Optimum Optimorum Research Articles

Global Optimization of the Shape of a Suborbital Space Vehicle

AbstractThe determination of the global optimized (GO) shapes of flying configurations leads to extended variational problems with free boundaries. The author has developed special optimization strategies called optimum optimorum and iterative optimum optimorum strategies and have used them for the design of GO shapes of three models, which are of minimum drag at three different supersonic cruising Mach numbers. These optimization strategies can be used for the determination of new GO shapes of more performant supersonic transport aircraft and space vehicles. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Bioeconomic Analysis of Habitat-Fishery Connections: Fishing on Cold Water Coral Reefs

We develop a bioeconomic model to study habitat-fishery connections such as cold water coral habitats, which are negatively affected by bottom trawling but remain unaffected by stationary gear harvest. Using dynamic optimization, we derive optimum optimorum values for both fish and cold water coral stocks. We find that when coral is a preferred habitat, the fish and coral stocks become substitutes in terms of unit cost savings of harvest, while an essential habitat implies competing cost and growth effects. Data are from the North East Arctic cod fishery, and the results are robust and in line with our theoretical prediction.

Endogenous fertility, endogenous lifetime and economic growth: the role of child policies

We examine the effects of child policies on both transitional dynamics and long-term demo-economic outcomes in an overlapping-generations neoclassical growth model à la Chakraborty (J Econ Theory 116(1):119–137, 2004) extended with endogenous fertility under the assumption of weak altruism towards children. The government invests in public health, and an individual’s survival probability at the end of youth depends on health expenditure. We show that multiple development regimes can exist. However, poverty or prosperity does not necessarily depend on the initial conditions, since they are the result of how a child policy is designed. A child tax, for example, can be used effectively to enable those economies that were entrapped in poverty to prosper. There is also a long-term welfare-maximising level of the child tax. We show that a child tax can be used to increase capital accumulation, escape from poverty and maximise long-term welfare also when (a) a public pay-as-you-go pension system is in place and (b) the government issues an amount of public debt. Interestingly, there also exists a couple child tax–health tax that can be used to find the second-best optimum optimorum. In addition, we show that results are robust to the inclusion of decisions regarding the child quantity–quality trade-off under the assumption of impure altruism. In particular, there exists a threshold value of the child tax below (resp. above) which child quality spending is unaffordable (resp. affordable) and different scenarios are in existence.

The Multipoint Global Shape Optimization of Flying Configuration with Movable Leading Edges Flaps

The aerodynamical global optimized (GO) shape of flying configuration (FC), at two cruising Mach numbers, can be realized by morphing. Movable leading edge flaps are used for this purpose. The equations of the surfaces of the wing, of the fuselage and of the flaps in stretched position are approximated in form of superpositions of homogeneous polynomes in two variables with free coefficients. These coefficients together with the similarity parameters of the planform of the FC are the free parameters of the global optimization. Two enlarged variational problems with free boundaries occur. The first one consists in the determination of the GO shape of the wing-fuselage FC, with the flaps in retracted position, which must be of minimum drag, at higher cruising Mach number. The second enlarged variational problem consists in the determination of the GO shape of the flaps in stretched position in such a manner that the entire FC shall be of minimum drag at the second lower Mach number. The iterative optimum-optimorum (OO) theory of the author is used for the solving of these both enlarged variational problems. The inviscid GO shape of the FC is used only in the first step of iteration and the own developed hybrid solutions for the compressible Navier- Stokes partial-differential equations (PDEs) are used for the determination of the friction drag coefficient and up the second step of iteration of OO theory.

