Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement

Most of existing neural methods for multi-objective combinatorial optimization (MOCO) problems solely rely on decomposition, which often leads to repetitive solutions for the respective subproblems, thus a limited Pareto set. Beyond decomposition, we propose a novel neural heuristic with diversity enhancement (NHDE) to produce more Pareto solutions from two perspectives. On the one hand, to hinder duplicated solutions for different subproblems, we propose an indicator-enhanced deep reinforcement learning method to guide the model, and design a heterogeneous graph attention mechanism to capture the relations between the instance graph and the Pareto front graph. On the other hand, to excavate more solutions in the neighborhood of each subproblem, we present a multiple Pareto optima strategy to sample and preserve desirable solutions. Experimental results on classic MOCO problems show that our NHDE is able to generate a Pareto front with higher diversity, thereby achieving superior overall performance. Moreover, our NHDE is generic and can be applied to different neural methods for MOCO.Comment: Accepted at NeurIPS 202

Efficient Meta Neural Heuristic for Multi-Objective Combinatorial Optimization

Recently, neural heuristics based on deep reinforcement learning have exhibited promise in solving multi-objective combinatorial optimization problems (MOCOPs). However, they are still struggling to achieve high learning efficiency and solution quality. To tackle this issue, we propose an efficient meta neural heuristic (EMNH), in which a meta-model is first trained and then fine-tuned with a few steps to solve corresponding single-objective subproblems. Specifically, for the training process, a (partial) architecture-shared multi-task model is leveraged to achieve parallel learning for the meta-model, so as to speed up the training; meanwhile, a scaled symmetric sampling method with respect to the weight vectors is designed to stabilize the training. For the fine-tuning process, an efficient hierarchical method is proposed to systematically tackle all the subproblems. Experimental results on the multi-objective traveling salesman problem (MOTSP), multi-objective capacitated vehicle routing problem (MOCVRP), and multi-objective knapsack problem (MOKP) show that, EMNH is able to outperform the state-of-the-art neural heuristics in terms of solution quality and learning efficiency, and yield competitive solutions to the strong traditional heuristics while consuming much shorter time.Comment: Accepted at NeurIPS 202

Mathematical models and solution algorithms for the vehicle routing problem with environmental considerations

Urban freight distribution is essential for the functioning of urban economies. However, it is contributing significantly to problems such as traffic congestion and environmental pollution. The main goal of this research is to contribute to greening urban freight distribution by developing new mathematical models and solution algorithms pertaining to the two major steams in Vehicle Routing Problems (VRPs) with environmental considerations: (i) VRPs with an explicit fuel consumption estimation component as a proxy for emissions, and (ii) VRPs with vehicles in the fleet that run on a cleaner alternative fuel such as electricity. In the first stream, this thesis develops and solves a new realistic multi-objective variant of the pollution-routing problem, referred to as the Steiner Pollution-Routing Problem (SPRP), that is studied directly on the original urban roadway network. The proposed variant is capable of incorporating the real operating conditions of urban freight distribution, and striking a balance between traditional business and environmental objectives, while integrating all factors that have a major impact on fuel consumption, including the time-varying congestion speed, vehicle load, vehicle’s physical and mechanical characteristics, and acceleration and deceleration rates. The thesis develops new combinatorial results that facilitate problem solution on the original roadway network and also introduces new mathematical models for synthesizing the expected second-by-second driving cycle of a vehicle over a given road-link at a given time of the day. New efficient multi-objective optimisation heuristics are also developed for addressing realistic instances of the SPRP. On the other hand, in the latter stream discussed above, to tackle the significantly impeding problem of range anxiety in the face of goods distribution using Electric Commercial Vehicles (ECVs), a paradigm shift in the routing of ECVs is proposed by introducing the Electric Vehicle Routing Problem with Synchronised Ambulant Battery Swapping/Recharging (EVRP-SABS). The proposed problem exploits new technological developments corresponding to the possibility of mobile battery swapping (or recharging) of ECVs using a Battery Swapping Van (BSV). In the EVRP-SABS, routing takes place in two levels for the ECVs that carry out delivery tasks, and for the BSVs that provide the running ECVs with fully charged batteries on their route. There is, therefore, a need to establish temporal and spatial synchronisations between the vehicles in the two levels and to do so new combinatorial results and a new solution algorithm is proposed

Integrated Production and Distribution planning of perishable goods

Tese de doutoramento. Programa Doutoral em Engenharia Industrial e Gestão. Faculdade de Engenharia. Universidade do Porto. 201

A dynamic multi-objective evolutionary algorithm based on polynomial regression and adaptive clustering

In this paper, a dynamic multi-objective evolutionary algorithm is proposed based on polynomial regression and adaptive clustering, called DMOEA-PRAC. As the Pareto-optimal solutions and fronts of dynamic multi-objective optimization problems (DMOPs) may dynamically change in the optimization process, two corresponding change response strategies are presented for the decision space and objective space, respectively. In the decision space, the potentially useful information contained in all historical populations is obtained by the proposed predictor based on polynomial regression, which extracts the linear or nonlinear relationship in the historical change. This predictor can generate good initial population for the new environment. In the objective space, in order to quickly adapt to the new environment, an adaptive reference vector regulator is designed in this paper based on K-means clustering for the complex changes of Pareto-optimal fronts, in which the adjusted reference vectors can effectively guide the evolution. Finally, DMOEA-PRAC is compared with some recently proposed dynamic multi-objective evolutionary algorithms and the experimental results verify the effectiveness of DMOEA-PRAC in dealing with a variety of DMOPs

