Neighboring Subproblems Research Articles

Competitive Decomposition-Based Multiobjective Architecture Search for the Dendritic Neural Model.

The dendritic neural model (DNM) is computationally faster than other machine-learning techniques, because its architecture can be implemented by using logic circuits and its calculations can be performed entirely in binary form. To further improve the computational speed, a straightforward approach is to generate a more concise architecture for the DNM. Actually, the architecture search is a large-scale multiobjective optimization problem (LSMOP), where a large number of parameters need to be set with the aim of optimizing accuracy and structural complexity simultaneously. However, the issues of irregular Pareto front, objective discontinuity, and population degeneration strongly limit the performances of conventional multiobjective evolutionary algorithms (MOEAs) on the specific problem. Therefore, a novel competitive decomposition-based MOEA is proposed in this study, which decomposes the original problem into several constrained subproblems, with neighboring subproblems sharing overlapping regions in the objective space. The solutions in the overlapping regions participate in environmental selection for the neighboring subproblems and then propagate the selection pressure throughout the entire population. Experimental results demonstrate that the proposed algorithm can possess a more powerful optimization ability than the state-of-the-art MOEAs. Furthermore, both the DNM itself and its hardware implementation can achieve very competitive classification performances when trained by the proposed algorithm, compared with numerous widely used machine-learning approaches.

Research on the strategy of using graphic creativity in visual communication design in the context of Internet+

Abstract With the rapid development of the times, new tools are constantly appearing in visual communication design, such as the use of graphic creativity in visual communication. With this as a starting point, this paper introduces the MOEA/D algorithm, which decomposes the MOP problem into a series of subproblems to be solved by decomposition techniques, using weight vectors to obtain the neighbors of each subproblem, followed by calculating the neighbor subproblems, dividing the individuals into segments, and obtaining the child individuals. Finally, the fitness of each offspring individual was calculated and cut to give the final level of each factor. Finally, the strategy of using graphic creativity in visual communication design in the context of Internet+ is calculated from the MOEA/D algorithm. The experimental results showed that by means of multiple control groups, the experimental group achieved a 30% correct rate for Q3 and Q9 quiz questions, and the experimental group had a significantly greater correct rate than the control group. Therefore, more design concepts and design thinking can be explored through the study and analysis of graphic creativity to help the use of graphic creativity in the work of visual communication design.

Virtual packaging model construction of visual images for visual communication in the context of modern information convergence

Abstract With the rapid development of the times, new tools are constantly appearing in visual communication design, such as the use of image packaging in visual communication. In order to speed up the transmission speed of visual images, ensure the integrity of visual images, and solve the transmission effect during visual communication. In this paper, based on the modern information fusion context, the object visualization image virtual packaging for model construction, the introduction of MOEA/D algorithm, the decomposition technique to decompose the MOP problem into a series of subproblems to solve, the use of weight vectors to obtain the neighbors of each subproblem, followed by the calculation of neighbor subproblems, the division of individuals into segments to obtain the child individuals. Finally, the fitness of each offspring individual was calculated and cut to give the final level of each factor. The final calculation of the proportion of images in different media communication from the MOEA/D algorithm leads to the strategy of using image virtual packaging in visual communication design. The experimental results showed that by means of multiple control groups, the experimental group achieved a 30% correct rate for Q3 and Q9 quiz questions, and the experimental group had a significantly greater correct rate than the control group. Therefore, more design concepts and design thinking can be explored through the study and analysis of image virtualization to help the use of image virtual packaging in visual communication design work.

