Diet optimization -
The work of Maillot et al. Finally, LP with cost constraints has been applied to specific dietary requirements. Raffensperger 58 used LP to study the lowest available cost of a low-carbohydrate diet in New Zealand. Introducing constraints for carbohydrate and fat, resulted in a big, non-linear increase of cost.
LP demonstrated to be an applicable tool to rigorously convert precise nutrient constraints into food combinations. Of the 20 studies with economic constraints, 3 used the Thrifty Food Plan as an example. Forty years ago, the USDA developed the TFP to solve the problem of selecting a healthy diet for low-income groups.
This dietary optimization program composed diets that fits within the constraints, using the 4, most popular foods. Since , the TFP has been the most successful program providing healthful and minimal-cost meal plans and market baskets for consumers with a limited budget: more than 28 million.
The TFP was updated in , , and The researchers used 15 nutritional constraints essential nutrients with official RDAs. In , Lino et al. In contrast with other studies, it was possible to increase the healthy components without changing the budget USDA met simultaneously food group constraints, a cost constraint, and other constraints The revision of the market baskets could meet food intake recommendations of the MyPyramid Food Guidance System e.
However, none of the market baskets was able to meet the sodium guideline, so sodium was limited for each age-gender group Wilde and Llobrera evaluated the TFP framework using constraints on food groups e. This stepwise approach is also applicable for other constraints and recently applied by Kramer et al.
The next step in the application of LP was the introduction of ecological constraints. Several studies—for instance in UK, and New Zealand—have successfully applied LP to optimize diets 4 , 19 , 33 , 38 , 39 , 44 , 46 , 47 , This section gives an overview of the 12 studies which have applied ecological constraints to 14 diets between and 13 , 16 — The studies are summarized in Table 1.
Macdiarmid et al. were the first to use greenhouse gas emissions GHGEs as constraint. Their study suggested that future work would need to integrate wider issues of sustainability into the modeling process and develop broader dietary advice In the same period, Vieux et al.
The studies of Macdiarmid et al. The study by Van Dooren 20 included most consumed Dutch food products, which is more realistic. It looked not only at GHGEs as an environmental parameter, but also at land use, energy use and ReCiPe score, which combines the three other parameters in an overall ecological pressure score.
Later, Vieux et al. He did not use LP, but looked for associations between GHGEs and nutritional quality This method was also applied by WWF to program the national diets of France, Spain, and Sweden, using local available datasets and nutritional constraints 18 , The same kind of modeling was applied in a New Zealand study Diets were first modeled without acceptability constraints.
Then they applied diets with popular foods consumed by the population, with realistic amounts as constraints. They also applied constraints for food costs, energy intake, macronutrients, and micronutrients 9 — 11 , 15 , 17 , 20 , 26 — 36 , 38 — 40 from national dietary recommended intakes.
But this diet was without acceptability constraints see section The Need for Acceptability Constraints The New Zealand study demonstrated similar reductions in GHGEs The cost to the consumer did not increase.
The modeled diets in France, Spain, and Sweden demonstrated similar results The New Zealand study optimized 16 diets for nutritional adequacy, cost, and GHGEs The latter study was of limited practical value, because the diets only include 14 to 19 foods, and drinks were not considered.
The two studies of Van Dooren 20 , 26 are more extensive, because they used 33 nutrients instead of 16 17 or 18 In conclusion, LP makes it possible to propose diets with lower impacts than diet scenario studies. Based on nutrition recommendations, Donati et al. Finally, the Sustainable Diet was recognized to reach simultaneously environmental and cost constraints.
Donati et al. used food items, but only 9 nutritional constraints The added value of the study is the use of multiple environmental parameters and new acceptability constraints. They created a new constraint modeling the connection between matching food groups biscuits as a complement with coffee or tea.
For instance, it is not usual to eat both beef and fish. Despite these acceptability constraints, the volume of the diets almost doubled. Nelson et al. Some LP studies added evidence. The New Zealand study was the first study applying three types of constraints: nutritional, economic and ecological GHGEs.
The result was a monotonous diet containing 10 to 19 foods selected from a database of 76 foods This study showed that the more food products and the higher the acceptability, the more expensive the diet was.
Van Dooren et al. In contrast, adding environmental constraints decreased costs In the second step of Van Dooren et al. This may be due to differences in price levels, or differences in dietary patterns between the two countries.
