arXiv subjects

Qingfu Zhang

Publications and source records attributed to Qingfu Zhang.

121 records · Page 7Linked to original sources

arXiv2019

Difficulty Adjustable and Scalable Constrained Multi-objective Test Problem Toolkit

Multi-objective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multi-objective optimization problems. In fact, many real-world multi-objective problems contain a number of constraints. To promote research on constrained multi-objective optimization, we first propose a problem classification scheme with three primary types of difficulty, which reflect various types of challenges presented by real-world optimization problems, in order to characterize the constraint functions in constrained multi-objective optimization problems (CMOPs). These are feasibility-hardness, convergence-hardness and diversity-hardness. We then develop a general toolkit to construct difficulty-adjustable and scalable CMOPs (DAS-CMOPs, or DAS-CMaOPs when the number of objectives is greater than three) with three types of parameterized constraint functions developed to capture the three proposed types of difficulty. Based on this toolkit, we suggest nine difficulty-adjustable and scalable CMOPs and nine CMaOPs. The experimental results reveal that mechanisms in MOEA/D-CDP may be more effective in solving convergence-hard DAS-CMOPs, while mechanisms of NSGA-II-CDP may be more effective in solving DAS-CMOPs with simultaneous diversity-, feasibility- and convergence-hardness. Mechanisms in C-NSGA-III may be more effective in solving feasibility-hard CMaOPs, while mechanisms of C-MOEA/DD may be more effective in solving CMaOPs with convergence-hardness. In addition, none of them can solve these problems efficiently, which stimulates us to continue to develop new CMOEAs and CMaOEAs to solve the suggested DAS-CMOPs and DAS-CMaOPs.

cs.NE↗

arXiv2018

PPLS/D: Parallel Pareto Local Search based on Decomposition

Pareto Local Search (PLS) is a basic building block in many metaheuristics for Multiobjective Combinatorial Optimization Problem (MCOP). In this paper, an enhanced PLS variant called Parallel Pareto Local Search based on Decomposition (PPLS/D) is proposed. PPLS/D improves the efficiency of PLS using the techniques of parallel computation and problem decomposition. It decomposes the original search space into L subregions and executes L parallel processes searching in these subregions simultaneously. Inside each subregion, the PPLS/D process is guided by a unique scalar objective function. PPLS/D differs from the well-known Two Phase Pareto Local Search (2PPLS) in that it uses the scalar objective function to guide every move of the PLS procedure in a fine-grained manner. In the experimental studies, PPLS/D is compared against the basic PLS and a recently proposed PLS variant on the multiobjective Unconstrained Binary Quadratic Programming problems (mUBQPs) and the multiobjective Traveling Salesman Problems (mTSPs) with at most four objectives. The experimental results show that, no matter whether the initial solutions are randomly generated or generated by heuristic methods, PPLS/D always performs significantly better than the other two PLS variants.

cs.DC↗

arXiv2018

Nonlinear Collaborative Scheme for Deep Neural Networks

Conventional research attributes the improvements of generalization ability of deep neural networks either to powerful optimizers or the new network design. Different from them, in this paper, we aim to link the generalization ability of a deep network to optimizing a new objective function. To this end, we propose a \textit{nonlinear collaborative scheme} for deep network training, with the key technique as combining different loss functions in a nonlinear manner. We find that after adaptively tuning the weights of different loss functions, the proposed objective function can efficiently guide the optimization process. What is more, we demonstrate that, from the mathematical perspective, the nonlinear collaborative scheme can lead to (i) smaller KL divergence with respect to optimal solutions; (ii) data-driven stochastic gradient descent; (iii) tighter PAC-Bayes bound. We also prove that its advantage can be strengthened by nonlinearity increasing. To some extent, we bridge the gap between learning (i.e., minimizing the new objective function) and generalization (i.e., minimizing a PAC-Bayes bound) in the new scheme. We also interpret our findings through the experiments on Residual Networks and DenseNet, showing that our new scheme performs superior to single-loss and multi-loss schemes no matter with randomization or not.

cs.LG↗

arXiv2018

A Batched Scalable Multi-Objective Bayesian Optimization Algorithm

The surrogate-assisted optimization algorithm is a promising approach for solving expensive multi-objective optimization problems. However, most existing surrogate-assisted multi-objective optimization algorithms have three main drawbacks: 1) cannot scale well for solving problems with high dimensional decision space, 2) cannot incorporate available gradient information, and 3) do not support batch optimization. These drawbacks prevent their use for solving many real-world large scale optimization problems. This paper proposes a batched scalable multi-objective Bayesian optimization algorithm to tackle these issues. The proposed algorithm uses the Bayesian neural network as the scalable surrogate model. Powered with Monte Carlo dropout and Sobolov training, the model can be easily trained and can incorporate available gradient information. We also propose a novel batch hypervolume upper confidence bound acquisition function to support batch optimization. Experimental results on various benchmark problems and a real-world application demonstrate the efficiency of the proposed algorithm.