A Note on the Valuation of Collective Goods: Overlooked Input Market Free Riding for Non-Individually Incrementable Goods

Abstract For at least fifty years economists have argued that vertically-aggregated marginal willingness to pay, when set equal to marginal provision cost, will result in optimal public good provision levels. This methodological approach would be expected to yield an exact analog, in terms of optimal levels of public good provision, to efficient provision of private goods in a perfect market setting. There is, however, a potentially serious flaw in the approach as actually practiced, since initial incomes are implicitly–and wrongly–taken to be optimal. From a given income, the output demand revelation problem has long been recognized–that there will be difficulty inferring true demands for public goods at that income (the traditional `free rider' problem). But what has failed to receive widespread recognition among theoreticians, and especially among practitioners, is that there will also be a concomitant `input demand revelation' problem. In any situation where workers cannot individually increment a class of goods by increasing their income (e.g. public goods), they will have no incentive to generate the income that would have been devoted to that class of goods. They will only generate income that is optimal to pay the higher taxes or prices associated with whatever initial public goods levels are provided. As a consequence, the benefit-cost practitioner will, even if somehow able to accurately guess marginal willingness-to-pay out of current income, observe only one apparent optima. There are an infinite number of such optima, one for each level of free riding in input markets, where aggregated marginal willingness-to-pay will appear to equal marginal provision cost. The one true Samuelson `optimum optimorum' occurs when there is free riding in neither output nor input markets (that is, when the `full' demand revelation problem is solved). As a consequence, pure public goods, as well as other `non-incrementable' goods and goods for which non-use values are of importance will be undervalued, hence under-provided. Evidence is presented that the problem raised here might be of importance, undermining the practical significance of the Coase theorem vis-à-vis Pigouvian taxation.

From Inviscid to Viscous Aerodynamical Global Optimal Shape's Design

AbstractThe refinement of the global aerodynamical optimal design (OD) of the shape of a flying configuration (FC) can be performed by improving of the start solutions for the optimization and/or of the optimization strategy itself. The proposed strategy is the own developed iterative optimum–optimorum theory. The study is here focused on the further improvement of her new, original, reinforced, zonal, spectral solutions for the partial–differential equations (PDEs) of the three–dimensional compressible Navier–Stokes layer (NSL), which govern the flow over the FCs, in subsonic and supersonic flow. These NSL's solutions, which are good suited for the computation and, especially, for the global optimal design, use the analytical potential solutions of the flow over the same FC twice: firstly as outer flow, at the NSL's edge (instead of the parallel flow used by Prandtl in his boundary layer theory) and, secondly, the velocity's components are products between the corresponding potential velocities and polynomial expansions with arbitrary coefficients, which are used to satisfy the NSL's PDEs. The use of analytical elliptical potential solutions leads to subsonic and the use of hyperbolical potential solutions leads to supersonic stabilized and rapid convergent NSL's solutions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Optimization of Hydraulic Machinery Bladings by Multilevel CFD Techniques

The numerical design optimization for complex hydraulic machinery bladings requires a high number of design parameters and the use of a precise CFD solver yielding high computational costs. To reduce the CPU time needed, a multilevel CFD method has been developed. First of all, the 3D blade geometry is parametrized by means of a geometric design tool to reduce the number of design parameters. To keep geometric accuracy, a special B-spline modification technique has been developed. On the first optimization level, a quasi-3D Euler code (EQ3D) is applied. To guarantee a sufficiently accurate result, the code is calibrated by a Navier-Stokes recalculation of the initial design and can be recalibrated after a number of optimization steps by another Navier-Stokes computation. After having got a convergent solution, the optimization process is repeated on the second level using a full 3D Euler code yielding a more accurate flow prediction. Finally, a 3D Navier-Stokes code is applied on the third level to search for the optimum optimorum by means of a fine-tuning of the geometrical parameters. To show the potential of the developed optimization system, the runner blading of a water turbine having a specific speednq=411/minwas optimized applying the multilevel approach.