The optimized French diets are monotonous and are expected to have a low social acceptability. Though, these cheaper diets consist of low quantities of fruits and vegetables.
For example, Jalava et al. They used QP to calculate stepwise the changes in diet gradually limit the percentage of animal protein to 50, 25, Although QP is an optimization method 14 , the goal was to find a diet that encounter the dietary guidelines per scenario with the lowest number of changes in the menu retaining the typical diet for each country.
The four applied scenarios resulted in reductions for the blue water footprint of 4, 6, 9, and The original diet was assigned as the optimization objective. QP resulted in estimated cost for any scenario.
Therefore, the result was close to the traditional, culturally acceptable diet and fulfilled the nutritional constraints QP has advantages over LP when the goal is to find small changes on population level.
The number of nutritional constraints vary from 5 to 37, which could have a major impact on the results of the studies: the lesser the number of constraints, the higher the risk of inadequacy of nutrient intake of the nutrients not considered.
Even with a high number of nutritional constraints, bioavailability of nutrients e. This could partly be solved by adding constraints on certain food groups rich in phytochemicals, e. Evaluating the limited number of studies using LP on diets, we conclude that the studies of Wilson et al.
Future LP diet studies should combine all three of these constraints. The most important challenge to improve future LP diet studies with ecological constraints, is to build bigger databases with more foods and more environmental data, with improved quality and consistency of the data.
Although the papers cited above 33 , 66 observed substantial reductions in GHGEs, it is striking that they found much higher emission levels—in absolute terms—than the Dutch study The found emission of 1.
On the other hand, one of Wilson et al. These differences may be explained by different methods used to calculate GHGEs per product or variances in food cultures and preferences.
Table 2 makes it clear that the studies differ in number of food items 13—; an indication of the completeness of diets , the size of the population, the number of nutritional constraints 5—33; an indication of the nutritional quality of the diets , the selected economic and ecological constraints, and the solutions to make the outcomes culturally acceptable.
One of the attempts to make outcomes culturally acceptable, is the introduction of acceptability constraints. Six studies demonstrated good examples of those constraints. From the first studies of Dantzig to date, researchers have struggled with the unrealistic outcomes of LP solutions. It was expected that adding acceptability constraints could help to prevent this.
A good example is Maillot et al. For any given food, upper limit on the quantity was defined by the 95th percentile of consumer intake. The vitamin D constraint was the most difficult to fulfill, followed by sodium, magnesium, and saturated fatty acids. However, the use of cultural acceptability constraints limits finding solutions.
In Parlesak et al. collected average prices for foods available within Copenhagen, Denmark. They calculated five different cost-minimized food baskets for a family of four. The food baskets that met food based dietary guidelines was twice the price.
Introducing cultural acceptability constraints increased the cost three times. So, variety in the diet and cultural acceptability has a price Thompson et al.
They also put an upper bound on most foods and removed foods with smaller amounts in the diet, as well as less healthy options such as full-fat milk. They applied lower bounds of consumption, particularly on popular foods.
For example, bread, potatoes and pasta have comparable GHGEs and prices, but the model will try to optimize one of the products for cultural reasons: for instance, consumption of potatoes was limited in Spain and pasta in Sweden Other examples of the improvement of LP methodology were demonstrated in literature by using more nutritional constraints 47 and selecting most frequently consumed foods 4 , improved LP models by using a goal function to maximize most frequently consumed foods, without replacing more than five products from the current diet 4.
For example, in the men's diet 50 of the 83 products were kept unchanged in number of calculated portions, and in the women's 55 of the 73 products. The Optimeal tool calculated a change in portions for 8 foods for men and 7 for women. Finally, 9 new food items were added to the men's diet and 8 to the women's unsalted peanuts, pear, kale, sauerkraut, lentils, marrowfats, soy drink, mackerel, and mussels.
Nevertheless, the diet was almost vegetarian, with less portions of meat and dairy. Likewise, new products such as soy drink, marrowfats and lentils were added to the diet, which are not consumed by the majority of the Dutch population A reality check is needed to determine if this would be acceptable for consumers.
Tyszler et al. The metric for changes was measured by a penalty score based on the popularity of foods. The reasoning behind this modeling is that diets which are like the current one is more likely to be accepted by most of the population than more extreme diets.
The figure indicates that, if the goal of the optimization is a diet with lower environmental load Vegetarian or Vegan are not the only options. There are many other solutions to this diet problem with a smaller number of adaptations in the diet Figure 3. Example of the application of acceptability constraints and the effects on the environmental impact of different diet scenarios M, males; F, females.
