A Perturbed Self-organizing Multiobjective Evolutionary Algorithm to solve Multiobjective TSP

Travelling Salesman Problem (TSP) is a very important NP-Hard problem getting focused more on these days. Having improvement on TSP, right now consider the multi-objective TSP (MOTSP), broadened occurrence of travelling salesman problem. Since TSP is NP-hard issue MOTSP is additionally a NP-hard issue. There are a lot of algorithms and methods to solve the MOTSP among which Multiobjective evolutionary algorithm based on decomposition is appropriate to solve it nowadays. This work presents a new algorithm which combines the Data Perturbation, Self-Organizing Map (SOM) and MOEA/D to solve the problem of MOTSP, named Perturbed Self-Organizing multiobjective Evolutionary Algorithm (P-SMEA). In P-SMEA Self-Organizing Map (SOM) is used extract neighborhood relationship information and with MOEA/D subproblems are generated and solved simultaneously to obtain the optimal solution. Data Perturbation is applied to avoid the local optima. So by using the P-SMEA, MOTSP can be handled efficiently. The experimental results show that P-SMEA outperforms MOEA/D and SMEA on a set of test instances

Shift-based density estimation for pareto-based algorithms in many-objective optimization

It is commonly accepted that Pareto-based evolutionary multiobjective optimization (EMO) algorithms encounter difficulties in dealing with many-objective problems. In these algorithms, the ineffectiveness of the Pareto dominance relation for a high-dimensional space leads diversity maintenance mechanisms to play the leading role during the evolutionary process, while the preference of diversity maintenance mechanisms for individuals in sparse regions results in the final solutions distributed widely over the objective space but distant from the desired Pareto front. Intuitively, there are two ways to address this problem: 1) modifying the Pareto dominance relation and 2) modifying the diversity maintenance mechanism in the algorithm. In this paper, we focus on the latter and propose a shift-based density estimation (SDE) strategy. The aim of our study is to develop a general modification of density estimation in order to make Pareto-based algorithms suitable for many-objective optimization. In contrast to traditional density estimation that only involves the distribution of individuals in the population, SDE covers both the distribution and convergence information of individuals. The application of SDE in three popular Pareto-based algorithms demonstrates its usefulness in handling many-objective problems. Moreover, an extensive comparison with five state-of-the-art EMO algorithms reveals its competitiveness in balancing convergence and diversity of solutions. These findings not only show that SDE is a good alternative to tackle many-objective problems, but also present a general extension of Pareto-based algorithms in many-objective optimization. © 2013 IEEE

CES-478 Comparison between MOEA/D and NSGA-II on the Multiobjective Travelling Salesman Problem

Most multiobjective evolutionary algorithms are based on Pareto dom- inance for measuring the quality of solutions during their search, among them NSGA-II is well-known. A very few algorithms are based on de- composition and implicitly or explicitly try to optimize aggregations of the objectives. MOEA/D is a very recent such an algorithm. One of the major advantages of MOEA/D is that it is very easy to use well-developed single optimization local search within it. This paper compares the perfor- mance of MOEA/D and NSGA-II on the multiobjective travelling sales- man problem and studies the e®ect of local search on the performance of MOEA/D