Exploring the Geographic Consequences of Public Policies Using Evolutionary Algorithms

Public policies with geographical consequences are often difficult to analyze because they affect multiple stakeholders with competing objectives. While such problems fall conceptually into the domain of multiobjective evaluation, associated analytical techniques often search for a single optimum solution. Within the context of geographical problems, optimality often means different things to different stakeholders and, thus, an optimum optimorum may not exist. In this article, we present a new technique based on an evolutionary algorithm (EA) that produces a large number of optimal and near-optimal solutions to a large class of land management problems. As implemented for this article, solutions represent landscape patterns that produce services that meet stakeholder needs to varying degrees. The construction of curves that illustrate the trade-offs among various services given limited resources is central to this approach. Decision makers can use these curves to help find solutions that strike a balance among conflicting objectives and, thus, meet stakeholder needs. To provide context to this work we consider the impact of the U.S. Department of Agriculture's (USDA) Conservation Reserve Program on rural landscapes. Three objectives are assumed: (1) maximize farm income, (2) maximize environmental quality, (3) minimize public investment in conservation programs; the first two are viewed as services desired by stakeholders. Analytical and visualization tools are developed to reduce the burden associated with exploring the large number of solutions that are produced by this technique. The results illustrate that the EA-based approach can produce results equal to and significantly more diverse than conventional integer programming techniques.

The viscous optimal shape design, via spectral solutions

The shape of a flying configuration is globally optimized if its camber, twist, thickness and the similarity parameters of its planform are determined in order to obtain a minimum drag at cruising Mach number. The optimum–optimorum (OO) theory of the author solves this problem by using a lower limit hyper-surface for the drag functional. A multipoint design is realized by using movable leading edge flaps. The iterative OO theory is used for the computation of the friction drag, for the determination of the viscosity effect in the optimal shape of the flying configuration and to perform the multidisciplinary design by including structure and thermal auxiliary conditions. A proposal of a fully-optimized shape of supersonic transport aircraft with twin integrated fuselages is also made. Copyright © 1999 John Wiley & Sons, Ltd.

The viscous optimal shape design, via spectral solutions

The shape of a flying configuration is globally optimized if its camber, twist, thickness and the similarity parameters of its planform are determined in order to obtain a minimum drag at cruising Mach number. The optimum–optimorum (OO) theory of the author solves this problem by using a lower limit hyper-surface for the drag functional. A multipoint design is realized by using movable leading edge flaps. The iterative OO theory is used for the computation of the friction drag, for the determination of the viscosity effect in the optimal shape of the flying configuration and to perform the multidisciplinary design by including structure and thermal auxiliary conditions. A proposal of a fully-optimized shape of supersonic transport aircraft with twin integrated fuselages is also made. Copyright © 1999 John Wiley & Sons, Ltd.

Optimal Trajectories for Earth-to-Mars Flight

This paper deals with the optimal transfer of a spacecraft from a low Earth orbit (LEO) to a low Mars orbit (LMO). The transfer problem is formulated via a restricted four-body model in that the spacecraft is considered subject to the gravitational fields of Earth, Mars, and Sun along the entire trajectory. This is done to achieve increased accuracy with respect to the method of patched conics. The optimal transfer problem is solved via the sequential gradient-restoration algorithm employed in conjunction with a variable-stepsize integration technique to overcome numerical difficulties due to large changes in the gravitational field near Earth and near Mars. The optimization criterion is the total characteristic velocity, namely, the sum of the velocity impulses at LEO and LMO. The major parameters are four: velocity impulse at launch, spacecraft vs. Earth phase angle at launch, planetary Mars/Earth phase angle difference at launch, and transfer time. These parameters must be determined so that ΔV is minimized subject to tangential departure from circular velocity at LEO and tangential arrival to circular velocity at LMO. For given LEO and LMO radii, a departure window can be generated by changing the planetary Mars/Earth phase angle difference at launch, hence changing the departure date, and then reoptimizing the transfer. This results in a one-parameter family of suboptimal transfers, characterized by large variations of the spacecraft vs. Earth phase angle at launch, but relatively small variations in transfer time and total characteristic velocity. For given LEO radius, an arrival window can be generated by changing the LMO radius and then recomputing the optimal transfer. This leads to a one-parameter family of optimal transfers, characterized by small variations of launch conditions, transfer time, and total characteristic velocity, a result which has important guidance implications. Among the members of the above one-parameter family, there is an optimum–optimorum trajectory with the smallest characteristic velocity. This occurs when the radius of the Mars orbit is such that the associated period is slightly less than one-half Mars day.

