Simple Optimization Model Research Articles

Biotechnological and economic assessment of the productivity of Chlorella vulgaris IBSS-19 microalgae under different cultivation regimes

The production of microalgae biomass and the management of productivity plays an important role in global biotechnology. This research aimed to study the kinetic characteristics of C. vulgaris growth, conduct an economic analysis of biomass production, and develop a simple optimization model for choosing the optimal cultivation regime. The results showed that the additional CO2 supply increased the specific growth rate of C. vulgaris by 35 % and increased productivity by 47 %. Analysis of the batch growth curve of microalgae revealed potentially effective cultivation cycles, which were two, four, and six days. Economic analysis revealed that the greatest biomass yield can be obtained using a two-day cultivation period. Depending on the biomass yield, the cost of production, net income, and profitability of production were calculated according to the cultivation cycles.

Optimization of the multi-level steam production and supply in industrial parks

Steam is an important medium for energy transmission in industrial parks. For providing steam to multiple users, it is key to determine the optimal number of steam levels in the design of steam system. With the increasing number of steam levels, the energy demand and supply can be better matched but the investment of steam pipeline network increases. In this paper, this trade-off is solved by a two-stage method. In the first step, a mixed-integer nonlinear programming (MINLP) model is established to minimize the total cost of the steam system of the industrial park, while a simple pipeline network optimization model is involved. The optimal scheme of steam production including the number of steam levels can be obtained automatically. In the second step, GeoSteiner algorithm is used for solving Rectilinear Steiner Minimum Tree (RSMT) model to further optimize the pipeline network separately. In a case study, the optimal number of steam levels is 3. The total annual cost (TAC) of the optimal steam system is 11.4%, 5.28%, and 1.43% lower than the schemes with the lowest pipeline network cost (1 level of steam), the best matching between heat supply and heat demand (6 levels of steam), and the largest electricity generation capacity (4 levels of steam), respectively. The sensitivity analysis indicates that the overall heat load required by consumers and the distance between the energy station and consumers can make a difference to the optimal number of steam levels.

Modularity of food-sharing networks minimises the risk for individual and group starvation in hunter-gatherer societies.

It has been argued that hunter-gatherers' food-sharing may have provided the basis for a whole range of social interactions, and hence its study may provide important insight into the evolutionary origin of human sociality. Motivated by this observation, we propose a simple network optimization model inspired by a food-sharing dynamic that can recover some empirical patterns found in social networks. We focus on two of the main food-sharing drivers discussed by the anthropological literature: the reduction of individual starvation risk and the care for the group welfare or egalitarian access to food shares, and show that networks optimizing both criteria may exhibit a community structure of highly-cohesive groups around special agents that we call hunters, those who inject food into the system. These communities appear under conditions of uncertainty and scarcity in the food supply, which suggests their adaptive value in this context. We have additionally obtained that optimal welfare networks resemble social networks found in lab experiments that promote more egalitarian income distribution, and also distinct distributions of reciprocity among hunters and non-hunters, which may be consistent with some empirical reports on how sharing is distributed in waves, first among hunters, and then hunters with their families. These model results are consistent with the view that social networks functionally adaptive for optimal resource use, may have created the environment in which prosocial behaviors evolved. Finally, our model also relies on an original formulation of starvation risk, and it may contribute to a formal framework to proceed in this discussion regarding the principles guiding food-sharing networks.

The hammer and the jab: Are COVID-19 lockdowns and vaccinations complements or substitutes?

The COVID-19 pandemic has devastated lives and economies around the world. Initially a primary response was locking down parts of the economy to reduce social interactions and, hence, the virus’ spread. After vaccines have been developed and produced in sufficient quantity, they can largely replace broad lock downs. This paper explores how lockdown policies should be varied during the year or so gap between when a vaccine is approved and when all who wish have been vaccinated. Are vaccines and lockdowns substitutes during that crucial time, in the sense that lockdowns should be reduced as vaccination rates rise? Or might they be complementary with the prospect of imminent vaccination increasing the value of stricter lockdowns, since hospitalization and death averted then may be permanently prevented, not just delayed? We investigate this question with a simple dynamic optimization model that captures both epidemiological and economic considerations. In this model, increasing the rate of vaccine deployment may increase or reduce the optimal total lockdown intensity and duration, depending on the values of other model parameters. That vaccines and lockdowns can act as either substitutes or complements even in a relatively simple model casts doubt on whether in more complicated models or the real world one should expect them to always be just one or the other. Within our model, for parameter values reflecting conditions in developed countries, the typical finding is to ease lockdown intensity gradually after substantial shares of the population have been vaccinated, but other strategies can be optimal for other parameter values. Reserving vaccines for those who have not yet been infected barely outperforms simpler strategies that ignore prior infection status. For certain parameter combinations, there are instances in which two quite different policies can perform equally well, and sometimes very small increases in vaccine capacity can tip the optimal solution to one that involves much longer and more intense lockdowns.