Evolutionary many-objective optimisation: pushing the boundaries

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonMany-objective optimisation poses great challenges to evolutionary algorithms. To start with, the ineffectiveness of the Pareto dominance relation, which is the most important criterion in multi-objective optimisation, results in the underperformance of traditional Pareto-based algorithms. Also, the aggravation of the conflict between proximity and diversity, along with increasing time or space requirement as well as parameter sensitivity, has become key barriers to the design of effective many-objective optimisation algorithms. Furthermore, the infeasibility of solutions' direct observation can lead to serious difficulties in algorithms' performance investigation and comparison. In this thesis, we address these challenges, aiming to make evolutionary algorithms as effective in many-objective optimisation as in two- or three-objective optimisation. First, we significantly enhance Pareto-based algorithms to make them suitable for many-objective optimisation by placing individuals with poor proximity into crowded regions so that these individuals can have a better chance to be eliminated. Second, we propose a grid-based evolutionary algorithm which explores the potential of the grid to deal with many-objective optimisation problems. Third, we present a bi-goal evolution framework that converts many objectives of a given problem into two objectives regarding proximity and diversity, thus creating an optimisation problem in which the objectives are the goals of the search process itself. Fourth, we propose a comprehensive performance indicator to compare evolutionary algorithms in optimisation problems with various Pareto front shapes and any objective dimensionality. Finally, we construct a test problem to aid the visual investigation of evolutionary search, with its Pareto optimal solutions in a two-dimensional decision space having similar distribution to their images in a higher-dimensional objective space. The work reported in this thesis is the outcome of innovative attempts at addressing some of the most challenging problems in evolutionary many-objective optimisation. This research has not only made some of the existing approaches, such as Pareto-based or grid-based algorithms that were traditionally regarded as unsuitable, now effective for many-objective optimisation, but also pushed other important boundaries with novel ideas including bi-goal evolution, a comprehensive performance indicator and a test problem for visual investigation. All the proposed algorithms have been systematically evaluated against existing state of the arts, and some of these algorithms have already been taken up by researchers and practitioners in the field.Department of Computer Science, Brunel University Londo

A Variable Neighborhood MOEA/D for Multiobjective Test Task Scheduling Problem

Test task scheduling problem (TTSP) is a typical combinational optimization scheduling problem. This paper proposes a variable neighborhood MOEA/D (VNM) to solve the multiobjective TTSP. Two minimization objectives, the maximal completion time (makespan) and the mean workload, are considered together. In order to make solutions obtained more close to the real Pareto Front, variable neighborhood strategy is adopted. Variable neighborhood approach is proposed to render the crossover span reasonable. Additionally, because the search space of the TTSP is so large that many duplicate solutions and local optima will exist, the Starting Mutation is applied to prevent solutions from becoming trapped in local optima. It is proved that the solutions got by VNM can converge to the global optimum by using Markov Chain and Transition Matrix, respectively. The experiments of comparisons of VNM, MOEA/D, and CNSGA (chaotic nondominated sorting genetic algorithm) indicate that VNM performs better than the MOEA/D and the CNSGA in solving the TTSP. The results demonstrate that proposed algorithm VNM is an efficient approach to solve the multiobjective TTSP

Multi-Line distance minimization: A visualized many-objective test problem suite

Studying the search behavior of evolutionary many objective optimization is an important, but challenging issue. Existing studies rely mainly on the use of performance indicators which, however, not only encounter increasing difficulties with the number of objectives, but also fail to provide the visual information of the evolutionary search. In this paper, we propose a class of scalable test problems, called multi-line distance minimization problem (ML-DMP), which are used to visually examine the behavior of many-objective search. Two key characteristics of the ML-DMP problem are: 1) its Pareto optimal solutions lie in a regular polygon in the two-dimensional decision space, and 2) these solutions are similar (in the sense of Euclidean geometry) to their images in the high-dimensional objective space. This allows a straightforward understanding of the distribution of the objective vector set (e.g., its uniformity and coverage over the Pareto front) via observing the solution set in the two-dimensional decision space. Fifteen well-established algorithms have been investigated on three types of 10 ML-DMP problem instances. Weakness has been revealed across classic multi-objective algorithms (such as Pareto-based, decomposition based and indicator-based algorithms) and even state-of-the-art algorithms designed especially for many-objective optimization. This, together with some interesting observations from the experimental studies, suggests that the proposed ML-DMP may also be used as a benchmark function to challenge the search ability of optimization algorithms.10.13039/501100000266-Engineering and Physical Sciences Research Council; 10.13039/501100001809-National Natural Science Foundation of China; 10.13039/501100000288-Royal Society

Joint 3D Trajectory Design and Time Allocation for UAV-Enabled Wireless Power Transfer Networks