Local-Diversity Evaluation Assignment Strategy for Decomposition-Based Multiobjective Evolutionary Algorithm

Decomposition-based multiobjective evolutionary algorithms (MOEAs) transform a multiobjective optimization problem (MOP) into a set of subproblems and then optimize them collaboratively. When two adjacent objective vectors are similar but the difference in the corresponding decision vectors is large, it is difficult to transfer from a solution of one subproblem to solutions of its neighboring subproblems. In this article, we argue that the key to overcoming this difficulty is the evaluation assignment for different subproblems based on local density and global utility. We propose a local-density measurement model to estimate the solution density around each subproblem. Based on the model, a local-diversity evaluation assignment strategy for the decomposition-based MOEA is designed to assign fitness evaluations among different subproblems. Two discrete MOPs are selected as test instances for experiments because they satisfy the premise that the difference in the corresponding decision vectors of adjacent objective vectors is large. Experimental results indicate that the proposed strategy enhances the population diversity. Besides, the combination of the proposed strategy and the evaluation assignment for high global utility subproblems can overcome the difficulty in transferring from a solution of one subproblem to solutions of its neighboring subproblems. The results also verify that the proposed algorithm significantly outperforms the state-of-the-art evaluation assignment MOEAs regarding the inverted generational distance and the hypervolume metrics.

Dynamic Neighborhood Adjustment Strategy for Multi-Objective Evolutionary Algorithm Based on Decomposition

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has achieved great success in the field of evolutionary multi-objective optimization. It decomposes a multi-objective optimization problem into a number of scalar optimization sub-problems. Each sub-problem is optimized by using information from its neighboring sub-problems. Therefore, the neighborhood size of each sub-problem plays an important role in MOEA/D. Different neighborhood sizes are tested in this paper. Experimental results demonstrate that larger neighborhood size helps achieve better convergence and diversity with more CPU time and vice versa. MOEA/D uses constant neighborhood size during the whole process, and it is difficult to balance the convergence, diversity and running time. Therefore, this paper propose an algorithm based on MOEA/D. The algorithm adjusts the neighborhood size dynamically in different generations and different sub-problems to reduce the running time while the convergence and diversity of this algorithm are similar or better than other state-of-the-art algorithms. Compared to the original MOEA/D, experimental results show that adjusting the neighborhood size dynamically is a good way to reduce the running time significantly while maintaining the convergence and diversity. Furthermore, the algorithm proposed in this paper is compared with five state-of-the-art algorithms based on MOEA/D. The experimental results show that the proposed algorithm outperforms the others in efficiency while performs similarly in convergence and diversity.

Evolutionary Optimization of Drone-Swarm Deployment for Wireless Coverage

The need for longer lasting and wider wireless coverage has driven the transition from a single drone to drone swarms. Unlike the single drone, drone swarms can collaboratively achieve full coverage over a target area. However, the existing literature on the drones’ wireless coverage has largely overlooked one important fact: that the network lifetime is determined by the minimum leftover energy among all drones. Hence, the maximum energy consumption is minimized in our drone-swarms deployment problem (DSDP), which aims to balance the energy consumption of all drones and maximize the full-coverage network lifetime. We present a genetic algorithm that encodes the solutions as chromosomes and simulates the biological evolution process in search of a favorable solution. Specifically, an integer code scheme is adopted to encode the sequence of the drones’ deployment. With the order of the drones’ sequence determined by the coding process, we introduce a feasibility checking operator with binary search to improve the performance. By relaxing the constraint of full coverage as an objective of coverage rate, we study the tradeoffs between energy consumption, number of drones, and coverage rate of the target area. By taking advantage of the MOEA/D framework with neighboring subproblems searching, we present a drone-swarms deployment algorithm based on MOEA/D (DSDA-MOEA/D) to find the best tradeoff between these objectives. Extensive simulations were conducted to evaluate the performance of the proposed algorithms.

A Hybrid Search Model for Constrained Optimization

This paper proposes a hybrid model based on decomposition for constrained optimization problems. Firstly, a constrained optimization problem is transformed into a biobjective optimization problem. Then, the biobjective optimization problem is divided into a set of subproblems, and different subproblems are assigned to different Fitness functions by the direction vectors. Different from decomposition‐based multiobjective optimization algorithms in which each subproblem is optimized by using the information of its neighboring subproblems, the neighbors of each subproblem are deFined based on corresponding direction vector only in the method. By combining three main components, namely, the local search model, the global search model, and the direction vector adjusting strategy, the population can gradually move toward the global optimal solution. Experiments on two sets of test problems and Five real‐world engineering design problems have shown that the proposed method performs better than or is competitive with other compared methods.

