Maximizing quantitative traits in the mating design problem via simulation-based Pareto estimation

In a highway asset maintenance management system involving more than one highway asset type, identifying an equitable optimal allocation of available budget to individual asset systems is a major challenge. This is because the following outcomes are desirable: (1) the maintenance needs of all assets are adequately addressed, (2) the objectives of individual asset systems are optimally satisfied in an equitable manner, and (3) the objectives of the overall highway asset system are achieved optimally. To achieve these desirable outcomes, this paper proposes a two-stage approach in solving the dual-level multiasset, multiobjective pavement network maintenance optimal budget allocation problem. Stage I of the approach analyzes the individual multiobjective asset systems independently to establish for each a family of optimal Pareto solutions. Minimization of maintenance cost is selected as a common objective for the individual asset systems. This serves as the link for interaction with the Stage II analysis. Stage II adopts an optimal algorithm to allocate budget to individual assets by performing a cross-asset trade-off to achieve the optimal budget solution for the given overall system-level objectives. By defining a minimum performance threshold level for each asset type, the Stage II optimization analysis aims to achieve an equitable allocation of budget by maintaining equivalent amounts of performance improvements for the individual asset systems above their respective minimum threshold levels. The conceptual framework of the proposed approach is presented in this paper with a numerical example to illustrate the detailed working of the procedure.

In this paper, a simulation-based optimization approach, named NHOCBA, for a typical resource allocation problem is presented. The hybrid algorithm based on neighborhood algorithm is applied to explore toward optimal direction in design space. For increasing efficiency, an optimal computing budget allocation (OCBA) is adopted to compute the optimal number of replications and to provide reliable evaluation of variance. In addition, we deal with the resource allocation problem which exist multiple global optima in design space. Therefore, a trim procedure which prevents to allocate extra numbers of replication to local optima has been proposed to enhance efficiency. Then, we use confidence interval at the end of algorithm procedure to find an optimal set instead of an optimal solution from design space. Finally, we compare the NHOCBA with different algorithms by experimentation study which shows that NHOCBA approach can perform better than the other algorithms under certain conditions.

Existing bridge performance metrics are limited in their ability to objectively reflect the safety and serviceability of bridges and identify effective Maintenance, Repair and Replacement (MR&R) actions for a large number of bridges in the face of budget constraints. This study presents a comprehensive optimal budget allocation framework with an integer linear programing formulation for a portfolio of bridges based on element-level inspection data. Considering budget constraints, this method determines optimal MR&R actions at element-level such that agency and user costs of repair actions required to have bridges in their like-new state at the next budget allocation year are minimized. The framework incorporates structural safety risks via the probability that the designated structural functionality of a bridge is or deemed to be compromised. The approach is applied to 484 National Highway Systems bridges in district 3 of Ohio. Results indicate that the proposed method can identify work plans comprising the optimal set of MR&R actions that maximize the network-level performance of bridge portfolios, while satisfying budgetary constraints. It is observed that this method consistently assigns higher priority to work plans that reduce structural safety risks of bridges, and to bridges with high traffic demands and long detour lengths.

Many applications in the areas of finance, environments, service systems, and statistical learning require the computation for a general function of the expected performances associated with one or many random objects. When complicated stochastic systems are involved, such computation needs to be done by stochastic simulation and the computational cost can be expensive. We design simulation algorithms that exploit the common random structure shared by all random objects, referred to as stratified splitting. We discuss the optimal simulation budget allocation problem for the proposed algorithms. A brief numerical experiment is conducted to illustrate the performance of the proposed algorithm with various budget allocation rules.

In this paper, we study a strategic model of marketing and product consumption in social networks. We consider two competing firms in a market providing two substitutable products with preset qualities. Agents choose their consumptions following a myopic best response dynamics which results in a local, linear update for the consumptions. At some point in time, firms receive a limited budget which they can use to trigger a larger consumption of their products in the network. Firms have to decide between marginally improving the quality of their products and giving free offers to a chosen set of agents in the network in order to better facilitate spreading their products. We derive a simple threshold rule for the optimal allocation of the budget and describe the resulting Nash equilibrium. It is shown that the optimal allocation of the budget depends on the entire distribution of centralities in the network, quality of products and the model parameters. In particular, we show that in a graph with a higher number of agents with centralities above a certain threshold, firms spend more budget on seeding in the optimal allocation. Furthermore, if seeding budget is nonzero for a balanced graph, it will also be nonzero for any other graph, and if seeding budget is zero for a star graph, it will be zero for any other graph too. We also show that firms allocate more budget to quality improvement when their qualities are close, in order to distance themselves from the rival firm. However, as the gap between qualities widens, competition in qualities becomes less effective and firms spend more budget on seeding.

