Survey of Robot 3D Path Planning Algorithms <s> Ant Colony <s> Shuffled Frog Leaping Algorithm (SFLA) is a meta-heuristic for solving discrete optimization problems. Here it is applied to determine optimal discrete pipe sizes for new pipe networks and for network expansions. SFLA is a population based, cooperative search metaphor inspired by natural memetics. The algorithm uses memetic evolution in the form of infection of ideas from one individual to another in a local search. The local search is similar in concept to particle swarm optimization. A shuffling strategy allows for the exchange of information between local searches to move toward a global optimum. This paper summarizes the development of SFLANET, a computer model that links SFLA and the hydraulic simulation software EPANET and its library functions. Application of SFLANET to literature network design problems is then described. Although the algorithm is in its initial stages of development, promising results were obtained. <s> BIB001 </s> Survey of Robot 3D Path Planning Algorithms <s> Ant Colony <s> Abstract Ant colony optimization (ACO) is successfully applied in optimization problems. Performance of the basic ACO for small problems with moderate dimension and searching space is satisfactory. As the searching space grows exponentially in the large-scale unit commitment problem, the basic ACO is not applicable for the vast size of pheromone matrix of ACO in practical time and physical computer-memory limit. However, memory-bounded methods prune the least-promising nodes to fit the system in computer memory. Therefore, the authors propose memory-bounded ant colony optimization (MACO) in this paper for the scalable (no restriction for system size) unit commitment problem. This MACO intelligently solves the limitation of computer memory, and does not permit the system to grow beyond a bound on memory. In the memory-bounded ACO implementation, A ∗ heuristic is introduced to increase local searching ability and probabilistic nearest neighbor method is applied to estimate pheromone intensity for the forgotten value. Finally, the benchmark data sets and existing methods are used to show the effectiveness of the proposed method. <s> BIB002 </s> Survey of Robot 3D Path Planning Algorithms <s> Ant Colony <s> Abstract Three-dimension path planning of uninhabited combat air vehicle (UCAV) is a complicated optimal problem, which mainly focuses on optimizing the flight route considering the different types of constrains under complicated combating environments. A new hybrid meta-heuristic ant colony optimization (ACO) and differential evolution (DE) algorithm is proposed to solve the UCAV three-dimension path planning problem. DE is applied to optimize the pheromone trail of the improved ACO model during the process of ant pheromone updating. Then, the UCAV can find the safe path by connecting the chosen nodes of the three-dimensional mesh while avoiding the threats area and costing minimum fuel. This new approach can accelerate the global convergence speed while preserving the strong robustness of the basic ACO. The realization procedure for this hybrid meta-heuristic approach is also presented in detail. In order to make the optimized UCAV path more feasible, the к-trajectory is adopted for smoothing the path. Finally, series experimental comparison results demonstrate that this proposed hybrid meta-heuristic method is more effective and feasible in UCAV three-dimension path planning than the basic ACO model. <s> BIB003 </s> Survey of Robot 3D Path Planning Algorithms <s> Ant Colony <s> Relative coordination has predominant advantage in uncertain environment path planning problem because it denies much of redundant information of the dynamic environment while avoids the rotation transformation which is a big burden in the traditional methods. Based on relative coordination, this paper proposes a trimmed Ant Colony Optimization (ACO) algorithm for three dimensional trajectory generation, i.e., path planning for target-pursuing and obstacle-avoiding (TPOA). We construct the city-map directly on the acceleration of the pursuing vehicle, an aerial robot. Then the robot's kinematics and the dynamics constraints will be embedded conveniently into the ACO formulation. As a result, the searching space in the ACO formulation shrinks greatly and the robot's movement is real and more feasible for application. This novel approach is verified by various simulations and the results show the good performance of efficiency. <s> BIB004 </s> Survey of Robot 3D Path Planning Algorithms <s> Ant Colony <s> Abstract In this paper, optimal paths in environments with obstacles for underwater vehicles are computed using a numerical solution of the nonlinear optimal control problem (NOCP). The underwater vehicle is modeled with six-dimensional nonlinear and coupled equations of motion, controlled by DC motors in all degrees of freedom. An energy performance index combined with a time consumption index is used. Both fixed and free final times are considered. Solving