A Fast CS-Based Reconstruction Model with Total Variation Constraint for MRI Enhancement in K-Space Domain.

Due to the fact that Magnetic Resonance Imaging (MRI) is still a relatively slow imaging modality, its application for dynamic imaging is restricted. The total variation is introduced into the CS-based MRI reconstruction model, and three regularization conditions are adopted to ensure that a high-quality reconstructed image is produced. In this paper, a simple yet fast CS-based optimization model for noisy MRI Enhancement is proposed. The alternative direction multiplier method is chosen to optimize the model, and the k-terms power series is applied in order to derive the LogDet function into the augmented Lagrange form. Following this, an approximation of the feature vector is achieved through the iterative process. The quality of the reconstructed image was much better than that of the CS-based MRI image reconstruction algorithm, as shown by experimental results under different noise conditions. The peak signal-to-noise ratio of the reconstructed image was able to be improved anywhere from 5 to 20 percent.

How can a central bank exit quantitative easing without rapidly shrinking its balance sheet?

An important question for the major central banks of the industrialized world is how to design desirable strategies to exit quantitative easing (QE). At the exit, if a central bank needs to reduce rapidly the liquidity created by its balance sheet expansion, issuing new interest-bearing liabilities would be preferable to rapidly shrinking the balance sheet by selling existing assets, both for the stability of those assets' markets and to be able to keep capital losses from being reflected in the balance sheet under amortized-cost accounting. Given that existing assets accumulated during the quantitative easing period have low interest returns, and new liabilities to be issued in the quantitative tightening period would have high interest payouts, the central bank may run a loss that may threaten its solvency, which may force the bank to expand the monetary base above the level that is consistent with the central bank's ideal price stability path. This study considers a central bank that exits QE by issuing liabilities and examines an optimal exit strategy while maintaining the solvency by constructing a simple dynamic optimization model. The model is then applied to the Bank of Japan and the Federal Reserve to examine their possible exits.

Scheduling management and optimization analysis of intermediate products transfer in a shipyard for cruise ships.

Shipbuilding is a complex and large-scale operation involving many intermediate products (blocks) and the frequent transfer of blocks among workshops and stockyards. The reasonable use of methods to complete the transfer scheduling of intermediate products is of great importance. In this paper, the blocks and the flat transporters are the research objects. Based on organizing the various logistical processes for blocks and the circulation process in the shipyard, we established a model that takes the task time window and other factors as constraints, and minimizes the sum of delay time and no-load time of flat transporters while satisfying the punctuality of scheduling tasks. Three conclusions are reached: (1)The flat transporter utilization rate is inversely related to the value of the objective function. The smaller the value of the objective function, the more the usage rate of a particular one (2) loading is the biggest obstacle to the overall working time of flat transporters, and a simple optimization model cannot solve this problem; and (3) based on the optimization model, the load efficiency of flat transporters can be improved, and the delivery time can be reduced.