Deep reinforcement learning and parameter transfer based approach for the multi-objective agile earth observation satellite scheduling problem

The agile earth observation satellite scheduling problem (AEOSSP) consists of selecting and scheduling a number of tasks from a set of user requests in order to optimize one or multiple criteria. In this paper, we consider a multi-objective version of AEOSSP (called MO-AEOSSP) where the failure rate and the timeliness of scheduled requests are optimized simultaneously. Due to its NP-hardness, traditional iterative problem-tailored heuristic methods are sensitive to problem instances and require massive computational overhead. We thus propose a deep reinforcement learning and parameter transfer based approach (RLPT) to tackle the MO-AEOSSP in a non-iterative manner. RLPT first decomposes the MO-AEOSSP into a number of scalarized sub-problems by a weight sum approach where each sub-problem can be formulated as a Markov Decision Process (MDP). RLPT then applies an encoder–decoder structure neural network (NN) trained by a deep reinforcement learning procedure to producing a high-quality schedule for each sub-problem. The resulting schedules of all scalarized sub-problems form an approximate pareto front for the MO-AEOSSP. Once a NN of a subproblem is trained, RLPT applies a parameter transfer strategy to reducing the training expenses for its neighboring sub-problems. Experimental results on a large set of randomly generated instances show that RLPT outperforms three classical multi-objective evolutionary algorithms (MOEAs) in terms of solution quality, solution distribution and computational efficiency. Results on various-size instances also show that RLPT is highly general and scalable. To the best of our knowledge, this study is the first attempt that applies deep reinforcement learning to a satellite scheduling problem considering multiple objectives.

A survey of decomposition approaches in multiobjective evolutionary algorithms

Since the multiobjective evolutionary algorithm based on decomposition (MOEA/D) was proposed by Zhang and Li in 2007, this interesting framework has attracted a considerable attention from researchers. In MOEA/D, a multiobjective optimization problem is decomposed into a series of aggregated subproblems, which are optimized simultaneously in a collaborative way by using the information from their neighboring subproblems. The decomposition approach has significant impact on MOEA/D as it directs the evolutionary search. Many improved MOEA/D variants proposed various kinds of decomposition approaches and have shown promising performance for different kinds of problems. In this paper, we give a survey of decomposition approaches, which are classified into five categories, i.e., the tradition decomposition, the modified Tchebycheff decomposition, the modified penalty-based boundary intersection decomposition, the constrained decomposition, and other special cases of decomposition. Moreover, discussions are further given in this paper to analyze the performance of different decomposition approaches. One clarifies the difference between Tchebycheff decomposition and Pareto-based domination. The other one compares the performance of various decomposition approaches on different benchmark problems. Experiments results have demonstrated that the Tchebycheff decomposition and its varieties are robust on solving most problems while some specific decomposition approaches are very effective for some problems with special features.

A multiobjective evolutionary algorithm based on decomposition for hybrid flowshop green scheduling problem

Energy saving has attracted growing attention due to the advent of sustainable manufacturing. By this motivation, this paper studies a hybrid flowshop green scheduling problem (HFGSP) with variable machine processing speeds. A multi-objective optimization model with the objectives of minimizing the makespan and total energy consumption is developed. To solve this complex problem, a multiobjective discrete artificial bee colony algorithm (MDABC) based on decomposition is suggested. In VND-based employed bee phase, the variable neighborhood descent (VND) with five designed neighborhood is employed to each subproblem to realize their self-evolution. In the collaborative onlooker bee phase, the promising subproblems selected by the order preference technique according to their similarity to an ideal solution (TOPSIS) is evolved by collaborating with the other neighboring subproblems. Particularly, a dynamic neighborhood strategy is developed to define the neighborhood relationship to retain the population diversity. In the solution exchange-based scout bee phase, a solution exchange strategy is developed to enhance the algorithm efficiency and enable the solutions to be exploited in different directions. Moreover, according to the problem-specific characteristics, encoding and decoding methodologies are developed to represent the solution space, and several definitions are proposed to implement objective normalization, and an energy saving procedure is designed to reduce the energy consumption. Through comprehensive computational comparisons and statistical analysis, the developed strategies and MDABC shows highly effective performance.