The lower the penalty score is, the closer the diet is to the current diet and the more acceptable Although the Diet Problem has a long history, most diet solutions are from or later, as computers with larger calculation capacity became widely available and LP tools were developed.
The literature shows that LP can be applied to a variety of diet problems: from food aid, national food programs, dietary guidelines, to individual solutions. In supporting dietary guidelines, LP has proven its value in many ways.
Most studies have used nutritional constraints combined with cost constraints. However, even when the number of constraints is increased, LP is not always able to find solutions.
Nutritional constraints should reflect at least the national dietary guidelines. In defining affordable diets and investigating the relationship between cost and health, LP studies provided insightful contradictions.
LP shows that cheaper and healthier foods can be found easily, but when price becomes a constraint, often a shift occurs to unusual food unless the right constraints are chosen.
LP can produce solutions that are not realistic for the population, especially when cultural acceptability is not considered. Introducing acceptability constraints is recommended, but none of the studies provide the ultimate solution for calculating acceptability.
LP can play a role in the future developments on acceptance of changes and personalized food. Table 2 demonstrated that the analyzed studies are not always clear about the choice of their programming tool and objective function. Arnould et al. It should be expected that the methods are clearly described.
The older software tools Rglpk package, R stat software and Solver in Excel are still in use and seem to function well, but because of the complexity of the diet problem, more sophisticated and tailor-made tools are built for specific application Optimeal and Cost of the Diet-tool.
Further development is needed to implement acceptability constraints. Quadratic Programming has many advantages over LP when you want small changes on population level.
QP differs from LP in that the functions are not linear but quadratic. An inherent limitation of LP is that it limits the amount of changes, while sometimes a wider range of small changes in products can give more useful solutions, e.
QP have this advantage above LP. LP also demonstrated to be an applicable tool to conscientiously convert predefined nutrient constraints into diets with unpredictable food combinations.
Only 12 studies applied and introduced ecological constraints and of these, only two also included cost constraints. These studies showed that the environmental impacts of diets can be halved, staying within the existing nutritional constraints.
LP makes it possible to propose diets with lower impacts than diet scenario studies. In other words, LP is an important tool for environmental optimization and has a lot of potential.
Important is consistency in methodology to derive environmental figures full scope and completeness of constraints. Future possibilities lie in finding LP solutions for diets by combining nutritional, cost, ecological, and acceptability constraints.
LP is clearly a very helpful instrument for finding solutions to a variety of very complex diet problems. The author confirms being the sole contributor of this work and approved it for publication. The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Lastly, Excel Solver was utilized to produce the linear programming model. Before running the program, the details of each macronutrient and micronutrient of food items, price per serving size, were filled in Microsoft Excel. The next step was setting up the constraints in the model such as upper bound UL and lower bound LB for energy, macronutrients and micronutrients.
From the suggested foods portion, a daily balanced menu was later planned The optimization model will be repeated several times to produce two more suggested palatable menus with the lowest possible costs.
Cancer prevention diet models with the lowest cost were planned. The formulation for Linear Programming is as follows:. The portion size of food item j is represented as x j ; a ij denotes the amount of nutrient i in one portion of food item j ; c j was the cost of a portion of food item j ; b i denotes the largest or smallest acceptable quantity of nutrient i.
In this study, the cost of food items z is the objective function that we want to minimize. The ideal energy of the subject was calculated using the Mifflin St-jeor Formula [ 22 ]. Choosing food items from the dietary recall of the subjects and avoiding the repetition or large portions of certain foods were also considered to ensure the palatability of the menu.
Anthropometric measurements were taken from the subjects. After the weight and height of the subjects were obtained, Body Mass Index BMI was calculated for each subject. All the macronutrients average intake of the subjects was met as shown in Table 1.
Fiber intake was only 7. In addition, the average intake of unprocessed grains and legumes were also below the recommendation 0. Malaysian Adult Nutrition Survey MANS [ 25 ] revealed that Malaysian adults on average do not consume sufficient fruits and vegetable in terms of frequency and amount, therefore does not achieve the recommended intake of fibers and other micronutrients.
In this study, no subject met the requirement for iron and folic acid. Other micronutrients intakes such as calcium, vitamin B3, B12, vitamin C, vitamin E, vitamins K were also poor. Similarly, the MANS [ 25 ] also reported that the intake of micronutrients in relation to RNI could be described as low particularly for calcium and vitamin C intake.