cs.NE↗

arXiv2018

Locating the boundaries of Pareto fronts: A Many-Objective Evolutionary Algorithm Based on Corner Solution Search

In this paper, an evolutionary many-objective optimization algorithm based on corner solution search (MaOEA-CS) was proposed. MaOEA-CS implicitly contains two phases: the exploitative search for the most important boundary optimal solutions - corner solutions, at the first phase, and the use of angle-based selection [1] with the explorative search for the extension of PF approximation at the second phase. Due to its high efficiency and robustness to the shapes of PFs, it has won the CEC'2017 Competition on Evolutionary Many-Objective Optimization. In addition, MaOEA-CS has also been applied on two real-world engineering optimization problems with very irregular PFs. The experimental results show that MaOEA-CS outperforms other six state-of-the-art compared algorithms, which indicates it has the ability to handle real-world complex optimization problems with irregular PFs.

cs.AI↗

arXiv2018

A New Cooperative Framework for Parallel Trajectory-Based Metaheuristics

In this paper, we propose the Parallel Elite Biased framework (PEB framework) for parallel trajectory-based metaheuristics. In the PEB framework, multiple search processes are executed concurrently. During the search, each process sends its best found solutions to its neighboring processes and uses the received solutions to guide its search. Using the PEB framework, we design a parallel variant of Guided Local Search (GLS) called PEBGLS. Extensive experiments have been conducted on the Tianhe-2 supercomputer to study the performance of PEBGLS on the Traveling Salesman Problem (TSP). The experimental results show that PEBGLS is a competitive parallel metaheuristic for the TSP, which confirms that the PEB framework is useful for designing parallel trajectory-based metaheuristics.

cs.DC↗

arXiv2017

A Simple Yet Efficient Rank One Update for Covariance Matrix Adaptation

In this paper, we propose an efficient approximated rank one update for covariance matrix adaptation evolution strategy (CMA-ES). It makes use of two evolution paths as simple as that of CMA-ES, while avoiding the computational matrix decomposition. We analyze the algorithms' properties and behaviors. We experimentally study the proposed algorithm's performances. It generally outperforms or performs competitively to the Cholesky CMA-ES.

cs.NE↗

arXiv2017

EB-GLS: An Improved Guided Local Search Based on the Big Valley Structure

Local search is a basic building block in memetic algorithms. Guided Local Search (GLS) can improve the efficiency of local search. By changing the guide function, GLS guides a local search to escape from locally optimal solutions and find better solutions. The key component of GLS is its penalizing mechanism which determines which feature is selected to penalize when the search is trapped in a locally optimal solution. The original GLS penalizing mechanism only makes use of the cost and the current penalty value of each feature. It is well known that many combinatorial optimization problems have a big valley structure, i.e., the better a solution is, the more the chance it is closer to a globally optimal solution. This paper proposes to use big valley structure assumption to improve the GLS penalizing mechanism. An improved GLS algorithm called Elite Biased GLS (EB-GLS) is proposed. EB-GLS records and maintains an elite solution as an estimate of the globally optimal solutions, and reduces the chance of penalizing the features in this solution. We have systematically tested the proposed algorithm on the symmetric traveling salesman problem. Experimental results show that EB-GLS is significantly better than GLS.

cs.AI↗

arXiv2017

Push and Pull Search for Solving Constrained Multi-objective Optimization Problems

This paper proposes a push and pull search (PPS) framework for solving constrained multi-objective optimization problems (CMOPs). To be more specific, the proposed PPS divides the search process into two different stages, including the push and pull search stages. In the push stage, a multi-objective evolutionary algorithm (MOEA) is adopted to explore the search space without considering any constraints, which can help to get across infeasible regions very fast and approach the unconstrained Pareto front. Furthermore, the landscape of CMOPs with constraints can be probed and estimated in the push stage, which can be utilized to conduct the parameters setting for constraint-handling approaches applied in the pull stage. Then, a constrained multi-objective evolutionary algorithm (CMOEA) equipped with an improved epsilon constraint-handling is applied to pull the infeasible individuals achieved in the push stage to the feasible and non-dominated regions. Compared with other CMOEAs, the proposed PPS method can more efficiently get across infeasible regions and converge to the feasible and non-dominated regions by applying push and pull search strategies at different stages. To evaluate the performance regarding convergence and diversity, a set of benchmark CMOPs is used to test the proposed PPS and compare with other five CMOEAs, including MOEA/D-CDP, MOEA/D-SR, C-MOEA/D, MOEA/D-Epsilon and MOEA/D-IEpsilon. The comprehensive experimental results demonstrate that the proposed PPS achieves significantly better or competitive performance than the other five CMOEAs on most of the benchmark set.