Sustainable Supplier Selection in Agri-Food Supply Chain Management

In recent times, sustainability of supply chains becomes the most interested subject by customers, firms, government bodies, academia, and suppliers as the environmental resources reveal as the most valuable and limited asset for human beings. One of the most important elements determining the performance of sustainable agri-food supply chain business is supplier’s commitment. A mainly inspiring feature in this domain is the wide range of factors influencing supplier selection decision-making process in Triple Bottom Line context must be analyzed. However, it is not easy to completely integrate and measure majority of these factors in a simple optimization model. Therefore, this paper starts with a comprehensive review of literature about supplier selection for sustainable supply chains (SSCs) development. Afterwards, a new two-steps hybrid solution method is suggested. In initial step, a set of criteria for supplier selection process is analyzed built on Fuzzy Analytic Network Process (FANP). The result of the first step is fed in to the second step of the analysis to design a model with multiple objectives for selection process of supplier using fuzzy VIKOR. All three dimensions of sustainability; specifically, factors such as weather, water and soil footprint, energy and material consumption, employment, social services and finally financial performance of supply chain are considered concurrently. The suggested approach generates a comprehensive model to help supply chain managers in supplier selection process. Numerical analysis is completed via exploiting data from a Turkish agri-food company case for validating effectiveness, also and success of the proposed solution. Final analytical results of the analysis provide valuable business policy oriented, operational and practical insights on the influence of economic, environmental, and social sustainability for enhanced supplier relationship management module in sustainable supply chain structure. Moreover, by tracking environmental impact indicators such as, emission and pollution rates, footprint rates, against social and cost indicators it would be possible to perform tradeoff analysis for giving more sustainable decisions on new supply chain investments.

Optimal parametric design of delayless subband active noise control system based on genetic algorithm optimization

Active noise control systems are generally application-specific, and an appropriate algorithm with an optimal configuration is desirable in the first stage of active noise control system design and deployment. This study presents a design of the subband active noise control system with optimal parameters for a practical broadband active noise control. Although the delayless subband active noise control has gained wide attention for broadband noise cancellation, an optimal design remains a challenge because of the complex interplay between multiple factors such as spectral leakage, delay and weight stacking distortion subject to a number of configurable parameters, and weight stacking method. The configurable parameters can hardly be optimized independently because the active noise control performance depends on the combined configuration. A simple near black box active noise control algorithm optimization model is thus established by incorporating the genetic algorithm optimization into the parametric design of the delayless subband algorithm. The automated process does not require an understanding of the performance characteristics for different parameters. The significance of applying the automated genetic algorithm optimization to the complex multiparameter nonlinear active noise control design is revealed by numerical simulations, particularly for the multichannel low-frequency broadband active noise control system configured with the delayless subband algorithms. This provides a way for the optimal parametric design of subband active noise control before being used in a practical complex scenario.

A new method for optimizing the topology of hinge‐free and fully decoupled compliant mechanisms with multiple inputs and multiple outputs

AbstractCompliant mechanisms with multiple inputs and multiple outputs have a wide range of applications in precision mechanics, for example, cell manipulations, electronic microscopes, and so on. The movement uncoupling and maximum desired output displacements among these devices all become critical because many inputs and outputs are involved. The topology optimization design of compliant mechanisms, which can solve output coupling and input coupling problems, hinge and gray region problems, and the multiple‐objective optimal problem, is an important topic of researches for achieving fully decoupled motion. It is also a challenge area of research due to serious conflicts of between the four of output and input uncoupling constraints, volume constraint, the hinge‐free requirement, and the good black/white solution requirement. In order to comprehensively solve these problems, a simple optimization model overcoming these serious conflicts is posed, which includes small change rate constraints of structural compliances corresponding to the driving input loads and output point virtual loads. Then, the multiple output displacement functions of the model are equivalently converted into non‐negative functions. The multiple‐objective model is converted into a single‐objective optimization model by using a bound variable. The method of moving asymptotes (MMA) algorithm is adopted to solve it. Several examples are presented to demonstrate the validity of the proposed method.

General Convergence Analysis of Stochastic First-Order Methods for Composite Optimization

In this paper, we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the most well-known classes of objective functions analyzed in the literature: nonsmooth Lipschitz functions and composition of a (potentially) nonsmooth function and a smooth function, with or without strong convexity. Based on the flexibility offered by our optimization model, we consider several variants of stochastic first-order methods, such as the stochastic proximal gradient and the stochastic proximal point algorithms. Usually, the convergence theory for these methods has been derived for simple stochastic optimization models satisfying restrictive assumptions, and the rates are in general sublinear and hold only for specific decreasing stepsizes. Hence, we analyze the convergence rates of stochastic first-order methods with constant or variable stepsize under general assumptions covering a large class of objective functions. For constant stepsize, we show that these methods can achieve linear convergence rate up to a constant proportional to the stepsize and under some strong stochastic bounded gradient condition even pure linear convergence. Moreover, when a variable stepsize is chosen we derive sublinear convergence rates for these stochastic first-order methods. Finally, the stochastic gradient mapping and the Moreau smoothing mapping introduced in the present paper lead to simple and intuitive proofs.

