Synthesis Of The Evolutionary Computational System For Engineering Optimization

Optimization may not be the best language for expressing a problem, but it is relatively simple and quite general - all problem can, at least in principle, be expressed as optimization problems. Herein optimization terminology is employed to describe a problem to be solved and furthermore used to design and analyze the problem-solving system.In history, a series of fundamental work has been done for direct optimization by means of the trail-and-error mode and the fruitful outcome was the emergence of the field of evolutionary computation, which utilize various adaptive and learning mechanisms inspired from nature or social systems.In earlier, theories on evolutionary computation were interested in simulating the dynamical behavior for a fixed computational model to explain the behavior after implemented. All the theories face the unsolvable computing bounden for real application. It can be learned that the reason is partly because that they all ignored the characteristics of the problem to be solved and the practical requirements of the solution performance. As a result, these theories are all too general to be used in real analysis and algorithmic design.Currently, many concerns has been put into introducing various evolution and learning mechanisms from natural world or social systems to invent various evolutionary algorithms with the plenty of names. With the growth of the applicable solution techniques, the terminology barrier has also been formed with the complicated names and terminologies. Obviously the diversity of the phenomena do not definitely represent the diversity of the adaptive mechanisms, instead many mechanisms of these newly termed algorithms overlaps in essence. Both of the addressed trends essentially appeal the formulation of an uniform framework 1) to design or develop new solution techniques that are learned from nature or society, and 2) to synthesize the involved solution techniques into a comprehensive environment for realization of a specific problem solving system for the particular problem under the required solution reliability. The philosophy on the uniform framework is to DIY the evolvable system for solving the specific problem, instead of negatively simulating a single adaptive mechanism. With synthesis of a evolutionary system in the specific application context, the resultant system is expected to behave as we designed.Before the proposal of the comprehensive evolution environment, the essential strategies including the stochastic strategy and heuristic strategy, principles including the optimality and the equivalence in evaluation and computational models for producing simulated evolutionary search are summarized and subtracted. The corresponding theoretical results are also studied. Firstly, the stochastic strategy is indispensable in building the variation and transit mechanisms for an evolutionary search scheme, due to its versatility, simplicity, robustness and flexibility. Realization for global scope search and localized search are exemplified and a range of optimality results are discussed. Furthermore the other essential mechanism of the heuristic strategy is addressed from the aspect of the implications and the exemplified implementation. Secondly, the fundamental principle of NFL theorem for design of the problem solving system has been emphasized. We follow the framework in [89, 91] and generalize it to the theorem of equivalence in evaluation. These theoretical results support the philosophy and methodology on system synthesis.Summary of the previous work, especially on essential principles and various models of evolutionary computation is critical for proposal of the evolutionary computational system and development of the theories and methodologies to realize a synthesized system in specific solution context. Since numerous simulated evolution models have been developed in line of the theoretical research and engineering application, thus instead of enumerating the variety of simulated evolution models in current EC field, we subtract three essential population based search schemes by investigating the core mechanisms of various models. These three schemes are named as genetic information based evolution, individual behavioral evolution, and the social behavioral evolution. Along with the emphasizing the merits from population based search, the three schemes prominently exemplify three basic population search patterns: encoded solution space variation, individual learning, and the multiple sampling learning. In traditional EC field, the three types of evolution and learning mechanisms have been independently utilized to form the simulated evolution models respectively. However, in the proposed comprehensive evolution environment, these schemes will be employed to devise a variety of ready-to-use variation operators, which are used as components to synthesize the problem solving system.Then, we put forward the evolutionary computational system (ECS) as the comprehensive environment to devise the various solution models, where variation operators, control operators, self-maintained hyper-individuals are essential elements. Two fundamental characteristics distinguish the ECS from others including 1) this comprehensive environment is capable to employ both the evolution or learning mechanisms and the traditional effective techniques simultaneously to design the operators and devise the coordination rules; 2) this environment is beyond the traditional meanings of computation, which is allowed to open the interactive interfaces to interact with outer computing systems or even human being as variation operators or control operators. Although it is referred to as the computational system, it