MOEA/D with the online agglomerative clustering based self-adaptive mating restriction strategy

In MOEA/D-DE, the appropriate value of the mating restriction probability varies with the evolutionary process. Furthermore, different subproblems have been solved in different degree during the evolution, so different subproblems have distinct requirements for exploitation and exploration. Additionally, MOEA/D-DE defines the neighborhood according to the distance between the weight vectors. However, the individuals corresponding to the neighbor subproblems may distribute far away in the decision space, which will affect the performance of exploitation. Accordingly, this paper proposes a MOEA/D with the online agglomerative clustering based self-adaptive mating restriction strategy (MOEA/D-OMR). MOEA/D-OMR utilizes the online agglomerative clustering algorithm to extract the neighborhood information in the decision space. The mating pool is then constructed by the neighbor population or the whole population based on the mating restriction probability. What is more, a separate mating restriction probability is assigned to each subproblem. The mating restriction probability is updated at each generation by the survival length, which is the number of generations that the solution has survived over the last certain period of time. Experimental results show that MOEA/D-OMR has a better performance than the comparison algorithms.

Distributed Optimal Traffic Lights Design for Large-Scale Urban Networks

In this paper, we deal with the problem of dynamical assignment of traffic light schedules in large-scale urban networks. We present a model for signalized traffic networks, based on the cell transmission model, and then a simplified model based on averaging theory. The control objective is to improve traffic, optimizing traffic indexes such as total travel distance and density balancing. We design a scheme that decides the duty cycles of traffic lights, by solving a convex program. The optimization is done in real time, at each cycle of traffic lights, so as to take into account variable traffic demands. The scalability problem is tackled through the synthesis of a distributed optimization algorithm; this reduces the computational load significantly, since the large optimization problem is broken into small local subproblems, whose size does not grow with the size of the network, together with iterative exchanges of messages with few neighbor subproblems. The performance of the proposed approach is evaluated via numerical simulations in two different scenarios: a macroscopic (MATLAB-based) Manhattan grid and a microscopic scenario (based on Aimsun simulator) reproducing a portion of the city of Grenoble, France.

Optimization of noise abatement aircraft terminal routes using a multi-objective evolutionary algorithm based on decomposition

Recently, a multi-objective evolutionary algorithm based on decomposition (MOEA/D) has emerged as a potential method for solving multi-objective optimization problems (MOPs) and attracted much attention from researchers. In MOEA/D, the MOPs are decomposed into a number of scalar optimization sub-problems, and these sub-problems are optimized concurrently by only utilizing the information from their neighboring sub-problems. Thanks to these advantages, MOEA/D has demonstrated to be more efficient than the non-dominated sorting genetic algorithm II (NSGA-II) and other methods. However, its applications to practical problems are still limited, especially in the domain of aerospace engineering. Therefore, this paper aims to present a new application of MOEA/D for the optimal design of noise abatement aircraft terminal routes. First, in order to optimize aircraft noise for aircraft terminal routes while taking into account the interests of various stakeholders, bi-objective optimization problems including noise and fuel consumption are formulated, in which both the ground track and vertical profile of a terminal route are optimized simultaneously. Then, MOEA/D is applied to solve these problems. Furthermore, to ensure the design space of vertical profiles is always feasible during the optimization process, a trajectory parameterization technique recently proposed is also used. This technique aims at reducing the number of model evaluations of MOEA/D and hence the computational cost will decrease significantly. The efficiency and reliability of the developed method are evaluated through case studies for departure and arrival routes at Rotterdam The Hague Airport in the Netherlands.