Healthy Eating Index for Malaysians showed that only a small percentage of Malaysian met dietary requirements and found that majority of the respondents As for zinc, selenium and phosphorous, all subjects achieved the recommended requirements set by the RNI However, the intake of processed food and salt was higher than the recommended amount.
Red meat consumption is associated with the formation of N-nitroso compounds. This increases the level of nitrogenous residues in the colon and is associated with the formation of DNA adducts in colon cells. High intake of red meat may result in more absorption of haem iron, greater oxidative stress and potential for DNA damage.
Beside, red meat is high in animal fat and is energy dense food. All these factors contribute for considering red and processed meat as a cause of colorectal cancer [ 27 ]. Linear programming has been used to formulate nutritionally optimal dietary patterns, to examine the relationship between diet cost and diet quality in Western countries and to develop food-based dietary guidelines in developing countries where residents need to achieve nutritional requirement with their limited income of diet [ 28 ].
Similarly, a Malaysian study done by Rajikan et al. developed a healthy and palatable diet for low income women at the minimum cost based on Malaysian Dietary Guidelines and Recommended Nutrient Intake via linear programming [ 29 ]. Optimization models provide an elegant mathematical solution that can help to determine that a set of dietary guidelines is achieved by Malaysian population subgroups.
There were three models produced by linear programming. The palatability factor was also considered by including servings from vegetable oil and palm oil. Looking at the three LP models as shown in Table 2 , iron, potassium and calcium only reached the lower limit of the constraint values.
However, other nutrients such as carbohydrate CHO , fat, vitamin A and fiber reached the upper limit of the maximum acceptable value of constraints.
The food list selected comprised mainly on fruits and vegetables with the highest serving, as complex mixture of phytochemicals present in whole vegetables and fruits may have additive and synergistic effects responsible for anti-cancer activities [ 6 ].
From the suggested food list of the models, it is understood that each model consisted of at least two servings of whole and unprocessed grains such as brown rice, oat, lentils, and whole meal bread, thus ensuring high fiber and nutrient contents.
The food list for each model also provides at least two servings of fruits and more than nine servings of vegetables, although it resulted in slight variation of the existing diets.
The production of every menu is different from another as it follows the list of food ingredients selected according to the LP models. For each model, every list of ingredients included in the model will have a slight difference by removing food items that have been selected in the previous menus or placing limits on the same food from a model to the next model so that quantities are different or not selected by the next model.
Therefore, the price is expected to increase from menu 1 to menu 3 as the models have stricter requirement and the cheapest nutritionally dense foods have been chosen in the previous model.
These foods are high in antioxidants carotenoids, beta-carotene, lycopene and Allium such as, pink sweet potatoes, papaya, tomato, onions, garlic, mango, carrots and fiber, which are low in energy density, and so, promote healthy weight.
In addition, we can observe that the menu also emphasizes on the intake of cruciferous vegetables, such as broccoli, mustard leaves, cabbage and cauliflower which are associated with the reduction in the risk of several types of cancer [ 30 ]. The traditional food tempeh, which is rich in phytoestrogens, is also included in the menu as seen in menu 3, as it is found to exhibit a plethora of different anti-cancer effects, including inhibiting proliferation [ 31 ].
Developing cancer prevention diet requires little modification from the existing diet mainly by increasing the vegetables and fruit serving. Studies showed that salt and salt-preserved foods are probably a cause of stomach cancer [ 32 ]. The other alternatives are to use natural flavoring to replace salt are turmeric, onions, garlic, chili and mustard leaves that contain lower sodium content.
The menu also restricted the use of added sugar and the intake of sugary drinks, except for sugar that is naturally found in fruits and vegetables. Instead, healthy high antioxidant drinks were suggested such as carrot and orange juice.
Furthermore, it is evident that the diet models do not include any processed meat, fast food, or sugary drinks; where lean proteins were the only protein source. Looking at the fat content in the three models, we can see that it emphasizes on less saturated fats and trans-fat by reducing the consumption of fat, which is mainly achieved by appropriate cooking methods.
Based on the menu that has been set up, almost all models use a minimal of 3 tablespoons of oil. Therefore, the menu is provided with many ways of cooking such as steaming, baking or grilling.
In a study conducted by Asmaa et al. However, there were few limitations in this study. The subjects in this study may have not been representative because they were not randomly sampled from the general Malaysian population, rather, they were only limited to a local university staff and students.
