Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization

The use of surrogate based optimization (SBO) is widely spread in engineering design to reduce the number of computational expensive simulations. However, “real-world” problems often consist of multiple, conflicting objectives leading to a set of competitive solutions (the Pareto front). The objectives are often aggregated into a single cost function to reduce the computational cost, though a better approach is to use multiobjective optimization methods to directly identify a set of Pareto-optimal solutions, which can be used by the designer to make more efficient design decisions (instead of weighting and aggregating the costs upfront). Most of the work in multiobjective optimization is focused on multiobjective evolutionary algorithms (MOEAs). While MOEAs are well-suited to handle large, intractable design spaces, they typically require thousands of expensive simulations, which is prohibitively expensive for the problems under study. Therefore, the use of surrogate models in multiobjective optimization, denoted as multiobjective surrogate-based optimization, may prove to be even more worthwhile than SBO methods to expedite the optimization of computational expensive systems. In this paper, the authors propose the efficient multiobjective optimization (EMO) algorithm which uses Kriging models and multiobjective versions of the probability of improvement and expected improvement criteria to identify the Pareto front with a minimal number of expensive simulations. The EMO algorithm is applied on multiple standard benchmark problems and compared against the well-known NSGA-II, SPEA2 and SMS-EMOA multiobjective optimization methods.     

Cost effective scheduling of imperfect inspections in systems with hidden failures and rescue possibility

Motivated by real-world critical applications such as aircraft, medical devices, and military systems, this paper models non-repairable systems subject to a delay-time failure process involving hidden and fatal failures in two stages during their missions. A hidden failure cannot cause the system to stop functioning while a fatal failure causes the entire system loss. The system undergoes scheduled inspections for detecting the hidden failure. In the case of a positive inspection result, the system main mission is aborted and a rescue operation is started to mitigate the risk of the entire system loss. The inspections are imperfect and may produce false positive and negative failures. We propose probabilistic models for evaluating performance metrics of the system considered, including mission success probability, system survival probability, expected number of inspections during the mission, and total expected losses. Based on the evaluation models, we formulate and solve an optimization problem of finding the optimal inspection schedule on a fixed mission time horizon to minimize the total expected loss. Examples are provided to demonstrate the proposed methodology and effects of key system parameters on system performance and optimization solutions.     

Integrated simulation and optimization models for tracking international fixed income indices

Portfolio managers in the international fixed income markets must address jointly the interest rate risk in each market and the exchange rate volatility across markets. This paper develops integrated simulation and optimization models that address these issues in a common framework. Monte Carlo simulation procedures generate jointly scenarios of interest and exchange rates and, thereby, scenarios of holding period returns of the available securities. The portfolio manager’s risk tolerance is incorporated either through a utility function or a (modified) mean absolute deviation function. The optimization models prescribe asset allocation weights among the different markets and also resolve bond-picking decisions. Therefore several interrelated decisions are cast in a common framework. Two models – an expected utility maximization and a mean absolute deviation minimization – are implemented and tested empirically in tracking a composite index of the international bond markets. Backtesting over the period January 1997 to July 1998 illustrate the efficacy of the optimization models in dealing with uncertainty and tracking effectively the volatile index. Of particular interest is the empirical demostration that the integrative models generate portfolios that dominate the portfolios obtained using classical disintegrated approaches. Received: November 24, 1998 / Accepted: October 1, 2000?Published online December 15, 2000     

The stochastic capacitated branch restructuring problem

Traditionally, in the fashion industry, purchasing decisions for retailers are made based on various factors such as budget, profit target, and interest rate. Since the market demand is highly volatile, risk is inherently present and it is critically important to incorporate risk consideration into the decision making framework. Motivated by the observed industrial practice, we explore via a mean-variance approach the multi-period risk minimization inventory models for fashion product purchasing. We first construct a basic multi-period risk optimization model for the fashion retailer and illustrate how its optimal solution can be determined by solving a simpler problem. Then, we analytically find that the optimal ordering quantity is increasing in the expected profit target, decreasing in the number of periods of the season, and increasing in the market interest rate. After that, we propose and solve several extended models which consider realistic and timely industrial measures such as minimum ordering quantity, carbon emission tax, and carbon quota. We analytically derive the necessary and sufficient condition(s) for the existence of the optimal solution for each model and show how the purchasing budget, the profit target, and the market interest rate affect the optimal solution. Finally, we investigate the supply chain coordination challenge and analytically illustrate how an upstream manufacturer can offer implementable supply contracts to optimize the supply chain.     

