Research On The Framework For Self-Adaptively Solving Multi-Objective Optimization Problems

Multi-objective optimization problems exist in many applications. Basic algorithms, such as traditional multi-objective optimization algorithms, multi-objective genetic algorithms and multi-objective particle swarm optimization algorithms, meet several drawbacks as trapped into local optima when handling complex realistic problems. The main reason lies in that the biases of them are too simple to take full use of problem features. Present algorithm design totally depends on experiences, needing repeatedly testing and modifying. Complexity of the algorithm would remarkably reduce its generalization ability, i.e., make it lack of reuse. To simplify algorithm design and reuse current algorithms is therefore of great importance.Through feature divide-and-rule and strategy reuse, the framework for self-adaptively solving multi-objective optimization problems proposed by this paper efficiently settles these two issues. Classifying the features of problem solving, using behavior of crowd effectively fulfilling tasks through dividing and cooperating for reference, the framework is designed to contain three phases, thirteen modules and many strategies. Phases depict the flow of the solving process and contain several modules; modules correspond to feature categories and contain several strategies; strategies deal with concrete features and become reusable units. Algorithm design now simplifies to choose proper strategies for modules in the framework, which also become easy after analysis and compare between strategies. If still unsure which strategy is the most suitable, the corresponding module could choose a group of feasible strategies, then the framework would learn the online performance and choose the best itself.Core ideas of modules are described as follows. Dimensional cooperation analyzes the correlativity between function dimensions and decreases search spaces; function transformation analyzes function shape and online adjusts it to make it easier to be optimized; multi-swarm analyzes function character and partitions search spaces; the three cooperatively decompose problems'correlativity. Initial distribution utilizes former knowledge to direct search; global exploration utilizes algorithms having good global search ability to make the algorithm quickly converge to global best region; local exploitation utilizes algorithms having good local search ability to make the algorithm quickly converge to local best of the region; the three cooperatively balance exploration and exploitation. Dominance rank utilizes the concept of Pareto dominance to build a partial order of excellence between individuals; diversity estimation utilizes spatial distance to estimate the distribution of individuals; optimal selection utilizes dominance rank and diversity estimation to choose individuals that are non-dominated or less-dominated and sparse distributed; the three cooperatively balance convergence and diversity. Result analysis utilizes quantity indicators to measure the total performance of the framework; strategy appraisement utilizes result analysis to evaluate the performance of strategies; strategy selection utilizes strategy appraisement to endow optimal ones with more chances to be selected by the framework; the three cooperatively realize self-adaptively choosing strategies. Parameter selection utilizes dynamic algorithm parameters to reduce the impact of artificial selection.The paper first defines multi-objective optimization problems and enumerates the defects of basic algorithms. Then it theoretically discusses the framework, analyzing problem solving, classifying problem features, studying behavior of crowd and proposing the framework. At last, using particle swarm optimization as the strategy of the global exploration module and splitting optimal selection into archive selection, personal best selection and global best selection, it describes the core idea of each module and compares the idea, bias, hypothesis and performance of each strategy in detail.