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To deal with group decision making (GDM) with interval multiplicative preference relations (IMPRs), this paper proposes a novel method based on multiplicative data envelopment analysis (DEA) cross-efficiency and stochastic weight space acceptability analysis. We first develop a multiplicative DEA model to evaluate the relative efficiency of all alternatives of a given multiplicative preference relation (MPR). Then, we present a method, free from consistency adjustment, to derive a priority vector using the multiplicative DEA cross-efficiency with respect to the given MPR. For GDM with IMPRs, we consider the decision makers’ weights as a uniform distribution for acceptability analysis. A modified unacceptability index is further defined to measure the unlikeliness for a particular alternative in a particular rank. Finally, we develop an assignment problem model to achieve an optimal ranking by minimizing the total rank unacceptability, and to compute the expected priority vector of all alternatives. Numerical examples are provided to show the applicability and justifications of the proposed GDM method.

This paper investigates the task assignment problem for a team of autonomous aerial/marine vehicles driven by constant thrust and maneuvering in a planar lateral drift field. The aim is to minimize the total traveling time in order to guide the vehicles to deliver a number of customized sensors to a set of target points with different sensor demands in the drift field. To solve the problem, we consider together navigation strategies and target assignment algorithms; the former minimizes the traveling time between two given locations in the drift field and the latter allocates a sequence of target locations to each vehicle. We first consider the effect of the weight of the carried sensors on the speed of each vehicle, and construct a sufficient condition to guarantee that the whole operation environment is reachable for the vehicles. Then from optimal control principles, time-optimal path planning is carried out to navigate each vehicle from an initial position to its given target location. Most importantly, to assign the targets to the vehicles, we combine the virtual coding strategy, multiple offspring method, intermarriage crossover strategy, and the tabu search mechanism to obtain a co-evolutionary multi-population genetic algorithm, short-named CMGA. Simulations on sensor delivery scenarios in both fixed and time-varying drift fields are shown to highlight the satisfying performances of the proposed approach against popular greedy algorithms.

Exploration of two population methods for Extremal Optimisation undertaken.Innovative use of intervention, interaction and collective memory strategies.Bi-objective version of generalised assignment problem with reference points given.General non-dominated local search algorithm developed and tested.Comparative analysis with NSGA-II. The power to solve intractable optimisation problems is often found through population based evolutionary methods. These include, but are not limited to, genetic algorithms, particle swarm optimisation, differential evolution and ant colony optimisation. While showing much promise as an effective optimiser, extremal optimisation uses only a single solution in its canonical form - and there are no standard population mechanics. In this paper, two population models for extremal optimisation are proposed and applied to a multi-objective version of the generalised assignment problem. These models use novel intervention/interaction strategies as well as collective memory in order to allow individual population members to work together. Additionally, a general non-dominated local search algorithm is developed and tested. Overall, the results show that improved attainment surfaces can be produced using population based interactions over not using them. The new EO approach is also shown to be highly competitive with an implementation of NSGA-II.

High-order graph matching aims at establishing correspondences between two sets of feature points using high-order constraints. It is usually formulated as an NP-hard problem of maximizing an objective function. This paper introduces a discrete particle swarm optimization algorithm for resolving high-order graph matching problems, which incorporates several re-defined operations, a problem-specific initialization method based on heuristic information, and a problem-specific local search procedure. The proposed algorithm is evaluated on both synthetic and real-world datasets. Its outstanding performance is validated in comparison with three state-of-the-art approaches.