A Survey of Multiobjective Evolutionary Algorithms based on Decomposition

Decomposition is a well-known strategy in traditional multiobjective optimization. However, the decomposition strategy was not widely employed in evolutionary multiobjective optimization until Zhang and Li proposed multiobjective evolutionary algorithm based on decomposition (MOEA/D) in 2007. MOEA/D proposed by Zhang and Li decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them in a collaborative manner using an evolutionary algorithm (EA). Each subproblem is optimized by utilizing the information mainly from its several neighboring subproblems. Since the proposition of MOEA/D in 2007, decomposition-based MOEAs have attracted significant attention from the researchers. Investigations have been undertaken in several directions, including development of novel weight vector generation methods, use of new decomposition approaches, efficient allocation of computational resources, modifications in the reproduction operation, mating selection and replacement mechanism, hybridizing decomposition- and dominance-based approaches, etc. Furthermore, several attempts have been made at extending the decomposition-based framework to constrained multiobjective optimization, many-objective optimization, and incorporate the preference of decision makers. Additionally, there have been many attempts at application of decomposition-based MOEAs to solve complex real-world optimization problems. This paper presents a comprehensive survey of the decomposition-based MOEAs proposed in the last decade.

An Improved Decomposition-Based Memetic Algorithm for Multi-Objective Capacitated Arc Routing Problem

Capacitated Arc Routing Problem (CARP) has attracted the attention of many researchers during the last few years, because it has a wide application in the real world. Recently, a Decomposition-Based Memetic Algorithm for Multi-Objective CARP (D-MAENS) has been demonstrated to be a competitive approach. However, the replacement mechanism and the assignment mechanism of the offspring in D-MAENS remain to be improved. First, the replacement after all the offspring are generated decreases the convergence speed of D-MAENS. Second, the representatives of these sub-problems are reassigned at each generation by only considering one objective function. In response to these issues, this paper presents an improved D-MAENS for Multi-Objective CARP (ID-MAENS). The two improvements of the proposed algorithm are as follows: (1) the replacement of the solutions is immediately done once an offspring is generated, which references to the steady-state evolutionary algorithm. The new offspring will accelerate the convergence speed; (2) elitism is implemented by using an archive to maintain the current best solution in its decomposition direction during the search, and these elite solutions can provide helpful information for solving their neighbor sub-problems by cooperation. Compared with the Multi-Objective CARP algorithm, experimental results on large-scale benchmark instances egl show that the proposed algorithm has performed significantly better than D-MAENS on 23 out of the total 24 instances. Moreover, ID-MAENS find all the best nondominated solutions on 13 egl instances. In the last section of this paper, the ID-MAENS also proves to be competitive to some state-of-art single-objective CARP algorithms in terms of quality of solutions and computational efficiency.

A decomposition based estimation of distribution algorithm for multiobjective traveling salesman problems

The traveling salesman problem (TSP) is a well known NP-hard benchmark problem for discrete optimization. However, there is a lack of TSP test instances for multiobjective optimization and some current TSP instances are combined to form a multiobjective TSP (MOTSP). In this paper, we present a way to systematically design MOTSP instances based on current TSP test instances, of which the degree of conflict between the objectives is measurable. Furthermore, we propose an approach, named multiobjective estimation of distribution algorithm based on decomposition (MEDA/D), which utilizes decomposition based techniques and probabilistic model based methods, to tackle the newly designed MOTSP test suite. In MEDA/D, an MOTSP is decomposed into a set of scalar objective sub-problems and a probabilistic model, using both priori and learned information, is built to guide the search for each sub-problem. By the cooperation of neighbor sub-problems, MEDA/D could optimize all the sub-problems simultaneously and thus find an approximation to the original MOTSP in a single run. The experimental results show that MEDA/D outperforms MOACO and MOEA/D-ACO, two ant colony based methods, on most of the given test instances and MEDA/D is insensible to its control parameters.

MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition

Decomposition is a basic strategy in traditional multiobjective optimization. However, it has not yet been widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by only using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and nondominated sorting genetic algorithm II (NSGA-II). Experimental results have demonstrated that MOEA/D with simple decomposition methods outperforms or performs similarly to MOGLS and NSGA-II on multiobjective 0-1 knapsack problems and continuous multiobjective optimization problems. It has been shown that MOEA/D using objective normalization can deal with disparately-scaled objectives, and MOEA/D with an advanced decomposition method can generate a set of very evenly distributed solutions for 3-objective test instances. The ability of MOEA/D with small population, the scalability and sensitivity of MOEA/D have also been experimentally investigated in this paper.