Kittipong Boonlong

Multi-objective Optimisation by Co-operative Co-evolution

This paper presents the integration between a co-operative co-evolutionary genetic algorithm (CCGA) and four evolutionary multi-objective optimisation algorithms (EMOAs): a multi-objective genetic algorithm (MOGA), a niched Pareto genetic algorithm (NPGA), a non-dominated sorting genetic algorithm (NSGA) and a controlled elitist non-dominated sorting genetic algorithm (CNSGA). The resulting algorithms can be referred to as co-operative co-evolutionary multi-objective optimisation algorithms or CCMOAs. The CCMOAs are benchmarked against the EMOAs in seven test problems. The first six problems cover different characteristics of multi-objective optimisation problems, namely convex Pareto front, non-convex Pareto front, discrete Pareto front, multi-modality, deceptive Pareto front and non-uniformity of solution distribution. In contrast, the last problem is a two-objective real-world problem, which is generally referred to as the continuum topology design. The results indicate that the CCMOAs are superior to the EMOAs in terms of the solution set coverage, the average distance from the non-dominated solutions to the true Pareto front, the distribution of the non-dominated solutions and the extent of the front described by the non-dominated solutions.

Compressed-objective genetic algorithm

A strategy for solving an optimisation problem with a large number of objectives by transforming the original objective vector into a two-objective vector during survival selection is presented. The transformed objectives, referred to as preference objectives, consist of a winning score and a vicinity index. The winning score, a maximisation criterion, describes the difference of the number of superior and inferior objectives between two solutions. The minimisation vicinity index describes the level of solution clustering around a search location, particularly the best value of each individual objective, is used to encourage the results to spread throughout the Pareto front. With this strategy, a new multi-objective algorithm, the compressed-objective genetic algorithm (COGA), is introduced. COGA is subsequently benchmarked against a non-dominated sorting genetic algorithm II (NSGA-II) and an improved strength Pareto genetic algorithm (SPEA-II) in six scalable DTLZ benchmark problems with three to six objectives. The results reveal that the proposed strategy plays a crucial role in the generation of a superior solution set compared to the other two techniques in terms of the solution set coverage and the closeness to the true Pareto front. Furthermore, the spacing of COGA solutions is very similar to that of SPEA-II solutions. Overall, the functionality of the multi-objective evolutionary algorithm (MOEA) with preference objectives is effectively demonstrated.

Co-Operative Co-Evolutionary Genetic Algorithms for Multi-Objective Topology Design

AbstractThis paper studies the effectiveness of incorporating co-operative co-evolutionary strategy into 4 evolutionary multi-objective optimisation algorithms – MOGA, NPGA, NSGA and CNSGA – for continuum topology design. Apart from the co-operative co-evolutionary concept, the algorithms employ the elitism and crowding distance techniques to promote the diversity within the set of preserved non-dominated solutions. Three-related 2D heat conduction problems with two design objectives are used as the case studies. The proposed co-operative co-evolution is found to improve the optimisation effectiveness significantly. The species arrangements and sizes have some impacts; the use of moderately small species barely improves the search performances due to the interference from species coupling. As these effects depend on physical meanings of problems, it is more expedient to estimate the parameters in practice.

Time Optimal and Time-Energy Optimal Control of Satellite Attitude Using Genetic Algorithms

This paper presents the use of genetic algorithms for solving time optimal and time-energy optimal control problems in a satellite attitude control system. The satellite attitude control system is a multi-input/multi-output non-linear system at which its continuous attitude-related states are driven by discrete-valued command torque input. The problems investigated cover the time optimal control with two-state input (−u, +u) and three-state input (−u, 0, u) and the time-energy optimal control with three-state input. With the use of two-state input, the control problem has been formulated as a multi-objective optimisation problem where the decision variables are composed of the time where an input-state switching occurs while the objectives consist of the final state errors and the trajectory time. A multi-objective genetic algorithm (MOGA) has been successfully used to obtain the time optimal solution which is superior to that generated by linearising the system and utilising a bang-bang control law. In contrast, with the use of three-state input, the control problems are reduced to single-objective optimisation problems. In the case of time optimal control, the objective is the trajectory time while a time-energy cost is used as the search objective in the time-energy optimal control. A single-objective genetic algorithm has been successfully used to generate the optimal control solutions for both problems. In addition, the effects of diversity control on the genetic algorithm performances in the control problems have also been identified.Copyright