is not the computer algorithm in traditional sense.The so-called synthesis focus on the solution context including the problem characteristics and solution requirements. It leaves the original terminology aside and emphasizes the comprehensive application and coordination of various solution techniques within the ECS framework. To perform the synthesis in practical meaning, the core work concentrates on building two bridges across 1) the problem characteristics with the design of operators and 2) the solution requirements with the organization of operators.With considerations of the two connections, we propose the synthesis theories for the ECS system. The first contribution is the theory and models on the operator design. Variation operators are divided into individual learning type and global learning type according to the number of operands (hyper-individuals); the functionality is devised into localized intensive search and global information involved search; and the realization mechanisms are based on random featured operators, heuristic featured operators and mathematical structure based operators. The related realization diagrams are exemplified and discussed in depth. Moveover, the control operators including the individual selection control, variation operator control, population maintenance control and interactive interfaces are studied. The design rules and mechanisms are presented and the related functionalities are discussed.The second is the theory and patterns on system synthesis, that is the organization of the involving operators and other components. Firstly, the synthesis objective and solution conditions are specified in details. Establishment of the bridge between solution requirements on optimality, and the bridge between reliability of speed and quality are studied respectively.The optimality principles are proposed with the presentation of convergence condition I and II, and correspondingly the synthesis patterns are formulated with respect to the two convergence conditions. The synthesis pattern I provides a foundation to modify a nonconver-gent evolutionary search process to a convergent one. In comparison, the synthesis pattern II outlines an effective synthesis scheme for organization of both exploitive variation operators and explorative operators to perform the search in collaboration. The synthesis pattern II is naturally employed as the default pattern to organize the variation and control operators only if some effective exploitation variation operator can be devised.The solution reliability concerns achieving the satisfying quality solutions within the allowed solution time slot. This is a balance of quality and time in practice, while separately they can be two criteria in the course of system synthesis process. Four types of combinatorial realization schemes are discussed; the performances are studied respectively; and the application principles are also provided.We illustrate the range of principles and methodologies with three engineering optimization problems which are all derived from our finished projects. The first application is a scheduling problem (a typical combinatorial optimization problem) for picking sequencing scheduling for an automated stereotype warehousing system. The second application is a target shape design optimization problem. The third application is parameter decision for materials modeling.To demonstrate the utilization of the theories and models of synthesizing the evolutionary computational system for solving the specific problem under the specific solution requirements. Three real engineering problems are selected including the order-pickup sequencing problem in the multi-carousal warehousing system, the calibration problem for the mechanism-based unified viscoplastic damage constitutive equations and the target shape design optimization problem.The case of the order-pickup sequencing problem belongs to the class of online problems, which requires the high speed solution and without the strict optimality but expected the best. In this case, we emphasize the employment of heuristic information on the characteristics of the problem to build the expletive variation operators and based on the synthesis pattern II to organize the control operators.For the last two problems, they are the cases of the off-line problems. In the study of the calibration of the descriptive system consisting of a set of mechanism-based unified viscoplastic damage constitutive equations, we mainly study the collaboration of multiple variation operators in the synthesized ECS system. At first we devise an effective exploitive variation operator and then to coordinate the exploitive search operator, we propose a new global learning variation operator, which has three adjustable items. To emphasize the explorative performance, we realize this variation operator in the explorative form, which satisfies the global reachable condition. Based on the synthesis pattern II, we devised the evolutionary computational system under the requirements of both solution optimality and solution reliability. The convergent result was proved and the reliability performance was demonstrated by the experimental comparisons. In comparison, in the study of the target shape design optimization problem, we ma-jorally demonstrate some secondary aspects on synthesizing an evolutionary computational system, addition to the forgoing two cases. We emphasize the influences of different evaluation mechanisms on the search process, a variable representation scheme on strategy parameter updating and introduction of the direct human expert as a non-computing variation operator. The influence of these secondary concerns are studied by a series of experiments and the general principles in practice are presented.