Analyzing securitization processes using simulation methods

The aim of this paper is to present an analysis of securitization processes using simulation and optimization methods. We discuss the main risk factors that may affect profitability of the process. These risk factors are interest rates and mortgage prepayments. We combine latest risk factor models to create a consistent framework to analyze and improve securitization processes. We then show that making ad hoc securitization decisions may be far less efficient than by solving optimization problems. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A simulation optimization method that considers uncertainty and multiple performance measures

Simulation optimization provides a structured approach to system design and configuration when analytical expressions for input/output relationships are unavailable. This research focuses on the development of a new simulation optimization technique applicable to systems having multiple performance measures. The aim of this research is to incorporate a simulation end user’s preference towards risk and uncertainty into the search process for the best decision alternative. Automation of the optimization procedure is a necessity. Therefore, this paper proposes a simulation optimization method that involves a preference model, specifically adapted for decision making with simulation models.     

Multi-Level Strategic Evaluation of Hospital Plans and Decisions

Strategic decision making in hospitals involves the assessment of linkages between decisions that are typically made in a hierarchical fashion. In hospitals, as in most large organizations, overall system performance is a function of how well the critical decisions are integrated. This paper focuses on the multi-level nature of the decisions and policies that typically need to be evaluated in hospital planning, highlighting that both optimization and simulation approaches may be required. An application involving a large general purpose urban hospital is used to illustrate the interdependency between the levels in the planning hierarchy. An optimization model is formulated to deal with facility layout and capacity allocation while a simulation model is proposed to capture the complexities of hospital operations. The linkages and information feedback between the models are shown to be critical in the design of a system that performs well and facilitates strategic hospital planning.     

Scheduling of production and logistics operations of steam production systems in food industries: a case study of the tomato processing industry

This study presents an optimization approach by mathematical modelling to support some of the main operational decisions in steam production systems with multiple industrial boilers. Decisions are related to boiler operations scheduling (start-up, warm-up and shutdown time), fuel replenishment (transportation and inventory management) and fuel composition consumed by each piece of equipment. These decisions are often taken based on practical experience of people involved, instead of any decision support tool using optimization techniques; as a consequence, unnecessary costs are likely to be incurred. The optimization approach is based on mixed integer programming and parameters experimental adjustment procedures. A case study of a large tomato processing plant in Brazil was carried out along 1 year using a 3-year database. Owing to the reasonably good outcomes achieved (annually potential savings around 10%), we consider the proposed approach as a suitable tool to support some of the key decisions in boiler scheduling and fuel logistics in steam production systems for tomato processing and other similar industries.     

Ensemble mutable smart bee algorithm and a robust neural identifier for optimal design of a large scale power system

The aim of the current study is to probe the potentials of ensemble bio-inspired approaches to handle the deficiencies associated with designing large scale power systems. Ensemble computing has been proven to be a very promising paradigm. The fundamental motivation behind designing such bio-inspired optimization models lies in the fact that interactions among different sole optimizers can afford much better income as compared with an individual optimizer. To do so, the authors propose an optimization technique called ensemble mutable smart bee algorithm (E-MSBA) which is based on the aggregation of several independent low-level optimizers. Here, each low-level unit of the proposed ensemble framework uses mutable smart bee algorithm (MSBA) for optimization procedure. The main provocations behind selecting MSBAs of different properties as components of ensemble are twofold. On the one hand, MSBA proved its capability for handling multimodal constraint problems. On the other hand, based on different experiments, it was demonstrated that MSBA can find the optimum solution with a relatively low computational cost. In this study, the authors intend to indicate that the proposed ensemble paradigm can efficiently optimize the operating parameters of a large scale power system which includes different mechanical components. To this end, E-MSBA and some rival methods are taken into account for the optimization procedure. The obtained results reveal that E-MSBA inherits some positive features of the MSBA algorithm. Additionally, it is observed that the ensembling approach enables the proposed method to effectively tackle the flaws associated with optimization of large scale problems.     