OPTIMAL CONTROL OF A HYSTERESIS SYSTEM BY MEANS OF CO-OPERATIVE CO-EVOLUTION

This paper presents the use of a co-operative co-evolutionary genetic algorithm (CCGA) for solving optimal control problems in a hysteresis system. The hysteresis system is a hybrid control system which can be described by a continuous multivalued state-space representation that can switch between two possible discrete modes. The problems investigated cover the optimal control of the hysteresis system with fixed and free final state/time requirements. With the use of the Pontryagin maximum principle, the optimal control problems can be formulated as optimisation problems. In this case, the decision variables consist of the value of control signal when a switch between discrete modes occurs while the objective value is calculated from an energy cost function. The simulation results indicate that the use of the CCGA is proven to be highly efficient in terms of the minimal energy cost obtained in comparison to the results given by the searches using a standard genetic algorithm and a dynamic programming technique. This helps to confirm that the CCGA can handle complex optimal control problems by exploiting a co-evolutionary effect in an efficient manner.

Using a co-operative co-evolutionary genetic algorithm to solve optimal control problems in a hysteresis system

This paper presents the use of a co-operative co-evolutionary genetic algorithm (CCGA) for solving optimal control problems in a hysteresis system. The hysteresis system is a hybrid control system which can be described by a continuous multivalued state-space representation that can switch between two possible discrete modes. The problems investigated cover the optimal control of the hysteresis system with fixed and free final state/time requirements. With the use of the Pontryagin maximum principle, the optimal control problems can be formulated as optimisation problems. In this case, the decision variables consist of the value of control signal when a switch between discrete modes occurs while the objective value is calculated from an energy cost function. The simulation results indicate that the use of the CCGA is proven to be highly efficient in terms of the minimal energy cost obtained in comparison to the results given by the searches using a standard genetic algorithm and a dynamic programming technique. This helps to confirm that the CCGA can handle complex optimal control problems by exploiting a co-evolutionary effect in an efficient manner.

Further investigations on friction compensation using a neuro-genetic based hybrid framework

This paper presents further investigations into the use of a neuro-genetic based hybrid framework within a model-based friction compensation scheme in a closed-loop robotic system. The hybrid framework is composed of a number of neural network modules and a genetic algorithm module. The neural networks are used to perform a function approximation task while the role of the genetic algorithm is to search for an optimal combination between different neural structures during the generalisation process. This paper covers the modification on the genetic algorithm described in the previous work (Chaiyaratana et al. (2000)) to include two additional genetic operators: fitness scaling and diversity control operators. In addition, the search for an optimal combination between different neural structures is also extended to the case of the combination between radial-basis function networks, multilayer perceptrons and modular networks. The simulation results indicate that the friction compensation performance is further improved after the genetic algorithm and the search space has been modified. This helps to reveal the full potential of the hybrid framework in the friction compensation task.

Determination of Erroneous Velocity Vectors by Co-operative Co-evolutionary Genetic Algorithms

The effects of incorporating co-operative co-evolutionary strategy into a genetic algorithm (GA) for the identification of erroneous velocity vectors in particle image velocimetry (PIV) are studied. The search objective is to eliminate vectors that are dissimilar to their adjacent neighbors. A simulated cavity flow, which is modified to contain 20% erroneous vectors, is used as the case study. The co-operative co-evolutionary strategy is found to decisively improve the search effectiveness. When the effect of species size and arrangement are considered, the search rate improves with smaller species, reflecting the weak linkage between species due to the locality nature of the objective function. Best results are obtained with the 25-bit species under square arrangement. It is also observed that the current vector similarity calculation as the objective function needs further assessments for the erroneous vector detection of complex velocity flows with high error rates