Benefit Assessment of Skidder Powertrain Hybridization Utilizing a Novel Cascade Optimization Algorithm

Over the last decade, off-road vehicles have been increasingly hybridized through powertrain electrification in terms of additional electrical machine-based propulsion and battery energy storage, with the goal of achieving significant gains in fuel economy and reductions in greenhouse gases emissions. Since hybrid powertrains consist of two or more different energy sources and may be arranged in many different configurations, there are many open questions in their design and powertrain energy management control, which may have influence on the hybridized powertrain purchase cost and efficiency. This paper presents simple backward optimization models of conventional and hybrid cable skidder powertrains. These models are then used in the optimization of control variables over one forest path in order to find the minimum possible fuel consumption. The optimization results show that 15% fuel efficiency improvement in winching and skid trail driving can be achieved with the selected hybrid powertrain. With that improvement, main hybrid drive components can be paid off in 13 years.

Occupational Variation in Quantity–Quality Trade-off in a Brawn-Based Economy

The paper revisits the theory of the quantity–quality trade-off and demonstrates that the relationship between quantity and health of children is subject to occupational variation in physical energy requirements. It embeds, in a simple household optimisation model, a minimum consumption requirement that rises with physical work intensity of occupation. Occupational differences in minimum consumption requirement generates variation in child nutritional status – the shadow price of quantity, which in turn generates varying quantity–quality relationships. The model yields an equilibrium relationship between the number and nutritional status of children that is positive for households in strenuous occupations and ambiguous for other households. A numerical example using a calibrated model illustrates that these trade-offs are consistent with the phenomenon of intergenerational persistence of nutritional status. These new insights into the nature of the quantity-quality trade-off help reconcile some inconsistent empirical findings on such trade-offs.

Seasonal strategies in the world’s oceans

Throughout much of the world’s oceans, life is organized around seasonal cycles of feast and famine. Here we seek to understand the life-history strategies by which marine organisms contend with seasonal variations through a range of adaptations and traits, including overwintering stages, dormancy, investment in reserves, and migration. Our perspective is broad, spanning across marine food webs, from unicellular plankton to whales, and covering all latitudes, from the equator to the poles. The analysis is organized around a simple mechanistic life history optimization model. The model generates several general hypotheses: (i) small organisms should cope with winters by making resting stages or by dormancy; (ii) medium-sized organisms should build reserves and perform seasonal vertical migration to reduce predation; (iii) large organisms should primarily employ latitudinal migrations to follow seasonal peaks in production. Subsequently, these hypotheses are tested against a large assemblage of observations and data reported in the literature. Body size, trophic level, and the intensity and duration of seasonal highs and lows appear to be closely related to seasonal strategies. Some, but not all of these hypotheses are borne out by our analysis of data. In particular, we find that organisms with a lifespan on the order of the seasonal length employ a multitude of strategies.

Economies of Scope for Electricity Storage and Variable Renewables

In this paper, we investigate whether and under which conditions jointly owning a variable renewable source of electricity (VRES) and an electricity storage generates economies of scope in competitive electricity markets. Using a simple stochastic optimization model that assumes frictionless markets, we analytically show that no economic benefit arises from combining the two assets. This finding is in contradiction to large parts of the literature, which claim that it is in the economic interest of owners of VRES to additionally own electricity storage. We also identify circumstances where our argument does not hold and the combination of storage and VRES could theoretically make economic sense on the level of individual agents. In the last part of the paper, we demonstrate in a numerical case study of the German market that even in cases where our theoretical results do not hold, tying together storage and VRES may produce suboptimal results.

Monetary Base Controllability after an Exit from Quantitative Easing

Abstract This study examines the problem that a central bank may face after exiting a monetary quantitative easing policy. It develops a simple dynamic optimization model of a central bank, which finds that if the bank needs to absorb a substantial amount of excess reserves when exiting, the monetary base may become uncontrollable. In this case, the bank has no option but to increase the monetary base by more than the target amount, which leads to an undesirable money supply expansion and, ultimately, to inflation pressures. The model shows the condition when a central bank faces such a challenging situation.