Strategic control and interests,its effects on decision outcomes

Application of the model to artificial data shows that actors with strong preferences in the center have more possibilities to realize good outcomes than other actors. On the basis of an empirical application it is shown that a Nash equilibrium does not always arise after a large number of iterations unless actors have learning capabilities or are severely restricted in their strategic behavior.

In political systems and large organizations, ultimate decision makers are usually just a small subset of all actors in the social system. To arrive at acceptable decisions, decision makers have to take into account the preferences of other actors in the system. Typically preferences of more interested and more powerful actors are weighted heavier than those of less interested and powerful actors. This implies that the total leverage of an actor on the decision is determined by the combination of his power (his potential) and his interest (his willingness to mobilize his power). As the exact level of an actor's leverage is difficult to estimate for the other actors in the system, an actor is able to optimize his effects on outcomes of decisions by providing strategic informatioa

In this paper, first an analytic solution is presented for the optimization of strategic leverage in collective decision making by one single actor. In this solution, the actor makes assumptions about the leverage other actors will show in decision making. Subsequently, the actor optimizes the outcomes of decisions by manipulating the distribution of his leverage over a set of issues.

The analytic solution can be theoretically interpreted by decomposing the solution into three terms, the expected external leverage of the other actors on the issue, the evaluation of the deviance of the expected from the preferred outcome of the issue, and the restrictions on the distribution of leverage over the issues. The higher the expectation of the leverages the other actors will allocate to the issue, the less an actor is inclined to allocate leverage to the issue. The higher the evaluation of the deviance, the more an actor is inclined to allocate leverage to the issue. This is restricted, however, by the required distribution of leverages over the issues. The researcher is able to manipulate these restrictions to investigate its consequences for the outcomes.

In the next step, we investigate whether we can find a Nash equilibrium if all actors optimize their leverage simultaneously. Under certain conditions, a Nash equilibrium can be found by an iterative process in which actors update their estimates oh each other's leverages on the basis of what the other actors have shown in previous iterations.     

A stochastic investiment model for a survival conscious firm

A stochastic investiment is analyzed to show the consequences of an unwillingness by the entrepreneur to accept any positive risk of the firm's failure. The entrepreneur does not invest in additional capacity, even in the face of continuing positive expected profits, if that investment would infringe on the firm's ability to survive. Survival of the firm conditions all investment decisions, which are functions (via the physical and financial capital accounts) of the random outcomes observed at the time of decision. This conditioning shows how worse than expected outcomes will affect the firm's net asset position and its ability to survive. Managerially, the entrepreneur has principles by which to explicitly consider unpleasant surprises in planning for the continued growth of the firm. In contrast, knowledge of the random outcomes is shown to be of no consequence in an alternative model where maximization of expected profits is the sole criterion of the entrepreneur. In that model, the optimal investiment decisions can be made at the beginning of the firm's life, because those decisions are not functions of the future yields. Reduction of the survival model to a linear programming (LP) problem highlights the additional complexity of the survival problem. This reduction means that the maximum value of the objective function for the primal (expected profits) equals the minimum value of the objective function for the dual (resource costs), which economists interpret as zero profits. The zero profit consequence is in accordance with Knight's long-standing economic conjecture: If all risks are measureable, total risk aversion will result in no profits. Also, LP methods provide a way in application to analyze a wide range of risk possibilities from acceptance of no risk of failure to acceptance of some risk of failure.The economist as such does not advocate criteria of optimality. He may invent them. ... the ultimate choice is made by the procedures of decision making inherent in the institutions, laws and customs of society. Tjalling C. Koopmans, Nobel Memorial Lecture, 11th December 1975.     

