequences. Hence, many heuristics were suggested for the problem. We consider a version of the MSA problem where the goal is to find an optimal alignment in which matches are restricted to positions in predefined matching segments. We present several techniques for making the dynamic programming algorithm more efficient, while still finding an optimal solution under these restrictions. We prove that it suffices to find an optimal alignment of the predefined sequence segments, rather than single letters, thereby reducing the input size and thus improving the running time. We also identify "shortcuts" that expedite the dynamic programming scheme. Empirical study shows that, taken together, these observations lead to an improved running time over the basic dynamic programming algorithm by 4 to 12 orders of magnitude, while still obtaining an optimal solution. Under the additional assumption that matches between segments are transitive, we further improve the running time for finding the optimal solution by restricting the search space of the dynamic programming algorithm     

An integrated scheduling and control model for multi-mode projects

In today’s highly competitive uncertain project environments, it is of crucial importance to develop analytical models and algorithms to schedule and control project activities so that the deviations from the project objectives are minimized. This paper addresses the integrated scheduling and control in multi-mode project environments. We propose an optimization model that models the dynamic behavior of projects and integrates optimal control into a practically relevant project scheduling problem. From the scheduling perspective, we address the discrete time/cost trade-off problem, whereas an optimal control formulation is used to capture the effect of project control. Moreover, we develop a solution algorithm for two particular instances of the optimal project control. This algorithm combines a tabu search strategy and nonlinear programming. It is applied to a large scale test bed and its efficiency is tested by means of computational experiments. To the best of our knowledge, this research is the first application of optimal control theory to multi-mode project networks. The models and algorithms developed in this research are targeted as a support tool for project managers in both scheduling and deciding on the timing and quantity of control activities.