There are many Dynamic Multiobjective Optimization Problems （DMOPs） in real life. For such problems， when the environment changes， Dynamic Multi-Objective Evolutionary Algorithm （DMOEA） is required to track the Pareto Front （PF） or Pareto Set （PS） quickly and accurately under the new environment. Aiming at the problem of poor performance of the existing algorithms on population prediction， a dynamic multi-objective optimization algorithm based on Weight Vector Clustering Prediction （WVCP） was proposed. Firstly， the uniform weight vectors were generated in the target space， and the individuals in the population were clustered. According to the clustering results， the distribution of the population was analyzed. Secondly， a time series was established for the center points of clustered individuals. For the same weight vector， the corresponding coping strategies were adopted to supplement individuals according to different clustering situations. If there were cluster centers at all adjacent moments， the difference model was used to predict individuals in the new environment. If there was no cluster center at a certain moment， the centroid of the cluster centers of adjacent weight vectors was used as the cluster center at that moment， and then the difference model was used to predict individuals. In this way， the problem of poor population distribution was solved effectively， and the accuracy of prediction was improved at the same time. Finally， the introduction of individual supplement strategy was beneficial to make full use of historical information. In order to verify the performance of the proposed algorithm， simulation comparison of this algorithm and four representative algorithms was carried out. Experimental results show that the proposed algorithm can solve DMOPs well.

Most of the Multi-objective Optimization Problems （MOP） in real life are Dynamic Multi-objective Optimization Problems （DMOP）， and the objective function， constraint conditions and decision variables of such problems may change with time， which requires the algorithm to quickly adapt to the new environment after the environment changes， and guarantee the diversity of Pareto solution sets while converging to the new Pareto frontier quickly. To solve the problem， an Adaptive Prediction Dynamic Multi-objective Optimization Algorithm based on New Evaluation Index （NEI-APDMOA） was proposed. Firstly， a new evaluation index better than crowding was proposed in the process of population non-dominated sorting， and the convergence speed and population diversity were balanced in different stages， so as to make the convergence process of population more reasonable. Secondly， a factor that can judge the strength of environmental changes was proposed， thereby providing valuable information for the prediction stage and guiding the population to better adapt to environmental changes. Finally， three more reasonable prediction strategies were matched according to environmental change factor， so that the population was able to respond to environmental changes quickly. NEI-APDMOA， DNSGA-Ⅱ-A （Dynamic Non-dominated Sorting Genetic Algorithm-Ⅱ-A）， DNSGA-Ⅱ-B （Dynamic Non-dominated Sorting Genetic Algorithm-Ⅱ-B） and PPS （Population Prediction Strategy） algorithms were compared on nine standard dynamic test functions. Experimental results show that NEI-APDMOA achieves the best average Inverted Generational Distance （IGD） value， average SPacing （SP） value and average Generational Distance （GD） value on nine， four and eight test functions respectively， and can respond to environmental changes faster.

In view of the problems of ant colony algorithm in global path planning under static environment， such as being unable to find the shortest path， slow convergence speed， great blindness of path search and many inflection points， an improved ant colony algorithm was proposed. Taking the grid map as the running environment of the robot， the initial pheromones were distributed unevenly， so that the path search tended to be near the line between the starting point and the target point； the information of the current node， the next node and the target point was added into the heuristic function， and the dynamic adjustment factor was introduced at the same time， so as to achieve the purpose of strong guidance of the heuristic function in the early stage and strengthening the guidance of pheromone in the later stage； the pseudo-random transfer strategy was introduced to reduce the blindness of path selection and speed up finding the shortest path； the volatilization coefficient was adjusted dynamically to make the volatilization coefficient larger in the early stage and smaller in the later stage， avoiding premature convergence of the algorithm； based on the optimal solution， B-spline curve smoothing strategy was introduced to further optimize the optimal solution， resulting in shorter and smoother path. The sensitivity analysis of the main parameters of the improved algorithm was conducted， the feasibility and effectiveness of each improved step of the algorithm were tested， the simulations compared with the traditional ant colony algorithm and other improved ant colony algorithms under 20×20 and 50×50 environments were given， and the experimental results verified the feasibility， effectiveness and superiority of the improved algorithm.

The reasonable exploration of the infeasible region in constrained multi-objective evolutionary algorithms for solving optimization problems with large infeasible domains not only helps the population to converge quickly to the optimal solution in the feasible region， but also reduces the impact of unpromising infeasible region on the performance of the algorithm. Based on this， a Constrained Multi-Objective Evolutionary Algorithm based on Space Shrinking Technique （CMOEA-SST） was proposed. Firstly， an adaptive elite retention strategy was proposed to improve the initial population in the Pull phase of Push and Pull Search for solving constrained multi-objective optimization problems （PPS）， so as to increase the diversity and feasibility of the initial population in the Pull phase. Then， the space shrinking technique was used to gradually reduce the search space during the evolution process， which reduced the impact of unpromising infeasible regions on the algorithm performance. Therefore， the algorithm was able to improve the convergence accuracy while taking account of both convergence and diversity. In order to verify the performance of the proposed algorithm， it was simulated and compared with four representative algorithms including C-MOEA/D （adaptive Constraint handling approach embedded MOEA/D）， ToP （handling constrained multi-objective optimization problems with constraints in both the decision and objective spaces）， C-TAEA （Two-Archive Evolutionary Algorithm for Constrained multi-objective optimization） and PPS on the test problems of LIRCMOP series. Experimental results show that CMOEA-SST has better convergence and diversity when dealing with constrained optimization problems with large infeasible regions.