Joint optimization of budget allocation and maintenance planning of multi-facility transportation infrastructure systems

Transportation infrastructure, such as pavements and bridges, is critical to a nation’s economy. However, a large number of transportation infrastructure is underperforming and structurally deficient and must be repaired or reconstructed. Maintenance of deteriorating transportation infrastructure often requires multiple types/levels of actions with complex effects. Maintenance management becomes more intriguing when considering facilities at the network level, which represents more challenges on modeling interdependencies among various facilities. This research considers an integrated budget allocation and preventive maintenance optimization problem for multi-facility deteriorating transportation infrastructure systems. We first develop a general integer programming formulation for this problem. In order to solve large-scale problems, we reformulate the problem and decompose it into multiple Markov decision process models. A priority-based two-stage method is developed to find optimal maintenance decisions. Computational studies are conducted to evaluate the performance of the proposed algorithms. Our results show that the proposed algorithms are efficient and effective in finding satisfactory maintenance decisions for multi-facility systems. We also investigate the properties of the optimal maintenance decisions and make several important observations, which provide helpful decision guidance for real-world problems.     

A strategic decision support system framework for energy-efficient technology investments

Energy systems optimization under uncertainty is increasing in its importance due to on-going global de-regulation of the energy sector and the setting of environmental and efficiency targets which generate new multi-agent risks requiring a model-based stakeholders dialogue and new systemic regulations. This paper develops an integrated framework for decision support systems (DSS) for the optimal planning and operation of a building infrastructure under appearing systemic de-regulations and risks. The DSS relies on a new two-stage, dynamic stochastic optimization model with moving random time horizons bounded by stopping time moments. This allows to model impacts of potential extreme events and structural changes emerging from a stakeholders dialogue, which may occur at any moment of the decision making process. The stopping time moments induce endogenous risk aversion in strategic decisions in a form of dynamic VaR-type systemic risk measures dependent on the system’s structure. The DSS implementation via an algebraic modeling language (AML) provides an environment that enforces the necessary stakeholders dialogue for robust planning and operation of a building infrastructure. Such a framework allows the representation and solution of building infrastructure systems optimization problems, to be implemented at the building level to confront rising systemic economic and environmental global changes.     

Twenty years of linear programming based portfolio optimization

Markowitz formulated the portfolio optimization problem through two criteria: the expected return and the risk, as a measure of the variability of the return. The classical Markowitz model uses the variance as the risk measure and is a quadratic programming problem. Many attempts have been made to linearize the portfolio optimization problem. Several different risk measures have been proposed which are computationally attractive as (for discrete random variables) they give rise to linear programming (LP) problems. About twenty years ago, the mean absolute deviation (MAD) model drew a lot of attention resulting in much research and speeding up development of other LP models. Further, the LP models based on the conditional value at risk (CVaR) have a great impact on new developments in portfolio optimization during the first decade of the 21st century. The LP solvability may become relevant for real-life decisions when portfolios have to meet side constraints and take into account transaction costs or when large size instances have to be solved. In this paper we review the variety of LP solvable portfolio optimization models presented in the literature, the real features that have been modeled and the solution approaches to the resulting models, in most of the cases mixed integer linear programming (MILP) models. We also discuss the impact of the inclusion of the real features.     

