Vector Optimization with Gaussian Process Bandits

Generative moment matching networks (GMMN) present a theoretically sound approach to learning deep generative mod-els. However, such methods are typically limited by the high sample complexity, thereby impractical in generating complex data. In this paper, we present a new strategy to train GMMN with a low sample complexity while retaining the theoretical soundness. Our method introduces some auxiliary variables, whose values are provided by a pre-trained model such as an encoder network in practice. Conditioned on these variables, we partition the distribution into a set of conditional distributions, which can be effectively matched with a low sample complexity. We instantiate this strategy by presenting an amortized network called GMMN-DP with shared auxiliary variable information for the data generation task, as well as developing an efficient stochastic training algorithm.The experimental results show that GMMN-DP can generate complex samples on datasets such as CelebA and CIFAR-10, where the vanilla GMMN fails.

In this paper, the problems of fuel cost and emission reduction based on multi-objective optimization are studied and solved. Various multi-objective optimization algorithms, such as the multi-objective ant lion optimization (MOALO), the multi-objective multiverse optimization (MOMVO), the multi-objective particle swarm optimization (MOPSO), the multi-objective thermal exchange optimization (MOTEO), and the multi-objective grasshopper optimization algorithm (MOGOA), are used to reduce the cost and emissions of generation fuel. With equality and inequality restrictions, the suggested work is carried out in an IEEE 30 bus system. To determine the lowest system-wide minimization of generating cost and emission, the results of several optimization strategies are compared. In terms of lowering fuel costs and emissions, the MOGOA performs better than any other multi-objective algorithms.

In this paper, we propose a Multi-objective Five-element Cycle Optimization algorithm based on Multi-strategy fusion (MOFECO-MS) to address the Bi-objective Traveling Thief Problem (BITTP), an extension of the Traveling Thief Problem that incorporates two conflicting objectives. The novelty of our approach lies in a unique individual selection strategy coupled with an innovative element update mechanism rooted in the Five-element Cycle Model. To balance global exploration and local exploitation, the algorithm categorizes the population into distinct groups and applies crossover operations both within and between these groups, while also employing a mutation operator for local searches on the best individuals. This coordinated approach optimizes parameter settings and enhances the search capabilities of the algorithm. Extensive experiments were conducted on nine BITTP instances, comparing MOFECO-MS against eight state-of-the-art multi-objective optimization algorithms. The results show that MOFECO-MS excels in both Hypervolume (HV) and Spread (SP) indicators, while also maintaining a high level of Pure Diversity (PD). Overall, MOFECO-MS outperformed the other algorithms in most instances, demonstrating its superiority and robustness in solving complex multi-objective optimization problems.

International audience

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

Battle Royale Optimizer (BRO) is a recently proposed optimization algorithm that has added a new category named game-based optimization algorithms to the existing categorization of optimization algorithms. Both continuous and binary versions of this algorithm have already been proposed. Generally, optimization problems can be divided into single-objective and multi-objective problems. Although BRO has successfully solved single-objective optimization problems, no multi-objective version has been proposed for it yet. This gap motivated us to design and implement the multi-objective version of BRO (MOBRO). Although there are some multi-objective optimization algorithms in the literature, according to the no-free-lunch theorem, no optimization algorithm can efficiently solve all optimization problems. We applied the proposed algorithm to four benchmark datasets: CEC 2009, CEC 2018, ZDT, and DTLZ. We measured the performance of MOBRO based on three aspects: convergence, spread, and distribution, using three performance criteria: inverted generational distance, maximum spread, and spacing. We also compared its obtained results with those of three state-of-the-art optimization algorithms: the multi-objective Gray Wolf optimization algorithm (MOGWO), the multi-objective particle swarm optimization algorithm (MOPSO), the multi-objective artificial vulture's optimization algorithm (MOAVAO), the optimization algorithm for multi-objective problems (MAOA), and the multi-objective non-dominated sorting genetic algorithm III (NSGA-III). The obtained results approve that MOBRO outperforms the existing optimization algorithms in most of the benchmark suites and operates competitively with them in the others.