In recent years, the issue of maximizing submodular functions has attracted much interest from research communities. However, most submodular functions are specified in a set function. Meanwhile, recent advancements have been studied for maximizing a diminishing return submodular (DR-submodular) function on the integer lattice. Because plenty of publications show that the DR-submodular function has wide applications in optimization problems such as sensor placement impose problems, optimal budget allocation, social network, and especially machine learning. In this research, we propose two main streaming algorithms for the problem of maximizing a monotone DR-submodular function under cardinality constraints. Our two algorithms, which are called StrDRS1 and StrDRS2, have (1/2−ϵ), (1−1/e−ϵ) of approximation ratios and O(nϵlog(logBϵ)logk), O(nϵlogB), respectively. We conducted several experiments to investigate the performance of our algorithms based on the budget allocation problem over the bipartite influence model, an instance of the monotone submodular function maximization problem over the integer lattice. The experimental results indicate that our proposed algorithms not only provide solutions with a high value of the objective function, but also outperform the state-of-the-art algorithms in terms of both the number of queries and the running time.

Optimizing budget allocation for educational facilities in Islamic boarding schools is essential to ensure sustainable education quality. This study aims to optimize budget allocation to support educational facilities at Al-Qutub Islamic Boarding School, Wonopringgo, Pekalongan Regency, using a Bayesian Decision Making approach with the Markov Chain Monte Carlo (MCMC) method. Data were collected through questionnaires, observations, and interviews to gather insights on facility conditions, current budget allocation, and additional facility needs. Data analysis employed the MCMC method, enabling decision-making based on the probabilistic distribution of the collected data. The findings indicate that budget allocation optimized through the Bayesian model results in a more effective distribution, addressing urgent facility priorities that directly enhance educational quality. This study contributes a budget analysis model applicable to Islamic educational institutions in Indonesia. Theoretically, it enriches the literature on educational budget management in Islamic boarding schools using Bayesian statistical approaches, while practically, it assists school administrators in allocating budgets more efficiently and accurately in line with educational needs.

We analyze optimal strategies for the allocation of a finite budget that can be invested in different advertising channels over time with the objective of influencing social opinions in a network of individuals. In our analysis, we consider both exogenous influence mechanisms, such as advertising campaigns, as well as endogenous mechanisms of social influence, such as word-of-mouth and peer-pressure, which are modeled using diffusion dynamics. We show that for a broad family of objective functions, the optimal influence strategy at every time uses all channels at either their maximum rate or not at all, i.e., a bang-bang strategy. Furthermore, we prove that the number of switches between these extremes is bounded above by a term that is typically much smaller than the number of agents. This means that the optimal influence strategy is to exert maximum effort in waves for every channel, and then cease effort and let the effects propagate. We also show that, at the beginning of the campaign, the total cost-adjusted reach of an exogenous advertising channel determines its relative value. In contrast, as we approach our investment horizon (e.g., election day), the optimal strategy is to invest in channels able to target individuals instead of broad-reaching channels. We demonstrate that the optimal influence strategies are easily computable in several practical cases, and explicitly characterize the optimal controls for the case of linear objective functions in closed form. Finally, we see that, in the canonical example of designing an election campaign, identifying late-deciders is a critical component in the optimal design.

This paper presents a mathematical model that provides soccer clubs with optimal player transfer recommendations. Using publicly available data on soccer clubs and players, we create a data-driven optimization model that aids soccer clubs in making informed decisions on how to optimally allocate their multi-million dollar transfer budgets. First, some performance attributes, market value, and salary of 7377 real players from across the world are forecasted using a simple moving average method. Next, these forecasted values are input into an integer programming model that solves for the optimal transfer decisions for any club with the objective of maximizing the club’s utility. This utility is a function of the forecasted values, and increases in the market values of the club’s players. Constraints are imposed to reflect the rules and regulations of club soccer. The model focuses on the Premier League (PL), the first-division soccer league in England and Wales. Numerical results are provided for twelve selected clubs in the PL, for the transfer periods during 2016–2017 and 2017–2018. The results show that transfers recommended by the model could help the clubs achieve better market values. The model can be easily customized to fit any club from any country. Our study provides significant contributions to the literature on optimal budget allocation and team selection in sports, by addressing some important ideas that are not considered in the literature.

