To find diversified solutions converging to true Pareto fronts (PFs), hypervolume (HV) indicator-based algorithms have been established as effective approaches in multiobjective evolutionary algorithms (MOEAs). However, the bottleneck of HV indicator-based MOEAs is the high time complexity for measuring the exact HV contributions of different solutions. To cope with this problem, in this paper, a simple and fast hypervolume indicator-based MOEA (FV-MOEA) is proposed to quickly update the exact HV contributions of different solutions. The core idea of FV-MOEA is that the HV contribution of a solution is only associated with partial solutions rather than the whole solution set. Thus, the time cost of FV-MOEA can be greatly reduced by deleting irrelevant solutions. Experimental studies on 44 benchmark multiobjective optimization problems with 2-5 objectives in platform jMetal demonstrate that FV-MOEA not only reports higher hypervolumes than the five classical MOEAs (nondominated sorting genetic algorithm II (NSGAII), strength Pareto evolutionary algorithm 2 (SPEA2), multiobjective evolutionary algorithm based on decomposition (MOEA/D), indicator-based evolutionary algorithm, and S-metric selection based evolutionary multiobjective optimization algorithm (SMS-EMOA)), but also obtains significant speedup compared to other HV indicator-based MOEAs.

Lately, the Vehicle Routing Problem (VRP) in the city, known as City VRP, has gained popularity with its importance in city logistics. Similar to city logistics, City VRP mainly differs from conventional VRP in terms of the stakeholders involved, namely the shipper, carrier, resident, and administrator. Accordingly, this paper surveys the City VRP literature categorized by stakeholders and summarizes the constraints, models, and solution methods for VRP in urban cities. City VRPs are also analyzed based on the problem of interest considered by the stakeholders and the corresponding models that have been proposed in response. Through this review, we identify the state of the art of City VRP, highlight the core challenging issues, and suggest some potential research area in this field that have remained underexplored.

Globalisation and lean initiatives increase the vulnerabilities of the supply chains (SC), where disruptions in any plant in a supply chain network (SCN) can propagate throughout the whole SCN. Redundancy is part of the SC re-engineering to improve supply chain resilience (SCRES). This paper presents a conceptual model of an SCN using graph theory, considering the relationships between plants and materials. Based on the model, the structural redundancy of the SCN is measured, which is used to assess SCRES. This assessment approach focuses on the resilience of the SCN against disruptions. Case studies are discussed to illustrate the applicability of this model and show that increasing structural redundancy of the SCN improves SCRES against disruptions.

Federated learning (FL) is a promising decentralized deep learning technique that allows users to collaboratively update models without sharing their own data. However, due to its decentralized nature, no one can monitor workers’ behavior, and they may thus deviate protocols (e.g., participating without updating any models). To solve this problem, many researchers have proposed blockchain-enabled FL to reward workers (or users) with cryptocurrencies to encourage workers to follow the protocols. However, there is a lack of theoretical discussions concerning how such rewards impact workers’ behavior and how much should be given to workers. In this paper, we propose a mechanism-design-oriented FL protocol on a public blockchain network. Mechanism design (MD) is often used to make a rule intended to achieve a specific goal. With MD in mind, we introduce the concept of competition into blockchain-based FL so that only workers who have contributed well can obtain rewards, which naturally prevents workers from deviating from the protocol. We then mathematically answer the following questions with contest theory, a novel field of study in economics: i) What behavior will workers take?; ii) how much effort should workers exert to maximize their profits?; iii) how many workers should be rewarded?; and iv) what is the best proportion for reward distribution?.