The use of iterative linear programming in practical applications of animal diet formulation

Background: Gelatin is a protein obtained by partial hydrolysis of collagen contained in skins, connective tissue and/or animal bones, which are by-products of the meat industry. The main raw material to produce bovine gelatin is the dermis of the skin, but there is a variation in fat and moisture content depending on the bovine skin origin. As a contribution to the circular economy and sustainability, these by-products with high fat content and the fat released from them during the gelatin production process can be managed for food industries, mainly in the development or formulation of animal feed. Methods: For the initial physicochemical characterization, moisture, fat, protein and ashes content were determined. Once the by-products with high fat content were identified, alteration parameters such as acidity, peroxide and saponification indexes were evaluated. Additionally, thermal, rheological and fatty acid composition characterization was carried out in order to study the possible applications of the by-products. Results and Discussion: The results showed that some of the by-products presented fat content values lower than 15.0%, so the viability of their use is limited. On the other hand, some by-products have more than 30% fat content, however, they can only be removed manually, and the efficiency of this process is low. By-products removed from the supernatant in the extractors presented 99.9 and 98.9% of fat, and there is the possibility of conditioning a mechanical method for their extraction. The determination of alteration and oxidation parameters, thermal and rheological characterization, fatty acid profile and solid fat content were carried out only on these by-products. According to the characterization, these by-products could be valued and used in the formulation of animal feed, however, they present some limitations for some applications such as biodiesel production or food industry.

This work presents the solution based on the augmenting sequence of linear programming problems (LPP) as a tool for intellectualizing home environment. The proposed solution empowers the intelligent decision making procedure which can be applied to various intelligent control applications. The augmenting self-training procedure based on LPP approach is presented as well, which allows making reasonable decisions having only limited data about the controlled environment. The method permits retraining the decision making system when new data is available. As a proof of concept, this solution is applied to intelligent light control application. The obtained simulation results show the method’s capability in making reasonable decisions according to users preferences. DOI: http://dx.doi.org/10.5755/j01.itc.44.2.10235

In this paper, a branch and bound approach is proposed for global optimization problem (P) of the sum of generalized polynomial fractional functions under generalized polynomial constraints, which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solving this problem. By utilizing an equivalent problem and some linear underestimating approximations, a linear relaxation programming problem of the equivalent form is obtained. Consequently, the initial non-convex nonlinear problem (P) is reduced to a sequence of linear programming problems through successively refining the feasible region of linear relaxation problem. The proposed algorithm is convergent to the global minimum of the primal problem by means of the solutions to a series of linear programming problems. Numerical results show that the proposed algorithm is feasible and can successfully be used to solve the present problem (P).

This article provides a unified framework for studying the identification of counterfactual parameters in a general class of discrete outcome models, allowing for endogenous regressors and multidimensional latent variables, all without parametric distributional assumptions. Our main theoretical result is that, when the covariates are discrete, the infinite-dimensional latent variable distribution can be replaced with a finite-dimensional version that is equivalent from an identification perspective. The finite-dimensional latent variable distribution is constructed in practice by enumerating regions of the latent variable space with a new and efficient cell enumeration algorithm for hyperplane arrangements. We then show that bounds on a certain class of counterfactual parameters can be computed by solving a sequence of linear programming problems, and show how the researcher can introduce additional assumptions as constraints in the linear programmes. Finally, we apply the method to a mobile phone choice example with heterogeneous choice sets, and to an airline entry game example.

Slaughterhouse Blood (SHB) is a rich source of protein, but it requires a suitable processing before its use as an ingredient in animal feed formulations. In this study, SHB was fermented using whey or pure culture of Lactobacillus acidophilus as the fermentation inoculums. Mixtures of SHB, fermentation inoculums and molasses were incubated at 35°C and microbiological and biochemical changes were determined every day until the end of fermentation. The results revealed that the fermentation of SHB by both the inoculums required 4 days to complete. The harmful microorganisms were removed or reduced to a negligible level after fermentation. Both the fermented products were also aerobically stable. Protein, lipid and essential amino acid contents of SHB were almost completely recovered after fermentation. The L. acidophilus fermented SHB (LFSHB) exhibited a better microbiological quality than the whey fermented SHB (WFSHB), while WFSHB exhibited a higher amount of free amino acid than the LFSHB. The present study concludes that fermentation is an appropriate technique to convert SHB into a nutritionally sound and microbiologically safe ingredient for the use in fish feed formulation. Whey can be used as an easily available and cost effective inoculum to carry out the fermentation.

Feed formulation is important in ensuring the quality of livestock production and sustaining the self-sufficient of the livestock industry in the country. Currently, local farmers have been feeding their lambs with goat pellets and this has caused an imbalance between nutrient feeding in lambs. In this study, a modified linear programming (LP) model is proposed to optimize a specific lamb feed formulation that satisfies the nutrient requirement at a minimum cost. The dietary nutritional requirements for lambs were derived from the standard criteria of the 1985 National Research Council. The modified LP model considers the nutrients needs of lambs according to their weight, the amount of nutrients to be consumed and the cost of each feedstuff. This study focuses on obtaining the optimal amount of feedstuff in the lamb feed that is determined based on the solution of a modified model. The analysis of the resulting price of goat pellets available in the local market was performed. The result shows that the new feed formulation for lamb recorded a price reduction of 53.65% compared to the commercial goat pellet yet fulfils the nutrient requirements for lamb.

