Improving Performance Insensitivity of Large-scale Multiobjective Optimization via Monte Carlo Tree Search

The large-scale multiobjective optimization problem (LSMOP) is characterized by simultaneously optimizing multiple conflicting objectives and involving hundreds of decision variables. {Many real-world applications in engineering fields can be modeled as LSMOPs; simultaneously, engineering applications require insensitivity in performance.} This requirement usually means that the results from the algorithm runs should not only be good for every run in terms of performance but also that the performance of multiple runs should not fluctuate too much, i.e., the algorithm shows good insensitivity. Considering that substantial computational resources are requested for each run, it is essential to improve upon the performance of the large-scale multiobjective optimization algorithm, as well as the insensitivity of the algorithm. However, existing large-scale multiobjective optimization algorithms solely focus on improving the performance of the algorithms, leaving the insensitivity characteristics unattended. {In this work, we propose an evolutionary algorithm for solving LSMOPs based on Monte Carlo tree search, the so-called LMMOCTS, which aims to improve the performance and insensitivity for large-scale multiobjective optimization problems.} The proposed method samples the decision variables to construct new nodes on the Monte Carlo tree for optimization and evaluation. {It selects nodes with good evaluation for further search to reduce the performance sensitivity caused by large-scale decision variables.} We compare the proposed algorithm with several state-of-the-art designs on different benchmark functions. We also propose two metrics to measure the sensitivity of the algorithm. The experimental results confirm the effectiveness and performance insensitivity of the proposed design for solving large-scale multiobjective optimization problems.Comment: 12 pages, 11 figure

A Recommender System Approach for Very Large-scale Multiobjective Optimization

We define very large multi-objective optimization problems to be multiobjective optimization problems in which the number of decision variables is greater than 100,000 dimensions. This is an important class of problems as many real-world problems require optimizing hundreds of thousands of variables. Existing evolutionary optimization methods fall short of such requirements when dealing with problems at this very large scale. Inspired by the success of existing recommender systems to handle very large-scale items with limited historical interactions, in this paper we propose a method termed Very large-scale Multiobjective Optimization through Recommender Systems (VMORS). The idea of the proposed method is to transform the defined such very large-scale problems into a problem that can be tackled by a recommender system. In the framework, the solutions are regarded as users, and the different evolution directions are items waiting for the recommendation. We use Thompson sampling to recommend the most suitable items (evolutionary directions) for different users (solutions), in order to locate the optimal solution to a multiobjective optimization problem in a very large search space within acceptable time. We test our proposed method on different problems from 100,000 to 500,000 dimensions, and experimental results show that our method not only shows good performance but also significant improvement over existing methods.Comment: 12 pages, 6 figure

Efficient stepwise-purification and mechanism of germanium-containing materials with ammonium

Germanium (Ge) is a dispersed metal and it is mainly recovered from secondary resources. In order to improve the purification efficiency of Ge-containing materials, a new method for purification of Ge-containing materials by ammonium was proposed. The results showed that the zinc (Zn) components in raw materials were complex, including water-soluble Zn and water-insoluble Zn, which should to be removed by the two-stage purification of primary water purification (PWP) and secondary ammonium purification (SAP). The results of single factor experiment on the process of SAP showed that under the optimal purification conditions of total ammonium concentration of 0.69 mol/L, pH of 2.5∼, liquid–solid ratio of 3:1 mL/g, reaction time of 10 min and reaction temperature of 20 °C, 95.68% Zn could be removed from raw materials. The purification mechanism indicated that the water-soluble Zn in the form of physical adsorption and water-insoluble Zn in the form of chemical adsorption can be removed in PWP stage and SAP stage, respectively. After the two-stage purification, the Zn component that was difficult to be removed by burning was greatly reduced, which provided favorable conditions for improving the quality of Ge concentrate

Inhibition of Fe4Ge3O12 formation in the leaching process of zinc oxide dust containing germanium by ultrasonic and iron powder

