Coalition Formation (CF) game emerges as a pioneering framework for the resource allocation in Unmanned Aerial Vehicles (UAVs) equipped with various types and complementary resources. However, both the overlapping-enabled collaborative CF and inter-coalition competitive behaviors significantly affect the system performance in complex multi-UAV scenarios. In this paper, we propose a Multiple Overlapping Coalitions (MOC) noncooperative game. Specifically, we first establish an optimization model encompassing coupled resource constraints. Subsequently, a task-priority-based incentive mechanism is designed to better motivate participation. To achieve the Nash equilibrium, a two-step solution technique incorporating relaxation and fine-tuning of resource granularity is designed. We propose a MOC noncooperative game-combined Multi-agent Proximal Policy Optimization (MAOPPPO). The simulation results substantiate that our approach outperforms the other five state-of-the-art learning countermeasures in terms of average reward with a gain of up to$4.59\%$after 800 of training episodes. In terms of throughput, the proposed MOC noncooperative game increases by$66.67\%$,$93.68\%$, and$11.76\%$compared with that of CF noncooperative game, non-CF noncooperative game, and consensus-based algorithm, respectively. For total resource contribution, the improvements are$62.99\%$,$94.59\%$, and$23.16\%$, respectively. The energy efficiency enhances by$6.82\%$,$23.68\%$, and$4.78\%$compared to the other three baselines, respectively.

A commonly used strategy for improving optimization algorithms is to restart the algorithm when it is believed to be trapped in an inferior part of the search space. Building on the recent success of BET-AND-RUN approaches for restarted local search solvers, we introduce a more generic version that makes use of performance prediction. It is our goal to obtain the best possible results within a given time budget t using a given black-box optimization algorithm. If no prior knowledge about problem features and algorithm behavior is available, the question about how to use the time budget most efficiently arises. We first start k ≥ 1 independent runs of the algorithm during an initialization budget t1 < t, pause these runs, then apply a decision maker D to choose 1 ≤ m < k runs from them (consuming t2 ≥ 0 time units in doing so), and then continue these runs for the remaining t3 = t−t1−t2 time units. In previous BET-AND-RUN strategies, the decision maker D = currentBest would simply select the run with the best-so-far results at negligible time. We propose using more advanced methods to discriminate between “good” and “bad” sample runs with the goal of increasing the correlation of the chosen run with the a-posteriori best one. In over 157 million experiments, we test different approaches to predict which run may yield the best results if granted the remaining budget. We show (1) that the currentBest method is indeed a very reliable and robust baseline approach, and (2) that our approach can yield better results than the previous methods.

This paper analyzes the stochastic runtime of the cross-entropy (CE) algorithm for the well-studied standard problems ONEMAX and LEADINGONES. We prove that the total number of solutions the algorithm needs to evaluate before reaching the optimal solution (i.e., its runtime) is bounded by a polynomial Q(n) in the problem size n with a probability growing exponentially to 1 with n if the parameters of the algorithm are adapted to n in a reasonable way. Our polynomial bound Q(n) for ONEMAX outperforms the well-known runtime bound of the 1-ANT algorithm, a particular ant colony optimization algorithm. Our adaptation of the parameters of the CE algorithm balances the number of iterations needed and the size of the samples drawn in each iteration, resulting in an increased efficiency. For the LEADINGONES problem, we improve the runtime of the algorithm by bounding the sampling probabilities away from 0 and 1. The resulting runtime outperforms the known stochastic runtime for a univariate marginal distribution algorithm, and is very close to the known expected runtime of variants of max-min ant systems. Bounding the sampling probabilities allows the CE algorithm to explore the search space even for test functions with a very rugged landscape as the LEADINGONES function.

Radial Basis Functions Neural Network (RBFNN) as the outcome of recent research provides a simple model for complex networks. This is achieved by employing the Radial Basis Function (RBF) in the network as hidden neuron patterns. The optimal properties of the RBFs pave the way for stable approximation. However, it is generally rather difficult to determine the locations of the centers and the shape parameter. In this article, we will present an evolutionary approach for learning parameters. The approach is based on genetic algorithms. It consists of three well-defined feed-forwarding Phases, and uses a very efficient fitness evaluation method, the so-called Power function.

Model-based search is an abstract framework that unifies the main features of a large class of heuristic procedures for combinatorial optimization, it includes ant algorithms, cross entropy and estimation of distribution algorithms. Properties shown for the model-based search therefore apply to all these algorithms. A crucial parameter for the long term behavior of model-based search is the learning rate that controls the update of the model when new information from samples is available. Often this rate is kept constant over time. We show that in this case after finitely many iterations, all model-based search algorithms will be absorbed into a state where all samples consist of a single solution only. Moreover, it cannot be guaranteed that this solution is optimal, at least not when the optimal solution is unique.

The discrete cross-entropy optimization algorithm iteratively samples solutions according to a probability density on the solution space. The density is adapted to the good solutions observed in the present sample before producing the next sample. The adaptation is controlled by a so-called smoothing parameter. We generalize this model by introducing a flexible concept of feasibility and desirability into the sampling process. In this way, our model covers several other optimization procedures, in particular the ant-based algorithms. The focus of this paper is on some theoretical properties of these algorithms. We examine the first hitting time τ of an optimal solution and give conditions on the smoothing parameter for τ to be finite with probability one. For a simple test case we show that runtime can be polynomially bounded in the problem size with a probability converging to 1. We then investigate the convergence of the underlying density and of the sampling process. We show, in particular, that a constant smoothing parameter, as it is often used, makes the sample process converge in finite time, freezing the optimization at a single solution that need not be optimal. Moreover, we define a smoothing sequence that makes the density converge without freezing the sample process and that still guarantees the reachability of optimal solutions in finite time. This settles an open question from the literature.