NOCP leads to a two point boundary value problem (TPBVP). Five intelligent evolutionary algorithms (EAs), which include genetic algorithm, memetic algorithm, particle swarm optimization, ant colony optimization and shuffled frog leaping algorithm, are applied to solve the NOCP. For comparison, a conjugate gradient penalty method is also used to solve the TPBVP. The simulation results show that the trajectories obtained by the intelligent methods are better than those of conjugate gradient method. After analyzing a simple path planning problem, the time-energy-optimal path planning problem in energetic environments is propounded and solved by EAs. The problem of static obstacle collision avoidance in an energetic environment is also studied. <s> BIB005 </s> Survey of Robot 3D Path Planning Algorithms <s> Ant Colony <s> Abstract Optimal path in an environment containing obstacles for underwater vehicle can be computed using a numerical solution of the nonlinear optimal control problem (NOCP). The underwater vehicle is modelled with six-dimensional nonlinear and coupled equations of motion, controlled by DC motors in all degrees of freedom. The intent of this computation is to offer a comprehensive perception of the behaviour of underwater autonomous vehicle and also to obtain the unknown parameters of the model which can be devoted in motion planning strategy of underwater robot. To execute tasks along a distinctive path in a convoluted environment, motion planning necessities to concede the underwater robot to be in motion between its current and final configurations without any collision within the encircling environment. Traditional optimization methods are not very effective to it, which are easy to plunge into local minimum. The optimization of path as well as time taken has been analysed here using modified shuffled frog leaping (SFL) optimization algorithm based on perception, cognition and sensor fusion. Path scheduling has to be executed for achieving integration of different preliminary robotic behaviours (e.g. obstacle avoidance, wall and edge following, escaping dead end and target seeking) in partially unknown territory (land or water). The optimal path is generated with this method when the robot reaches its target. The simulation studies ensure that the heuristic navigational approach possesses intelligent decision-making capabilities in negotiating hazardous terrain conditions during the under-water robot motion. <s> BIB006
Optimization. Animals such as ants could manage to establish shortest path from their colony to the feeding source and back home by group cooperation; researchers mimic the behavior and proposed Ant Colony Optimization (ACO) method. ACO introduces two basic concepts, which are "intensity of trail" and "visibility" to form the transition probability which at last decides which way to go, thus to formulate the shortest path. "Intensity of trail" on edge ( , ) at time + is expressed by the following formula:  where Δ is the sum of all ants' "pheromone" laid on the edge ( , ) between time and + , Δ is the th ant "pheromone" laid, is a constant, and is the th ant tour length. "Visibility" on edge ( , ) can be described as where is the Euclidean distance between and and determines the degree of how close the state is to state . ACO aims to find the best path by evaluating the pheromone density in each step. The process runs flexibly in dynamic environments only needing to change the representation of "intensity of trail" of a certain edge. The algorithm is proved to be able to deal with multiobjective path planning problems, and it is also able to tackle continuous planning problems  . ACO is now widely implemented in 3D environment BIB003 BIB004 for path planning. However, it must be emphasized that the basic ACO is not applicable to handle vast size of pheromone matrix in practical time with computer memory limitation. Thus it is validated in simulation, but not practical in real time planning situations in most cases. Authors in BIB003 proposed a differential evolution (DE) ACO method by applying differential evolution to optimize the pheromone tail. DE is a simple population-based algorithm; it tends to be more efficiency; thus the work takes advantage of DE crossover operation to achieve faster convergence. Method proposed in BIB004 started with relative coordinates, which can avoid rotation transformation for UAV, to reduce time consumption for generating an optimal path. Saber and Alshareef BIB002 came up with using A * to increase the local searching ability and introduced probabilistic nearest neighbor method to estimate the pheromone intensity; it is proved to be effective. The other three Evolutionary Algorithms, Memetic Algorithm  , Particle Swarm Optimization  , and Shuffled Frog Leaping Algorithm BIB001 , all almost share the same exploring process, and their shortcomings and advantages are also almost the same. Although compared to GA and ACO they have a lower degree of implementation, still a lot of works BIB005 BIB006  have been done with these methods.