Algorithms For Two Kinds Of Complex Optimization Problems

Many real-world application problems can be formulated as optimization problems.Global optimization problems(GOPs)and large-scale multi-objective optimization problems(LSMOPs)are two kinds of complex optimization problems.The main difficulties in solving these problems are: 1)Many global problems are complex and have numerous local minima.It is difficult for the existing algorithms to jump out the local minima and find the global optimal solution.2)With the increasing number of decision variables,the decision variable space increases exponentially.The existing algorithms cannot search the whole decision variable space within the limited computing resources.3)For LSMOPs,how to balance the convergence and diversity of solutions while ensuring the search efficiency of the algorithm is also a difficult problem.To overcome these difficulties,this thesis designs many new algorithms and strategies.The main innovations are as follows:1.When solving the complex global optimization problems with numerous local minima,the algorithms often fall into the local minima and cannot jump out.To overcome this difficulty,we propose a new filled function method.Firstly,we use a flatten technique to eliminate many local minima.Based on this,a new continuously filled function without any adjustable parameter is constructed.To make the algorithm easier to jump out the local minima,an adaptive strategy for determining the initial points is proposed by dynamically increasing the directions uniformly distributed around the current optimal solution.Furthermore,we propose a narrow valley widening strategy which can make it much easier for the filled function method to get a more superior minimum in the narrow valleys.The experimental results show that the developed method performs better than the compared algorithms for solving global optimization problems.2.The decision variable space is too large for the existing algorithms to search within the limited computing resources when solving large-scale global optimization problems.To overcome this difficulty,a modified self-adaptive discrete scan method is applied to scan the whole search space roughly,where the shrink rate can be adaptively adjusted with the different evolution stages,which would make the search focus on the promising regions.Then,a integrated optimization method is developed to tackle the separable and non-separable problems by using different strategies.It combines different optimization algorithms and assigns them to different problems and different groups dynamically.Based on these,a two-stage integrated optimization algorithm is proposed.The numerical experimental results show that our algorithm is more effective and competitive than the compared state-of-the-art algorithms in terms of solution accuracy.3.To overcome the two difficulties in solving LSMOPs,we propose a new reference point selection and direction guiding algorithm.We first design a new reference points selection strategy to enhance the diversity of algorithms which selects not only a part of non-dominated solutions with the largest crowding distance,but also a part of relatively uniformly distributed solutions as the reference points.Second,we propose a direction-guided offspring generation strategy,where a type of potential direction is designed to generate promising solutions which can balance the population convergence and diversity.The numerical experimental results show that the developed algorithm is more effective and can obtain significantly better solutions than the compared algorithms.4.For LSMOPs,it is very important to use the limited computation resource to explore and exploit the key regions.For this purpose,we propose a learning and potential area-mining evolutionary algorithm to accelerate the optimization.Firstly,we mine the population gathered areas as the promising areas,i.e.key areas,by clustering.Then,the directions with convergence or diversity potential are constructed according to the proposed multi-guiding points scheme to guide the population evolution.The search range is narrowed down from the whole space to the uniformly distributed potential areas,which greatly reduces the consumption of computing resources.Subsequently,a local search and a global search schemes are designed to enhance the population convergence while ensuring its diversity.The experimental results show that the designed algorithm can obtain significantly better solutions than the compared algorithms and is more competitive in solving LSMOPs.