Reaching Consensus Based on the Opinion Dynamics in Social Networks

This paper studies the minimum consensus cost strategy in the whole group decision-making (GDM) process under the condition of experts’ opinion and weight evolving over time. Based on the traditional minimum cost consensus model (MCCM), the updated algorithm of opinion dynamics is introduced to obtain the expert’s opinion value and weight, which is used for the optimal strategy of group consensus decision making. In the existing MCCM, the consensus mechanism is established through a simple optimization model, in which each expert’s opinion value and weight coefficient are in a static state and do not change dynamically with time. However, in actual GDM, the expert’s opinion and their own importance (weight coefficient) are random and easily affected by the decision-making environment. Therefore, this paper proposes three novel kinds of MCCMs based on opinion dynamics in social networks. Numerical results show that this method can reach a higher degree of consensus in a reasonable time compared with traditional consensus model. In addition, some comparative experimental data also show that compared with some static consensus, the optimal decision strategy proposed can greatly reduce the cost. In particular, the MCCM model with confidence parameter reduces the consensus cost to the lowest and obtains the highest degree of consensus.

Adaptive Deep Cascade Broad Learning System and Its Application in Image Denoising

This article proposes a novel regularization deep cascade broad learning system (DCBLS) architecture, which includes one cascaded feature mapping nodes layer and one cascaded enhancement nodes layer. Then, the transformation feature representation is easily obtained by incorporating the enhancement nodes and the feature mapping nodes. Once such a representation is established, a final output layer is constructed by implementing a simple convex optimization model. Furthermore, a parallelization framework on the new method is designed to make it compatible with large-scale data. Simultaneously, an adaptive regularization parameter criterion is adopted under some conditions. Moreover, the stability and error estimate of this method are discussed and proved mathematically. The proposed method could extract sufficient available information from the raw data compared with the standard broad learning system and could achieve compellent successes in image denoising. The experiments results on benchmark datasets, including natural images as well as hyperspectral images, verify the effectiveness and superiority of the proposed method in comparison with the state-of-the-art approaches for image denoising.

Dual Approach to the Harmonized Model between Inventory Reduction and Heijunka (Production Leveling) based on the Minimum Average-energy Principle

A major issue in manufacturing is the balance between inventory reduction and heijunka (i.e., production leveling). To address this issue in aggregate production planning, linear programming models that consider many factors and use “exponential smoothing” as an approximate leveling method have been mainly studied. However, this methodology has problems that may limit its use as an optimal solution approximate method, and impair the timeliness required for aggregate production planning by the complexity of these models. To solve this issue, we have been developing harmonized models to balance between lowering the inventory management energy and increasing the heijunka entropy, based on demand and inventory quantities as simple optimization models. In this study, we develop a dual approach to the previously proposed model to maximize the heijunka entropy and propose a new model to minimize the inventory management energy based on the “minimum average-energy principle.” We show that the proposed model’s inventory state is lower than that of traditional exponential smoothing through numerical experiments. This study, therefore, theoretically enables a new optimal solution to the harmonized (balancing) problem, based on the concept of entropy and energy, and practically enables aggregate production planning in a timely and simple manner.

Occupational variation in the relationship between child health and family size.

Empirical evidence for quantity-quality trade-off is hardly ubiquitous, especially when quality is measured by child health outcomes. The paper offers a new explanation to this puzzle. It shows that the quantity-quality relationships are subject to occupational variation when quality is given by nutritional status, and occupations differ in their physical labor intensity. It embeds, in a simple household optimization model, a minimum consumption requirement that rises with physical work intensity of occupation. The occupational differences in subsistence consumption requirement generate variation in child nutritional status, and hence, in the shadow price of children. The nature of the quantity-quality relationship, therefore, varies with work intensity of occupations. The model yields an equilibrium relationship between the number and nutritional status of children that is positive for households in strenuous occupations and ambiguous for other households. These results help reconcile some inconsistent findings on quantity-quality trade-off, which may partly be explained by the omission of occupational variation in nutritional status.