Infeasible solution repair and MOEA/D sharing weight vectors for solving multi-objective set packing problems

MOEA/D decomposes a multi-objective optimization problem into a number of single objective optimization problems. Each single objective optimization problem is defined by a scalarizing function using a weight vector. In MOEA/D, there are several scalarizing approaches such as the weighted Tchebycheff, the weighted sum, and the PBI (penalty-based boundary intersection). However, these conventional scalarizing approaches face a difficulty to approximate a widely spread Pareto front in some problems. To enhance the spread of Pareto optimal solutions in the objective space and improve the search performance of MOEA/D especially in many-objective optimization problems, in this work we propose the inverted PBI scalarizing approach which is an extension of the conventional PBI. We use many-objective knapsack problems and WFG4 problems with 2-8 objectives, and compare the search performance of NSGA-III and four MOEA/Ds using the weighted Tchebycheff, the weighted sum, the PBI and the inverted PBI. As results, we show that MOEA/D using the inverted PBI achieves higher search performance than other algorithms in problems with many-objectives and the difficulty to obtain a widely spread Pareto front in the objective space.

A MOEA/D with adaptive weight subspace for regular and irregular multi-objective optimization problems

The Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) is a popular algorithm for solving Multi-Objective Problems (MOPs). The main component of MOEA/D is to decompose a MOP into easier sub-problems using a set of weight vectors. The choice of the number of weight vectors significantly impacts the performance of MOEA/D. However, the right choice for this number varies, given different MOPs and search stages. We adaptively change the number of vectors by removing unnecessary vectors and adding new ones in empty areas of the objective space. Our MOEA/D variant uses the Consolidation Ratio to decide when to change the number of vectors and to decide where to add or remove these weighted vectors. We investigate the effects of this adaptive MOEA/D against MOEA/D with a poorly chosen set of vectors, a MOEA/D with fine-tuned vectors and MOEA/D with Adaptive Weight Adjustment on two commonly used benchmark functions. We analyse the algorithms in terms of hypervolume, IGD and entropy performance. Our results show that the proposed method is equivalent to MOEA/D with fine-tuned vectors and superior to MOEA/D with poorly defined vectors. Thus, our adaptive mechanism mitigates problems related to the choice of the number of weight vectors in MOEA/D, increasing the final performance of MOEA/D by filling empty areas of the objective space and avoiding premature stagnation of the search progress.

The Pareto front (Pareto set) of a continuous optimization problem with m objectives is a (m-1) dimensional piecewise continuous manifold in the objective space (the decision space) under some mild conditions. Based on this regularity property in the objective space, we have recently developed several multiobjective estimation of distribution algorithms (EDAs). However, this property has not been utilized in the decision space. Using the regularity property in both the objective and decision space, this paper proposes a simple EDA for multiobjective optimization. Since the location information has not efficiently used in EDAs, a combination of EDA and differential evolution (DE) is suggested for improving the algorithmic performance. The hybrid method and the pure EDA method proposed in this paper, and a DE based method are compared on several test instances. Experimental results have shown that the algorithm with the proposed strategy is very promising.

Computer‐Aided Optimization of Surveillance Cameras Placement on Construction Sites

A decomposition-based many-objective evolutionary algorithm updating weights when required

The multiobjective combinatorial optimization problems (MOCOPs) have a wide range of real-world applications. Designing an effective algorithm has an important and practical significance. Due to the huge search space and limited time, it is generally difficult to obtain the optimal solution of this kind of problem by traditional exact and heuristic algorithms. Recently, learning-based algorithms have achieved good results in solving MOCOPs, but the quality and diversity of found solutions can be further improved. In this paper, we propose a Weight-Specific-Decoder Attention Model (WSDAM) to better approximate the whole Pareto set. It embeds a weight-adaptive layer into the decoder to concentrate on the information of different weight vectors. During the model training, the weight vector is sampled from the Dirichlet distribution, which can further strengthen the learning of boundary solutions. We evaluate our method on two classic MOCOPs, i.e., the multiobjective traveling salesman problem (MOTSP) and multiobjective capacitated vehicle routing problem (MOCVRP). The experimental results show that our proposed method outperforms current state-of-the-art learning-based methods in both solution quality and generalization ability.

In this paper, we propose an improved ideal point setting method in the framework of MOEA/D. MOEA/D decomposes a multi-objective optimisation problem into a number of scalar optimisation problems and optimise them simultaneously. The performance of MOEA/D is highly relate to its decomposition method, and the proposed ideal point setting approach is used in the weighted Tchebycheff (TCH) and penalty-based boundary intersection (PBI) decomposition approach. It expands the region of search in the objective space by transforming the original ideal point into its symmetric point and changes the search direction of each subproblems in MOEA/D. In order to address the proposed ideal point setting method, we design a set of multi-objective problems(MOPs). The proposed method is compared with original MOEA/D-TCH and MOEA/D-PBI on MOPs. The experimental results demonstrate that our proposed ideal point setting method is very effective in terms of both diversity and convergence.