Optimal Level and Allocation of Cybersecurity Spending: Model and Formula

Efficient Global Optimization (EGO) is a popular method that searches sequentially for the global optimum of a simulated system. EGO treats the simulation model as a black-box, and balances local and global searches. In deterministic simulation, EGO uses ordinary Kriging (OK), which is a special case of universal Kriging (UK). In our EGO variant we use intrinsic Kriging (IK), which eliminates the need to estimate the parameters that quantify the trend in UK. In random simulation, EGO uses stochastic Kriging (SK), but we use stochastic IK (SIK). Moreover, in random simulation, EGO needs to select the number of replications per simulated input combination, accounting for the heteroscedastic variances of the simulation outputs. A popular selection method uses optimal computer budget allocation (OCBA), which allocates the available total number of replications over simulated combinations. We derive a new allocation algorithm. We perform several numerical experiments with deterministic simulations and random simulations. These experiments suggest that (1) in deterministic simulations, EGO with IK outperforms classic EGO; (2) in random simulations, EGO with SIK and our allocation rule does not differ significantly from EGO with SK combined with the OCBA allocation rule.

Measuring and maximizing resilience of freight transportation networks

With the deepening of multi-energy flow coupling and the diversification of energy utilization demand, integrated energy system (IES) puts forward higher requirements for the economy and reliability of capacity allocation scheme. However, there is a complex relationship between economy and reliability, which makes it difficult for them to achieve coordinated optimization. Therefore, an economic and reliability optimal capacity allocation method of IES based on improved co-evolution algorithm is proposed. Firstly, the timing scenario reduction method of “wind power-electrical load” based on ordered clustering algorithm and K-means clustering algorithm is proposed. Aiming at minimizing the expected annual cost of construction investment, operation and maintenance, carbon emission and energy purchase cost, and constrained by equipment operation and energy flow balance, a multi-scenario economic operation model is constructed. Considering the dissatisfaction degree of comprehensive energy consumption, the energy supply reliability evaluation model based on Markov chain Monte Carlo (MCMC) method is established. On this basis, the IES multi-objective optimal capacity allocation model is established. Further, based on the orthogonal test method, the influence factors of decision variables on IES economy and reliability are calculated, and the evolution subpopulation of economy and reliability is established, and then the optimization model’s solution method based on improved co-evolution algorithm is proposed. Finally, an example simulation analysis is carried out combined with the actual data of a certain region. The simulation results show that the proposed model can cooperatively improve the economy and reliability of IES capacity allocation scheme, and provide a reference for the optimal capacity allocation of equipment in IES.

In this correspondence, we propose a constant quality rate allocation algorithm for fine granularity scalability (FGS) coded videos. The rate allocation problem is formulated as a constrained minimization of quality fluctuation. The minimization is solved using a composite rate distortion (R-D) analysis. For a set of video frames, a composite R-D curve is first computed and then used for computing the optimal rate allocation. This algorithm is efficient because it is neither iterative nor recursive. After the composite R-D curve is computed, it can be used for optimal rate allocation of any rate budget. Moreover, the composite R-D curve can be updated efficiently over sliding windows. Experimental results have shown both the effectiveness and the efficiency of the proposed algorithm.

Simulation-based Optimization (SbO) assumes that the simulation model is valid, and that the probability distributions used therein are accurate. However, in practice, the input probability distributions (input models) are estimated by sampling data from the real system. The errors in such estimates can have a profound impact on the optimal solution obtained by SbO. The existing two-stage framework for SbO under computational budget constraint considers only the stochastic uncertainty. In our variant, we consider the input model parameter uncertainty as well. Our algorithmic procedure is based on the stochastic kriging metamodel-assisted bootstrapping with an efficient global optimization technique which sequentially searches the optimum and incorporates Optimal Computational Budget Allocation (OCBA). This framework is also used for determining tighter worst-case bounds of the SbO with input uncertainty. The proposed framework is illustrated with the M/M/1 queuing model.