<div>Continuous rubber track systems for heavy applications are typically designed using multiple iterations of full-scale physical prototypes. This costly and time-consuming approach limits the possibility of exploring the design space and understanding how the design space of that kind of system is governed. A multibody dynamic simulation has recently been developed, but its complexity (due to the number of model’s inputs) makes it difficult to understand and too expensive to be used with multi-objective optimization algorithms (approximately 3 h on a desktop computer).</div> <div>This article aims to propose a first design space exploration of continuous rubber track systems via multi-objective optimization methods. Using an existing expensive multibody dynamic model as original function, surrogate models (artificial neural networks) have been trained to predict the simulation responses. These artificial neural networks are then used to explore the design space efficiently by using optimization algorithms. Sensitivity studies and multi-objective optimization were carried out on surrogate models to identify high-impact design parameters and potential improvements ranging from 2.24% to 17.2% compared to the current design of reference (CTS halftrack system) on wheel load, track pinch, and maximum required torque to cross a bump.</div>

A surrogate-assisted multi-objective evolutionary algorithm with dimension-reduction for production optimization

Pressure swing adsorption (PSA) is an energy-efficient technology for gas separation, while the multi-objective optimization of PSA is a challenging task. To tackle this, we propose a hybrid optimization framework, which integrates three steps. In the first step, we establish surrogate models for the constraints using Gaussian processes (GPs) and employ multi-objective Bayesian optimization to search for feasible points that satisfy the constraints. In the second step, we establish surrogate models for the objective function and constraints using GPs and utilize constrained multi-objective Bayesian optimization to search for an approximate Pareto front. In the third step, we perform a local search based on the approximate Pareto front. By employing the trust region filter method, we construct quadratic models for each constraint and objective function and refine the Pareto front to achieve local optimality. This framework demonstrates the efficiency of Bayesian optimization and the local optimality of the trust region method. A comparison with the popular evolutionary algorithm, Nondominated Sorting Genetic Algorithm II (NSGA-II), showed that this framework had a higher hypervolume of the Pareto front while halving the runtime and reducing the number of simulations by a factor of 20.

A chaos ant colony optimization algorithm for continuous domain is proposed based on chaos optimization theory and ant colony optimization algorithm. The searching abilities of optimization algorithms with different coding methods are compared, and the results indicate that the proposed algorithm has better performance than genetic algorithm and particle swarm optimization algorithm. Based on the non-dominated sorting concept and niching method, a multi-objective chaos ant colony optimization algorithm is also constructed and numerical results show that the improved algorithm performs well at solving multi-objective optimization problems. An optimal support vector regression model based on radial basis kernel function is developed for the small sample size and nonlinear characteristics of streamlined head optimization. On the basis of the above work, a multi-objective optimization design for the aerodynamic head shape of high-speed train is developed using a modified vehicle modeling function parametric approach. The optimization results demonstrate that the new optimization design method has exceptional searching abilities and high prediction accuracy. After optimization, the aerodynamic drag of the simplified train with three carriages is reduced by 10.52% and the aerodynamic lift of the tail car is reduced by 35.70%. The optimization approach proposed in the present paper is simple yet efficient and sheds light on the engineering design of aerodynamic shape of high-speed trains.

Many evolutionary algorithms are designed to solve black-box multi-objective optimization problems MOPs using stochastic operators, where neither the form nor the gradient information of the problem is accessible. In some real-world applications, e.g. surrogate-based global optimization, the gradient of the objective function is accessible. In this case, it is straightforward to use a gradient-based multi-objective optimization algorithm to achieve fast convergence speed and the stability of the solution. In a relatively recent approach, the hypervolume indicator gradient in the decision space is derived, which paves the way for the method for maximizing the hypervolume indicator of a fixed size population. In this paper, several mechanisms which originated in the field of evolutionary computation are proposed to make this gradient ascent method applicable. Specifically, the well-known non-dominated sorting is used to help steering the dominated points. The principle of the so-called cumulative step-size control that is originally proposed for evolution strategies is adapted to control the step-size dynamically. The resulting algorithm is called Hypervolume Indicator Gradient Ascent Multi-objective Optimization HIGA-MO. The proposed algorithm is tested on ZDT problems and its performance is compared to other methods of moving the dominated points as well as to some evolutionary multi-objective optimization algorithms that are commonly used.