A bottom-up biofuel market equilibrium model for policy analysis

Although the biofuel market remains at its early stage, it is expected to play an important role in climate policy in the future in the transportation sector. In this paper, we develop a bottom-up equilibrium model to study the supply chain of the biofuel market, explicitly formulating the interactions among farmers, biofuel producers, blenders, and consumers. The model is built on optimization problems faced by each entity and considers decisions associated with farmers’ land allocation, biomass transportation, biofuel production, and biofuel blending. As such, the model is capable of and appropriate for policy analysis related to interactions among multiple stakeholders. For example, the model can be used to analyze the impacts of biofuel policies on market outcomes, pass-through of taxes or subsidies, and distribution of consumers’ or producers’ surplus. The equilibrium model can also serve as an analytical tool to study the price impact of biomass, biofuel, and Renewable Identification Numbers (RINs) for biofuels. We demonstrate the model by applying it to a case study of Iowa. We specifically focus on the effects of market structure, i.e., points-of-implementation on subsidies on market outcomes. The results indicate that some entities can benefit greatly at the expense of others when they possess market power. Government oversight is therefore needed to safeguard the development of the sector.     

INTEGRATING MARINE PROTECTED AREAS INTO MODELS FOR FISHERY ASSESSMENT AND MANAGEMENT

ABSTRACT. Marine protected areas (MPAs) have been proposed as an insurance policy against fishery management failures and as an integral part of an optimal management system for some fisheries. However, an incorrectly designed MPA can increase the risk of depletion of some species, and can reduce the value of the system of fisheries it impacts. MPAs may alter structural processes that relate fishery outcomes to management variables and thereby compromise the models that are used to guide decisions. New models and data gathering programs are needed to use MPAs effectively. This paper discusses the motivations and methods for incorporating explicitly spatial dynamics of both fish and fishermen into fishery models so that they can be used to assess spatial policies such as MPAs. Some important characteristics and capabilities which these models should have are outlined, and a topical review of some relevant modeling methodologies is provided.     

A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns

Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean–variance model, entropy optimization model, chance constrained programming model and so on. In order to solve these nonlinear optimization models, a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm, neural network and fuzzy simulation techniques, where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network. Since these models are used to be solved by genetic algorithm, some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples, which imply that the hybrid intelligent algorithm is robust and more effective. In particular, it reduces the running time significantly for large size problems.     

Decision analysis models in reinsurance

Decision analysis models are developed and illustrated for the reinsurance (risk transfer) decisions made by insurance companies. Decision analytic models were found to be useful tools both for structuring multistage reinsurance decisions and for comparing alternative options. The insurer is faced with many possible choices involving reinsurance type and extent, and an expected utility model provided insight both as a screening device and as an evaluation criterion. Decision analytic models appeared to be superior to other approaches such as mean/variance and risk of ruin models both because of their flexibility and their more comprehensive treatment the important elements of the decision, namely the complete claims distribution, the cost of reinsurance and the insurer's risk attitude.     

基于Monte-Carlo模拟的最小亏损套期保值策略研究

把终期的期望亏损定义为风险,研究了标的资产价格服从跳扩散结构时的自筹资最小亏损风险套期保值.首先通过Monte-Carlo模拟生成标的资产若干条价格路径并用所有路径上的终期亏损平均值作为优化目标期望值的估计,然后引入基函数作为套期保值头寸的近似逼近,最后通过数值方法得到最优套期保值策略.最后通过实例分析表明:1)套期保值头寸调整的频率相对较高时,可以更好地应对市场出现的价格波动,从而降低可能面临的损失风险,达到较好的保值效果;2)欧式看涨期权的交割价格与对冲头寸呈反向变化,交割价格越高,可适当调低持有的对冲头寸,反之则反,这样,即对冲风险又节约成本.     

PHAB scores: proportional hazards analysis behavioural scores

Credit scoring is one of the most widely used applications of quantitative analysis in business. Behavioural scoring is a type of credit scoring that is performed on existing customers to assist lenders in decisions like increasing the balance or promoting new products. This paper shows how using survival analysis tools from reliability and maintenance modelling, specifically Cox's proportional hazards regression, allows one to build behavioural scoring models. Their performance is compared with that of logistic regression. Also the advantages of using survival analysis techniques in building scorecards are illustrated by estimating the expected profit from personal loans. This cannot be done using the existing risk behavioural systems.