Low leaching efficiency of germanium has always been a difficult point hindering the efficient utilization of zinc oxide dust containing germanium. Based on the previous research results that the formation of insoluble Fe4Ge3O12 leads to germanium loss in the leaching process, a new process of reduction leaching of zinc oxide dust containing germanium enhanced by ultrasonic and iron powder is proposed. Under optimized conditions, the germanium leaching efficiency can be increased by 9.17%, reaching 93.43%. When leaching, the addition of iron powder can reduce the Fe3+ formed in the leaching process and hinder the formation of insoluble Fe4Ge3O12, which can increase the leaching efficiency of germanium by 5.30%. At the same time, strong mechanical action of ultrasonic can fully disperse the iron powder in the leaching system, avoiding the phenomenon of insufficient local reduction. More importantly, the addition of ultrasonic can reduce the dissolved oxygen in the solution system and produce strong reducing hydrogen free radicals (·H), strengthening the reduction leaching effect, thus the germanium leaching efficiency is further increased by 3.87%. The research results provide a new method and theoretical guidance for the efficient utilization of zinc oxide dust containing germanium, which is of great significance

Study on the mechanism of ultrasonic enhanced removal of zinc and germanium from lead residue

Lead residue is the residue from the leaching process of zinc oxide dust containing germanium, which comprises a certain amount of valuable elements such as zinc and germanium. Conventional water washing treatment cannot effectively remove zinc and germanium from lead residue, resulting in a backlog of zinc and germanium in the system and raising production costs for enterprises. By using a dilute sulfuric acid solution and introducing ultrasonic waves for enhanced washing, the easily separated zinc and germanium are basically removed, while the residual zinc occurred as ZnS and germanium wrapped in lead sulfate are difficult to elute. The removal efficiency of zinc and germanium can reach 53.82% and 50.24%, respectively, which are 12.67% and 6.10% higher than conventional acid washing efficiency, and 31.10% and 22.51% higher than conventional water washing efficiency. During water washing, the hydrolysis of Zn2+ and Fe3+ results in low elution efficiency. While in pickling process, hydrolysis can be effectively inhibited. When use ultrasonic to enhance sulfuric acid washing, some ZnS dissolves, while the silica gel colloid that adsorbs germanium is destroyed, and germanium is released into the solution again, thus improving the removal efficiency of zinc and germanium. This article has reused more than half of the residual zinc and germanium in lead residue, and points out the direction for further reducing zinc and germanium residues in lead residue. It is of great significance for the comprehensive utilization of zinc and germanium resources

Research on the mechanism of lead sulfate adsorption of germanium and ultrasonic inhibition during the leaching process of zinc oxide dust containing germanium

In response to the problem of germanium adsorption loss caused by lead sulfate adsorption during the leaching process of zinc oxide dust containing germanium, this article simulates and identifies the mechanism of lead sulfate adsorbing germanium, and innovatively introduces ultrasonic to suppress the adsorption of germanium by lead sulfate. Research has shown that the adsorption process of lead sulfate on germanium conforms to the pseudo-second-order kinetic adsorption model. The diffusion process of germanium adsorbed on lead sulfate particles can be divided into three stages: fast, slow, and equilibrium. The adsorption of germanium by lead sulfate conforms to the Langmuir isotherm adsorption model, and is mainly monolayer adsorption and chemical adsorption. In addition, the adsorption at 298–328 K is a spontaneous, endothermic, and entropy increasing process, while at 328–358 K it is a spontaneous, exothermic, and entropy decreasing process. At the same time, it was also found that low temperature, high temperature, and high-power ultrasonic can inhibit the adsorption process. Under ultrasound conditions of 358 K and 60.0 W, the equilibrium adsorption capacity of lead sulfate on germanium was 7.48 mg/g, and the germanium adsorption efficiency was 18.09%, which was 48.01% and 6.73% lower than conventional methods, respectively. Moreover, the leaching efficiency of germanium in actual dust leaching is increased by 6.17%, reaching 89.64%, verifying the simulation results. The new process of ultrasonic suppression of germanium adsorption by lead sulfate in the leaching process of zinc oxide dust containing germanium established in this article can effectively achieve efficient recovery of germanium from zinc oxide dust, providing a process and theoretical basis for the sustainable development of the world's germanium industry, and is of great significance for ensuring the safety of the world's important strategic resource supply chain