With the complexity of mechanical manufacturing system design increasing, the traditional single-objective optimization method can no longer meet the needs of multi-objective optimization, such as lightweight, high efficiency, low energy consumption and long life. Multi-objective optimization algorithm is widely used in mechanical design and manufacturing process planning because of its good convergence and diversity. Taking robot motion planning as an example, this paper analyzes the application methods of multi-objective optimization algorithm in mechanical structure design in detail, including problem description, multi-objective optimization model construction, algorithm application and performance analysis. Through the application of Genetic Algorithm (GA), this paper shows how the multi-objective optimization algorithm can balance multiple objectives such as path length, energy consumption and obstacle avoidance effect, and realize more intelligent and efficient solutions in robot motion planning. Performance analysis shows that GA is superior to single-objective optimization and random search algorithm in optimization effect, computational efficiency and stability. In addition, this paper also discusses the influence of the change of target weight and algorithm parameters on the optimization results, which provides valuable reference for future algorithm optimization and practical application. Multi-objective optimization algorithm shows obvious advantages in mechanical manufacturing system, which provides new ideas and methods for realizing more efficient, more environmentally friendly and more intelligent mechanical manufacturing design.

With the rapid development of mobile networks and the proliferation of mobile devices, spatial crowdsourcing, which refers to recruiting mobile workers to perform location-based tasks, has gained emerging interest from both research communities and industries. In this paper, we consider a spatial crowdsourcing scenario: in addition to specific spatial constraints, each task has a valid duration, operation complexity, budget limitation, and the number of required workers. Each volunteer worker completes assigned tasks while conducting his/her routine tasks. The system has a desired task probability coverage and budget constraint. Under this scenario, we investigate an important problem, namely heterogeneous spatial crowdsourcing task allocation (HSC-TA), which strives to search a set of representative Pareto-optimal allocation solutions for the multi-objective optimization problem, such that the assigned task coverage is maximized and incentive cost is minimized simultaneously. To accommodate the multi-constraints in heterogeneous spatial crowdsourcing, we build a worker mobility behavior prediction model to align with allocation process. We prove that the HSC-TA problem is NP-hard. We propose effective heuristic methods, including multi-round linear weight optimization and enhanced multi-objective particle swarm optimization algorithms to achieve adequate Pareto-optimal allocation. Comprehensive experiments on both real-world and synthetic data sets clearly validate the effectiveness and efficiency of our proposed approaches.

An important challenge in black-box optimization is to be able to understand the relative performance of different algorithms on problem instances. This challenge has motivated research in exploratory landscape analysis and algorithm selection, leading to a number of frameworks for analysis. However, these procedures often involve significant assumptions, or rely on information not typically available. In this paper we propose a new, model-based framework for the characterization of black-box optimization problems using Gaussian Process regression. The framework allows problem instances to be compared to each other in a relatively simple way. The model-based approach also allows us to assess the goodness of fit and Gaussian Processes lead to an efficient means of model comparison. The implementation of the framework is described and validated on several test sets as one benchmark problem is slowly transformed into another.

In order to solve the problem of the multi-objective spectrum allocation on the joint optimization of maximal network utility and fairness of users in cognitive radio network, based on quantum bee colony theory and membrane computing, a novel multi-objective discrete combinatorial optimization algorithm, named membrane-inspired quantum bee optimization, is proposed. The global optimal solution of single objective can be searched in the elementary membranes, and Pareto front solutions which take account of network utility and fairness, can be obtained from skin membrane with the proposed method. The multi-objective optimization algorithm, which can solve both single objective and multi-objective optimization problems at the same time, is designed by the communication rules between membranes, the cooperative evolution of foraging behavior based on quantum state, and non-dominated sorting. Compared with classical color-sensitive graph coloring algorithm, genetic algorithm, quantum genetic algorithm, and particle swarm optimization under different objective functions, the proposed spectrum allocation method can search the global optimal solution of single objective as shown by the simulation results, and it is superior to classical spectrum allocation algorithms and existing intelligence spectrum allocation methods. The optimal Pareto front solutions of multi-objective spectrum allocation are also obtained.