cs.NE↗

arXiv2017

Evolutionary Multitasking for Multiobjective Continuous Optimization: Benchmark Problems, Performance Metrics and Baseline Results

In this report, we suggest nine test problems for multi-task multi-objective optimization (MTMOO), each of which consists of two multiobjective optimization tasks that need to be solved simultaneously. The relationship between tasks varies between different test problems, which would be helpful to have a comprehensive evaluation of the MO-MFO algorithms. It is expected that the proposed test problems will germinate progress the field of the MTMOO research.

cs.NE↗

arXiv2017

Evolutionary Many-Objective Optimization Based on Adversarial Decomposition

The decomposition-based method has been recognized as a major approach for multi-objective optimization. It decomposes a multi-objective optimization problem into several single-objective optimization subproblems, each of which is usually defined as a scalarizing function using a weight vector. Due to the characteristics of the contour line of a particular scalarizing function, the performance of the decomposition-based method strongly depends on the Pareto front's shape by merely using a single scalarizing function, especially when facing a large number of objectives. To improve the flexibility of the decomposition-based method, this paper develops an adversarial decomposition method that leverages the complementary characteristics of two different scalarizing functions within a single paradigm. More specifically, we maintain two co-evolving populations simultaneously by using different scalarizing functions. In order to avoid allocating redundant computational resources to the same region of the Pareto front, we stably match these two co-evolving populations into one-one solution pairs according to their working regions of the Pareto front. Then, each solution pair can at most contribute one mating parent during the mating selection process. Comparing with nine state-of-the-art many-objective optimizers, we have witnessed the competitive performance of our proposed algorithm on 130 many-objective test instances with various characteristics and Pareto front's shapes.

cs.NE↗

arXiv2017

Matching-Based Selection with Incomplete Lists for Decomposition Multi-Objective Optimization

The balance between convergence and diversity is a key issue of evolutionary multi-objective optimization. The recently proposed stable matching-based selection provides a new perspective to handle this balance under the framework of decomposition multi-objective optimization. In particular, the stable matching between subproblems and solutions, which achieves an equilibrium between their mutual preferences, implicitly strikes a balance between the convergence and diversity. Nevertheless, the original stable matching model has a high risk of matching a solution with a unfavorable subproblem which finally leads to an imbalanced selection result. In this paper, we propose an adaptive two-level stable matching-based selection for decomposition multi-objective optimization. Specifically, borrowing the idea of stable matching with incomplete lists, we match each solution with one of its favorite subproblems by restricting the length of its preference list during the first-level stable matching. During the second-level stable matching, the remaining subproblems are thereafter matched with their favorite solutions according to the classic stable matching model. In particular, we develop an adaptive mechanism to automatically set the length of preference list for each solution according to its local competitiveness. The performance of our proposed method is validated and compared with several state-of-the-art evolutionary multi-objective optimization algorithms on 62 benchmark problem instances. Empirical results fully demonstrate the competitive performance of our proposed method on problems with complicated Pareto sets and those with more than three objectives.

cs.NE↗

arXiv2016

Learning from Non-Stationary Stream Data in Multiobjective Evolutionary Algorithm

Evolutionary algorithms (EAs) have been well acknowledged as a promising paradigm for solving optimisation problems with multiple conflicting objectives in the sense that they are able to locate a set of diverse approximations of Pareto optimal solutions in a single run. EAs drive the search for approximated solutions through maintaining a diverse population of solutions and by recombining promising solutions selected from the population. Combining machine learning techniques has shown great potentials since the intrinsic structure of the Pareto optimal solutions of an multiobjective optimisation problem can be learned and used to guide for effective recombination. However, existing multiobjective EAs (MOEAs) based on structure learning spend too much computational resources on learning. To address this problem, we propose to use an online learning scheme. Based on the fact that offsprings along evolution are streamy, dependent and non-stationary (which implies that the intrinsic structure, if any, is temporal and scale-variant), an online agglomerative clustering algorithm is applied to adaptively discover the intrinsic structure of the Pareto optimal solution set; and to guide effective offspring recombination. Experimental results have shown significant improvement over five state-of-the-art MOEAs on a set of well-known benchmark problems with complicated Pareto sets and complex Pareto fronts.

cs.NE↗