Design optimization of broadband extreme ultraviolet polarizer in high-dimensional objective space

With the purpose of designing the extreme ultraviolet polarizer with many objectives, a combined application of multiobjective genetic algorithms is theoretically proposed. Owing to the multiobjective genetic algorithm, the relationships between different designing objectives of extreme ultraviolet polarizer have been obtained by analyzing the distribution of nondominated solutions in the 4D objective space, and the optimized multilayer design can be obtained by guiding the searching in the desired region based on the multiobjective genetic algorithm with reference direction. Comparing with the conventional method of multilayer design, our method has a higher probability of achieving the optimal multilayer design. Our work should be the first research in optimizing the optical multilayer designs in the high-dimensional objective space, and our results demonstrate a potential application of our method in the designs of optical thin films.

Network Models for Multiobjective Discrete Optimization

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest-path problem in an auxiliary network. We design techniques for exploiting network models in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows.

Evolutionary Multiobjective Optimization with Endmember Priori Strategy for Large-Scale Hyperspectral Sparse Unmixing

Mixed pixels inevitably appear in the hyperspectral image due to the low resolution of the sensor and the mixing of ground objects. Sparse unmixing, as an emerging method to solve the problem of mixed pixels, has received extensive attention in recent years due to its robustness and high efficiency. In theory, sparse unmixing is essentially a multiobjective optimization problem. The sparse endmember term and the reconstruction error term can be regarded as two objectives to optimize simultaneously, and a series of nondominated solutions can be obtained as the final solution. However, the large-scale spectral library poses a challenge due to the high-dimensional number of spectra, it is difficult to accurately extract a few active endmembers and estimate their corresponding abundance from hundreds of spectral features. In order to solve this problem, we propose an evolutionary multiobjective hyperspectral sparse unmixing algorithm with endmember priori strategy (EMSU-EP) to solve the large-scale sparse unmixing problem. The single endmember in the spectral library is used to reconstruct the hyperspectral image, respectively, and the corresponding score of each endmember can be obtained. Then the endmember scores are used as a prior knowledge to guide the generation of the initial population and the new offspring. Finally, a series of nondominated solutions are obtained by the nondominated sorting and the crowding distances calculation. Experiments on two benchmark large-scale simulated data to demonstrate the effectiveness of the proposed algorithm.

Adaptive Multi-Objective Particle Swarm Optimization Using Three-Stage Strategy

It is one of the crucial problems in solving multi-objective problems (MOPs) that balance the convergence and diversity of the algorithm to obtain an outstanding Pareto optimal solution set. In order to elevate the performance further and improve the optimization efficiency of multi-objective particle swarm optimization (MOPSO), a novel adaptive MOPSO using a three-stage strategy (tssAMOPSO) is proposed in this paper, which can effectively balance the exploration and exploitation of the population and facilitate the convergence and diversity of MOPSO. Firstly, an adaptive flight parameter adjustment, formulated by the convergence contribution of nondominated solutions, can ameliorate the convergence and diversity of the algorithm enormously. Secondly, the population carries out the three-stage strategy of optimization in each iteration, namely adaptive optimization, decomposition, and Gaussian attenuation mutation. The three-stage strategy remarkably promotes the diversity and efficiency of the optimization process. Moreover, the convergence of three-stage optimization strategy is analyzed. Then, memory interval is equipped with particles to record the recent positions, which vastly improves the reliability of personal best selection. In the maintenance of external archive, the proposed fusion index can enhance the quality of nondominated solutions directly. Finally, comparative experiments are designed by a series of benchmark instances to verify the performance of tssAMOPSO. Experimental results show that the proposed algorithm achieves admirable performance compared with other contrast algorithms.

A Hybrid Strategic Oscillation with Path Relinking Algorithm for the Multiobjective k-Balanced Center Location Problem

This paper presents a hybridization of Strategic Oscillation with Path Relinking to provide a set of high-quality nondominated solutions for the Multiobjective k-Balanced Center Location problem. The considered location problem seeks to locate k out of m facilities in order to serve n demand points, minimizing the maximum distance between any demand point and its closest facility while balancing the workload among the facilities. An extensive computational experimentation is carried out to compare the performance of our proposal, including the best method found in the state-of-the-art as well as traditional multiobjective evolutionary algorithms.