Adaptive neighborhood selection for many-objective optimization problems

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI linkIt is generally accepted that conflicts between convergence and distribution deteriorate with an increase in the number of objectives. Furthermore, Pareto dominance loses its effectiveness in many-objectives optimization problems (MaOPs), which have more than three objectives. Therefore, a more valid selection method is needed to balance convergence and distribution. This paper presents a many-objective evolutionary algorithm, called Adaptive Neighborhood Selection for Many-objective evolutionary algorithm(ANS-MOEA), to deal with MaOPs. This method defines the performance of each individual by two types of information, convergence information (CI) and distribution information (DI). In the critical layer, a well-converged individual is selected first from the population, and its neighbors, calculated by DI, are pushed into neighbor collection (NC) soon afterwards. Then, the proper distribution of the population is ensured by competition individuals with large DI go back to the population and individuals with small DI remain in the collection. Four state-of-the-art MaOEAs are selected as the competitive algorithms to validate ANS-MOEA. The experimental results show that ANS-MOEA can solve a MaOP and generate a set of remarkable solutions to balance convergence and distribution

Large Language Model for Multi-objective Evolutionary Optimization

Multiobjective evolutionary algorithms (MOEAs) are major methods for solving multiobjective optimization problems (MOPs). Many MOEAs have been proposed in the past decades, of which the search operators need a carefully handcrafted design with domain knowledge. Recently, some attempts have been made to replace the manually designed operators in MOEAs with learning-based operators (e.g., neural network models). However, much effort is still required for designing and training such models, and the learned operators might not generalize well on new problems. To tackle the above challenges, this work investigates a novel approach that leverages the powerful large language model (LLM) to design MOEA operators. With proper prompt engineering, we successfully let a general LLM serve as a black-box search operator for decomposition-based MOEA (MOEA/D) in a zero-shot manner. In addition, by learning from the LLM behavior, we further design an explicit white-box operator with randomness and propose a new version of decomposition-based MOEA, termed MOEA/D-LO. Experimental studies on different test benchmarks show that our proposed method can achieve competitive performance with widely used MOEAs. It is also promising to see the operator only learned from a few instances can have robust generalization performance on unseen problems with quite different patterns and settings. The results reveal the potential benefits of using pre-trained LLMs in the design of MOEAs

A fuzzy decision variables framework for large-scale multiobjective optimization

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In large-scale multiobjective optimization, too many decision variables hinder the convergence search of evolutionary algorithms. Reducing the search range of the decision space will significantly alleviate this puzzle. With this in mind, this paper proposes a fuzzy decision variables framework for largescale multiobjective optimization. The framework divides the entire evolutionary process into two main stages: fuzzy evolution and precise evolution. In fuzzy evolution, we blur the decision variables of the original solution to reduce the search range of the evolutionary algorithm in the decision space so that the evolutionary population can quickly converge. The degree of fuzzification gradually decreases with the evolutionary process. Once the population approximately converges, the framework will turn to precise evolution. In precise evolution, the actual decision variables of the solution are directly optimized to increase the diversity of the population so as to be closer to the true Pareto optimal front. Finally, this paper embeds some representative algorithms into the proposed framework and verifies the framework’s effectiveness through comparative experiments on various large-scale multiobjective problems with 500 to 5000 decision variables. Experimental results show that in large-scale multiobjective optimization, the framework proposed in this paper can significantly improve the performance and computational efficiency of multiobjective optimization algorithms

An investigation of multi-objective hyper-heuristics for multi-objective optimisation

In this thesis, we investigate and develop a number of online learning selection choice function based hyper-heuristic methodologies that attempt to solve multi-objective unconstrained optimisation problems. For the first time, we introduce an online learning selection choice function based hyperheuristic framework for multi-objective optimisation. Our multi-objective hyper-heuristic controls and combines the strengths of three well-known multi-objective evolutionary algorithms (NSGAII, SPEA2, and MOGA), which are utilised as the low level heuristics. A choice function selection heuristic acts as a high level strategy which adaptively ranks the performance of those low-level heuristics according to feedback received during the search process, deciding which one to call at each decision point. Four performance measurements are integrated into a ranking scheme which acts as a feedback learning mechanism to provide knowledge of the problem domain to the high level strategy. To the best of our knowledge, for the first time, this thesis investigates the influence of the move acceptance component of selection hyper-heuristics for multi-objective optimisation. Three multi-objective choice function based hyper-heuristics, combined with different move acceptance strategies including All-Moves as a deterministic move acceptance and the Great Deluge Algorithm (GDA) and Late Acceptance (LA) as a nondeterministic move acceptance function. GDA and LA require a change in the value of a single objective at each step and so a well-known hypervolume metric, referred to as D metric, is proposed for their applicability to the multi-objective optimisation problems. D metric is used as a way of comparing two non-dominated sets with respect to the objective space. The performance of the proposed multi-objective selection choice function based hyper-heuristics is evaluated on the Walking Fish Group (WFG) test suite which is a common benchmark for multi-objective optimisation. Additionally, the proposed approaches are applied to the vehicle crashworthiness design problem, in order to test its effectiveness on a realworld multi-objective problem. The results of both benchmark test problems demonstrate the capability and potential of the multi-objective hyper-heuristic approaches in solving continuous multi-objective optimisation problems. The multi-objective choice function Great Deluge Hyper-Heuristic (HHMO_CF_GDA) turns out to be the best choice for solving these types of problems