This paper considers a rotary-wing unmanned aerial vehicle (UAV)-enabled wireless power transfer system, where a UAV is dispatched as an energy transmitter (ET), transferring radio frequency (RF) signals to a set of energy receivers (ERs) periodically. We aim to maximize the energy harvested at all ERs by jointly optimizing the UAV's three-dimensional (3D) placement, beam pattern and charging time. However, the considered optimization problem taking into account the drone flight altitude and the wireless coverage performance is formulated as a non-convex problem. To tackle this problem, we propose a low-complexity iterative algorithm to decompose the original problem into four sub-problems in order to optimize the variables sequentially. In particular, we first use the sequential unconstrained convex minimization based algorithm to find the globally optimal UAV two-dimensional (2D) position. Subsequently, we can directly obtain the optimal UAV altitude as the objective function of problem is monotonic decreasing with respect to UAV altitude. Then, we propose the multiobjective evolutionary algorithm based on decomposition (MOEA/D) based algorithm to control the phase of antenna array elements, in order to achieve high steering performance of multi-beams. Finally, with the above solved variables, the original problem is reformulated as a single-variable optimization problem where charging time is the optimization variable, and can be solved using the standard convex optimization techniques. Furthermore, we use the branch and bound method to design the UAV trajectory which can be constructed as traveling salesman problem (TSP) to minimize flight distance. Numerical results validate the theoretical findings and demonstrate that significant performance gain in terms of sum received power of ERs can be achieved by the proposed algorithm in UAV-enabled wireless power transfer networks

Evolutionary Computation 2020

Intelligent optimization is based on the mechanism of computational intelligence to refine a suitable feature model, design an effective optimization algorithm, and then to obtain an optimal or satisfactory solution to a complex problem. Intelligent algorithms are key tools to ensure global optimization quality, fast optimization efficiency and robust optimization performance. Intelligent optimization algorithms have been studied by many researchers, leading to improvements in the performance of algorithms such as the evolutionary algorithm, whale optimization algorithm, differential evolution algorithm, and particle swarm optimization. Studies in this arena have also resulted in breakthroughs in solving complex problems including the green shop scheduling problem, the severe nonlinear problem in one-dimensional geodesic electromagnetic inversion, error and bug finding problem in software, the 0-1 backpack problem, traveler problem, and logistics distribution center siting problem. The editors are confident that this book can open a new avenue for further improvement and discoveries in the area of intelligent algorithms. The book is a valuable resource for researchers interested in understanding the principles and design of intelligent algorithms

Joint 3D Trajectory Design and Time Allocation for UAV-Enabled Wireless Power Transfer Networks

This paper considers a rotary-wing unmanned aerial vehicle (UAV)-enabled wireless power transfer system, where a UAV is dispatched as an energy transmitter (ET), transferring radio frequency (RF) signals to a set of energy receivers (ERs) periodically. We aim to maximize the energy harvested at all ERs by jointly optimizing the UAV's three-dimensional (3D) placement, beam pattern and charging time. However, the considered optimization problem taking into account the drone flight altitude and the wireless coverage performance is formulated as a non-convex problem. To tackle this problem, we propose a low-complexity iterative algorithm to decompose the original problem into four sub-problems in order to optimize the variables sequentially. In particular, we first use the sequential unconstrained convex minimization based algorithm to find the globally optimal UAV two-dimensional (2D) position. Subsequently, we can directly obtain the optimal UAV altitude as the objective function of problem is monotonic decreasing with respect to UAV altitude. Then, we propose the multiobjective evolutionary algorithm based on decomposition (MOEA/D) based algorithm to control the phase of antenna array elements, in order to achieve high steering performance of multi-beams. Finally, with the above solved variables, the original problem is reformulated as a single-variable optimization problem where charging time is the optimization variable, and can be solved using the standard convex optimization techniques. Furthermore, we use the branch and bound method to design the UAV trajectory which can be constructed as traveling salesman problem (TSP) to minimize flight distance. Numerical results validate the theoretical findings and demonstrate that significant performance gain in terms of sum received power of ERs can be achieved by the proposed algorithm in UAV-enabled wireless power transfer networks