Cooperative and Non-Cooperative Exploitation of the Arcto-Norwegian Cod Stock

A two-agent model for the exploitation of the Arcto-Norwegian cod stock is developed to investigate the economic benefits that can be realized from the resource, and the effect of exploitation on stock sustainability under cooperation and non-cooperation. The two agents are identified in this study as a trawl fishery versus a coastal fishery. Unlike in Munro (1979), where conflicts in the management strategies of agents arise from differences in the perceptions of the discount factor, fishing effort costs, and consumer preferences, here conflicts arise mainly from the differences in fishing gear and grounds, and the age group of cod targeted by the two agents. Using a game theoretic framework, we show that given available data, the optimum optimorum is obtained under cooperation with side payments and no predetermined harvest shares, in which case the coastal fishery buys out the trawl fishery. However, sensitivity analysis shows that if the price premium assumed for mature cod is taken away, the trawl fishery takes over as the producer of the optimum optimorum.

Nontraded Goods, Variable Returns to Scale and Welfare

The implications of variable returns to scale (VRS) for the theory of international trade have been extensively studied by trade theorists. [5; 7; 8; 11; 14] It is, however, notable that no attempt has been made to ascertain the role of VRS in conjunction with nontraded goods. Some of the major trade theorems have been examined by Komiya [12] in an extended Heckscher-Ohlin-Samuelson (H.O.S.) model with a nontraded good. Despite its pioneering contribution, Komiya's analysis is confined to the production side of a small open economy. More recently, Batra [2] has investigated the welfare effects of several trade policies in a nontraded goods model by incorporating the presence of factor market distortions. The purpose of this paper is to explore the welfare implications of a change in the terms of trade and the rate of tariff, as well as the relative effectiveness of some trade policy instruments in the three-commodity (two traded and one nontraded) and two-factor trade model allowing the presence of VRS. The issue is important for two reasons. First, the existence of nontraded goods is an indisputable phenomenon characterizing the real world.' Second, to the extent that VRS have impacts on commercial policy, its implication in the presence of nontraded goods must be thoroughly examined. Several significant results are obtained from this analysis. For example, free trade may turn out to be the first best policy (optimum optimorum) even when returns to scale are divergent among industries. When the industries in an economy operate under identical returns to scale, with constant returns to scale (CRS) as a special case, an improvement in the terms of trade necessarily enhances welfare, but a higher rate of tariff may not result in a lower welfare. Unlike the result derived by Bhagwati [3] from the standard two-commodity (H.O.S.) model with production externalities, a consumption subsidy (tax), rather than a production tax-cum-subsidy, may turn out to be the optimum optimorum in our nontraded good model; this occurs specifically when VRS distortions exist in the nontraded good industry only. Under divergent returns to scale among industries, the output elasticities of

COLLEGE FOOTBALL TELECASTS: WHERE ARE THEY GOING?

Observed Nielsen ratings for college football games show a decreasing trend in the number of viewers in recent years. As the market for these telecasts becomes more competitive, both buyers and sellers should adjust rights fees for quality differences. A model of full income allocation is proposed to isolate pure quality changes from true changes. Using a sample of weekly national collegiate telecasts the optimum optimorum is determined from the set of generalized Box‐Cox forms. Regional data provide an application of the model. Quality and hedonic indexes show not only a deterioration in quality over time but also a downward trend in demand for quality‐adjusted units. Implications for alternative television policies are discussed.

Optimal Product Quality under Asymmetric Information and Moral Hazard

In the use of incentive contracts to compel a supplier to produce a product of optimal quality, the supplier's payoff typically depends on observed product quality. When the observable measure of quality employed in the contract varies also with the buyer's care or maintenance of the product, it becomes impossible to impute the product's performance to two unobservable casual determinants: innate product quality and buyer's care. In this article we characterize and give examples of the types of mechanisms that can be used to obtain the optimum optimorum allocation. In the context of product quality and product liability problems there exist mechanisms that can avoid the moral hazard problem.