Animal feed formulation: Rapid and non-destructive measurement of components from waste by-products

Global optimization of signomial geometric programming using linear relaxation

The problem of finding a point of a linear manifold with a minimal weighted Chebyshev norm is considered. In particular, to such a problem, the Chebyshev approximation is reduced. An algorithm that always produces a unique solution to this problem is presented. The algorithm consists in finding relatively internal points of optimal solutions of a finite sequence of linear programming problems. It is proved that the solution generated by this algorithm is the limit to which the Holder projections of the origin of coordinates onto a linear manifold converge with infinitely increasing power index of the Holder norms using the same weight coefficients as the Chebyshev norm.

In this paper we extend the classical min–max model predictive control framework to a class of uncertain discrete event systems that can be modelled using the operations maximization, minimization, addition and scalar multiplication, and that we call max–min-plus-scaling (MMPS) systems. Provided that the stage cost is an MMPS expression and considering only linear input constraints then the open-loop min–max model predictive control problem for MMPS systems can be transformed into a sequence of linear programming problems. Hence, the min–max model predictive control problem for MMPS systems can be solved efficiently, despite the fact that the system is non-linear. A min–max feedback model predictive control approach using disturbance feedback policies is also presented, which leads to improved performance compared to the open-loop approach.

Generalized bang–bang control for feedforward constrained regulation

This paper proposes an effective separable relaxation algorithm to address the challenges associated with the sum of linear ratios problem (SLRP), which is characterized by a large number of ratios and low-dimensional variables. First, by introducing auxiliary variables and applying equivalent transformations, the equivalent problem (EP) corresponding to the SLRP is derived. Subsequently, using an innovative linearization technique, the relaxation problem (LRP) of the (EP) is formulated, demonstrating separable properties. Within this framework, solving a sequence of linear programming problems is sufficient to obtain a globally optimal solution to the (SLRP), significantly reducing computational effort. Furthermore, the paper provides a rigorous proof of the convergence properties of the proposed algorithm and estimates the maximum number of iterations required. Numerical experiments are conducted to validate the practicality and efficiency of the proposed algorithm.

Achieving energy efficiency to prolong the network lifetime is an important design criterion for wireless sensor networks. In this article, we propose a novel approach that exploits the broadcast nature of the wireless medium for energy conservation in spatially correlated wireless sensor networks. Since wireless transmission is inherently broadcast, when one sensor node transmits, other nodes in its coverage area can receive the transmitted data. When data collected by different sensors are correlated, each sensor can utilize the data it overhears from other sensors to compress its own data and conserve energy in its own transmissions. We apply this idea to a class of cluster-based wireless sensor networks in which each sensing node transmits collected data directly to its cluster head using time division multiple access (TDMA). We formulate the problem in which sensors in each cluster collaborate their transmitting, receiving, and compressing activities to optimize their lifetimes. We show that this lifetime optimization problem can be solved by a sequence of linear programming problems. We also propose a heuristic scheme which has low complexity and achieves near optimal performance. Important characteristics of wireless sensor networks such as node startup cost and packet loss due to transmission errors are also considered. Numerical results show that by exploiting the broadcast nature of the wireless medium, our control schemes achieve significant improvement in the sensors' lifetimes.

Sunflower stands out as a significant oilseed crop, pivotal not only in the production of edible oil and biofuels but also in the formulation of nutritious animal feed. Particularly noteworthy are the diverse opportunities presented by sunflower by-products. From the nutrient-rich sunflower oil cake to the versatile sunflower wax utilized in cosmetics and pharmaceuticals, the potential applications are manifold. Additionally, the burgeoning interest in sunflower-derived biofuels as sustainable alternatives to conventional energy sources highlights the crop's growing importance in modern agriculture. However, to meet the evolving demands sustainably, an in-depth analysis of sunflower cultivation practices and nutrient management strategies for optimal productivity is imperative. This review provides a comprehensive overview of sunflower cultivation techniques, processing methods, and avenues for value addition across various sectors. Renowned for its vibrant flowers and seeds brimming with high-quality oil, sunflower holds a significant economic value. Its oil, rich in beneficial unsaturated fatty acids and essential vitamins, has garnered acclaim for its health benefits, including cholesterol reduction and cardiovascular health promotion. Thriving primarily in warm climates and exhibiting resilience to drought conditions, sunflowers have witnessed a surge in demand for their sprouts, roasted seeds, oil, and even agricultural tourism ventures. With sunflower seeds and oil serving as essential components in integrated production systems, the scope for creating diverse food and non-food products continues to expand. By offering this comprehensive synthesis, this review aims to guide stakeholders towards maximizing the utilization of sunflowers across multiple domains.

Multiple-Objective (Goal) Programming Model for Feed Formulation: An Example for Reducing Nutrient Variation