Multiobjective Sensor Ontology Matching Technique with User Preference Metrics

Due to the problem of data heterogeneity in the semantic sensor networks, the communications among different sensor network applications are seriously hampered. Although sensor ontology is regarded as the state-of-the-art knowledge model for exchanging sensor information, there also exists the heterogeneity problem between different sensor ontologies. Ontology matching is an effective method to deal with the sensor ontology heterogeneity problem, whose kernel technique is the similarity measure. How to integrate different similarity measures to determine the alignment of high quality for the users with different preferences is a challenging problem. To face this challenge, in our work, a Multiobjective Evolutionary Algorithm (MOEA) is used in determining different nondominated solutions. In particular, the evaluating metric on sensor ontology alignment’s quality is proposed, which takes into consideration user’s preferences and do not need to use the Reference Alignment (RA) beforehand; an optimization model is constructed to define the sensor ontology matching problem formally, and a selection operator is presented, which can make MOEA uniformly improve the solution’s objectives. In the experiment, the benchmark from the Ontology Alignment Evaluation Initiative (OAEI) and the real ontologies of the sensor domain is used to test the performance of our approach, and the experimental results show the validity of our approach.

Matheuristics for Multi-UAV Routing and Recharge Station Location for Complete Area Coverage

This paper presents matheuristics for routing a heterogeneous group of capacitated unmanned air vehicles (UAVs) for complete coverage of ground areas, considering simultaneous minimization of the coverage time and locating the minimal number of refueling stations. Whereas coverage path planning (CPP) is widely studied in the literature, previous works did not combine heterogeneous vehicle performance and complete area coverage constraints to optimize UAV tours by considering both objectives. As this problem cannot be easily solved, we designed high-level path planning that combines the multiobjective variable neighborhood search (MOVNS) metaheuristic and the exact mathematical formulation to explore the set of nondominated solutions. Since the exact method can interact in different ways with MOVNS, we evaluated four different strategies using four metrics: execution time, coverage, cardinality, and hypervolume. The experimental results show that applying the exact method as an intraroute operator into the variable neighborhood descent (VND) can return solutions as good as those obtained by the closest to optimal strategy but with higher efficiency.

Multi-objective Optimization of a Hybrid Nanogrid/Microgrid: Application to Desert Camps in Hafr Al-Batin

This paper presents an optimal design for a nanogrid/microgrid for desert camps in the city of Hafr Al-Batin in Saudi Arabia. The camps were designed to operate as separate nanogrids or to operate as an interconnected microgrid. The hybrid nanogrid/microgrid considered in this paper consists of a solar system, storage batteries, diesel generators, inverter, and load components. To offer the designer/operator various choices, the problem was formulated as a multi-objective optimization problem considering two objective functions, namely: the cost of electricity (COE) and the loss of power supply probability (LPSP). Furthermore, various component models were implemented, which offer a variety of equipment compilation possibilities. The formulated problem was then solved using the multi-objective evolutionary algorithm, based on both dominance and decomposition (MOEA/DD). Two cases were investigated corresponding to the two proposed modes of operation, i.e., nanogrid operation mode and microgrid operation mode. The microgrid was designed considering the interconnection of four nanogrids. The obtained Pareto front (PF) was reported for each case and the solutions forming this front were discussed. Based on this investigation, the designer/operator can select the most appropriate solution from the available set of solutions using his experience and other factors, e.g., budget, availability of equipment and customer-specific requirements. Furthermore, to assess the quality of the solutions found using the MOEA/DD, three different methods were used, and their results compared with the MOEA/DD. It was found that the MOEA/DD obtained better results (nondominated solutions), especially for the microgrid operation mode.

Big Archive-Assisted Ensemble of Many-Objective Evolutionary Algorithms

Multiobjective evolutionary algorithms (MOEAs) have witnessed prosperity in solving many-objective optimization problems (MaOPs) over the past three decades. Unfortunately, no one single MOEA equipped with given parameter settings, mating-variation operator, and environmental selection mechanism is suitable for obtaining a set of solutions with excellent convergence and diversity for various types of MaOPs. The reality is that different MOEAs show great differences in handling certain types of MaOPs. Aiming at these characteristics, this paper proposes a flexible ensemble framework, namely, ASES, which is highly scalable for embedding any number of MOEAs to promote their advantages. To alleviate the undesirable phenomenon that some promising solutions are discarded during the evolution process, a big archive that number of contained solutions be far larger than population size is integrated into this ensemble framework to record large-scale nondominated solutions, and also an efficient maintenance strategy is developed to update the archive. Furthermore, the knowledge coming from updating archive is exploited to guide the evolutionary process for different MOEAs, allocating limited computational resources for efficient algorithms. A large number of numerical experimental studies demonstrated superior performance of the proposed ASES. Among 52 test instances, the ASES performs better than all the six baseline algorithms on at least half of the test instances with respect to both metrics hypervolume and inverted generational distance.