Nondominated-sorting plays an important role in multi-objective evolutionary algorithm in recent decades. However, it fails to work well when the target multi-objective problem has a complex Pareto front, brusque nondominated-sorting virtually steers by the conflicting nature of objectives, which leads to irrationality. In this paper, a novel mixed-factor evolutionary algorithm is proposed. A normalization procedure, i.e. mixed-factor, is introduced in the objective space, which links all the objectives for all the solutions of the problem to ease the conflicting nature. In the process of nondominated-sorting, the mixed factors of individual substitute the raw objectives. In order to ensure that the population are thoroughly steered through the normalized objective space, hybrid ageing operator and static hypermutation with first constructive mutation are used to guide the searching agents converge towards the true Pareto front. The algorithm proposed is operated on multi-objective knapsack problem. The effectiveness of MFEA is compared with five state-of-the-art algorithms, i.e., NSGA-II, NSGA-III, MOEA/D, SPEA2 and GrEA, in terms of five performance metrics. Simulation results demonstrate that MFEA achieves better performance.KeywordsMulti-objective evolutionary algorithmMixed-factor evolutionary algorithmMulti-objective Knapsack ProblemNormalization procedure

A particle swarm optimization algorithm based on modified crowding distance for multimodal multi-objective problems

This paper proposes a flexible method for designing frequency-invariant (FI) beamformers, which is suitable for circular arrays mounted on acoustically transparent and infinite rigid cylinders. The closed-form weighting vectors at each frequency are accurately derived by approximating to a general complex-weighted desired beampattern from the minimum mean square error perspective. It is found that these obtained weighting vectors are all closed-form functions of the desired complex weighting vectors. A multiple-constraint optimization problem is formulated, and its solution gives the optimal desired weighting vector subject to different constraints. Then, the weighting vectors at other frequencies can be straightforwardly computed based on the previously derived analytical functions. The proposed method provides flexible schemes to design different FI beamformers for circular sensor arrays. The good performance of the proposed method is demonstrated using simulations and experimental results.

This paper proposes an alternative method to generate the weight vector set for the decomposition-based evolutionary multi- and many-objective optimization. Since each weight vector specifies an approximation point on the Pareto front, the distribution of the weight vector set has an enormous impact on the total approximation quality of the Pareto front. The conventional simplex-lattice design has scalability on the number of weight vectors by a decomposition parameter and generates a uniformly distributed weight vector set. However, the generated set involves fewer inner weight vectors for the approximation of the central area of the Pareto front. A variant, the two-layered simplex-lattice design, generates an additional layer to introduce inner weight vectors but sacrifices the distribution uniformity. The proposed method, the incremental lattice design, also has scalability on the number of weight vectors by a decomposition parameter and always includes the intermediate weight vector pointing to the center of the Pareto front for any the decomposition parameter while keeping the distribution uniformity. Experimental results show that the proposed method achieves higher approximation quality of the Pareto front than the conventional simplex-lattice and two-layered simplex-lattice designs.

With the increasing number of satellites and rising user demands, the volume of satellite data transmissions is growing significantly. Existing scheduling systems suffer from unequal resource allocation and low transmission efficiency. Therefore, effectively addressing the large-scale multi-objective satellite data transmission scheduling problem (SDTSP) within a limited timeframe is crucial. Typically, swarm intelligence algorithms are used to address the SDTSP. While these methods perform well in simple task scenarios, they tend to become stuck in local optima when dealing with complex situations, failing to meet mission requirements. In this context, we propose an improved method based on the minimum angle particle swarm optimization (MAPSO) algorithm. The MAPSO algorithm is encoded as a discrete optimizer to solve discrete scheduling problems. The calculation equation of the sine function is improved according to the problem’s characteristics to deal with complex multi-objective problems. This algorithm employs a minimum angle strategy to select local and global optimal particles, enhancing solution efficiency and avoiding local optima. Additionally, the objective space and solution space exhibit symmetry, where the search within the solution space continuously improves the distribution of fitness values in the objective space. The evaluation of the objective space can guide the search within the solution space. This method can solve multi-objective SDTSPs, meeting the demands of complex scenarios, which our method significantly improves compared to the seven algorithms. Experimental results demonstrate that this algorithm effectively improves the allocation efficiency of satellite and ground station resources and shortens the transmission time of satellite data transmission tasks.

To improve the real-time performance and positioning accuracy of space object surveillance using an optoelectronic telescope,a fast recognition and precise orientation system for space objects was established.The algorithms for the motion characteristics,fast recognition,star centroid computing,and the astronomical orientation of space objects were investigated.The system constitution and working principle of the opto-electric observing system for space objects were introduced,the motion characteristics of space objects in a visible field of the CCD chip were analyzed and a fast recognition algorithm was presented firstly.Then the fast recognition for space objects was implemented by using the frame subtraction and the mathematical morphology.Finally,the astronomical orientation methodwas investigated and the precise orientation of space objects was realized in the usage of Tycho-2catalogue.Experimental results indicate that the average processing time of fast recognition and real-time astronomical orientation for space objects is respectively 10 ms and 25 ms,and the precision of realtime astronomical orientation is less than 4″.It concludes that the results obtained satisfy the requirements of space object surveillance for high real-time,high precision,good stability and reliability.

In this paper, we focus on multiobjective two-level fuzzy random programming problems with simple recourses, in which multiple objective functions are involved in each level, shortages and excesses resulting from the violation of the constraints with fuzzy random variables are penalized, and sums of the objective functions and expectation of the amount of the penalties are minimized. To deal with such problems, the concept of estimated Pareto Stackelberg solutions of the leader is introduced under the assumption that the leader can estimate the preference of the follower as a weighting vector of the weighting problems. Employing the possibility measure for fuzzy numbers, weighting method for multiobjective programming problems, and Kuhn-Tucker approach for two-level programming problems, a nonlinear optimization problem under complementarity conditions is formulated to obtain the estimated Pareto Stackelberg solutions for the leader. A numerical example illustrates the proposed method for a multiobjective two-level fuzzy random programming problem with simple recourses. Several types of estimated Pareto Stackelberg solutions are derived corresponding to the weighting vectors and permissible possibility levels specified by the leader.