A larger number of subjects were from different economic and social background and thus more lists of food items should be included in the model to increase the variety of food choices in future studies. In general, the use of linear programming is a very effective tool in producing a balanced diet and can easily interpret dietary recommendations into a nutritional model that is based on local market prices.
It formulated the current guidelines for cancer prevention by creating a balanced and optimal diet for cancer prevention at minimum cost with more specific details and accuracy. In addition, because this research focuses on the specific nutrients needed at minimal cost, the menus produced are ideal for people who want to maintain healthy eating habits but experience financial difficulties.
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Linear Programming Deit Diet optimization used in this paper optimizaiton find minimum Cauliflower and pineapple fried rice and quantity of food items for selection of proper diet Diett sufficient nutrition elements over a week Diet optimization three Kptimization age groups. For optimixation purpose, first a linear programming optimization o;timization Diet optimization selected and Diett three data optimizatjon defining the various food items with their corresponding cost and nutrition elements appropriate to three distinct age groups are constructed. Finally, the model files and the data files are solved to obtain output cost and amount of food items to be purchased. The optimal solution demonstrates distinct cost and amount of food for different age groups. It also shows different level of complexity while obtaining objective values for different age groups. Optimization ModelDiet SelectionDiet CostOptimal SolutionObjective Value. A mathematical optimization model is a decision tool to quantitatively express a problem and find the optimal solution for best interest.Diet optimization -
The variables for milk and bread are both at their upper bounds and have negative dual variable values, while the variable for corn is between its lower and upper bounds and has a zero dual variable value.
A simple interpretation of this information is that the cost of the menu could be decreased if the upper bounds on the number of servings of milk and bread were increased. The cost of the menu would not change in response to an increase in the upper bound on the number of servings of corn.
Consider now the two nutrient constraints on vitamin A and calories. The level of vitamin A in the original solution is , which is between its minimum and maximum allowable levels, and therefore the corresponding dual variable values for both bounds are zero.
The number of calories in the original solution is , however, which is the minimum required. The corresponding dual variable value for the lower bound on the number of calories is 0.
The GHGE of the observed diet was 4. The Nutri and NutriHealth models were not constrained for GHGE but had nevertheless lower GHGE than the observed diet: 3.
The GHGE of the Nutri-Iron and NutriHealth-Iron diets were 4. The high diet departure score of the Danish plant-rich diet was mainly driven by very large relative changes from the observed diet in a few food sub-groups, i.
All mathematically optimized diets implemented in the present study to obtain climate reduction alone GHGE diet , nutritional adequacy alone Nutri or combined with health-based targets for food amounts NutriHealth and climate reduction NutriHealthGHGE contained less animal-based foods in favor of more plant-based foods compared to the average observed diet among Danes.
In agreement with our findings, a recent review identified a dietary transition toward more plant-based diets as the main finding of 12 studies optimizing the health and sustainability of diets in different countries Although decreased, a moderate amount of animal-based foods remained in the optimized NutriHealthGHGE diet but the types of animal-based foods were redistributed toward less beef and cheese, in particular, in favor of eggs, milk, and moderately more fish.
In addition, in the NutriHealthGHGE diet we observed a shift in the dietary energy contribution away from animal-based foods and discretionary energy i. The Danish plant-rich diet prompts a similar dietary shift 16 , and an increase in grains and starches has also been observed in the majority of previous optimizations studies In a recent review, Poutanen et al.
highlight the importance of grains as a source of environmentally sustainable and healthy plant proteins that could play an important role in the transition to healthy diets from sustainable food systems These results indicate that with a starting point in the observed Danish diet, focusing on nutritional adequacy and health alone will result in lower GHGE.
The synergistic benefits to diet quality and GHGE were mainly driven by a decrease in high-fat animal-based foods cheese, butter, and other high-fat dairy products , which catered to lowering the content of saturated fat and simultaneously resulted in lower GHGE.
In the NutriHealth and NutriHealth-Iron diets, the health-based upper limit on the content of red meat additionally contributed to lower GHGE.
To reduce GHGE in the GHGE-constrained optimized diets, a large reduction in ruminant meat was required, consistent with findings from previous optimization studies in several different countries 15 , 21 , 28 , 38 , 40 — The GHGE model, while meeting the GHGE target of 3.
Therefore, when the observed diet is the starting point, focusing on lowering GHGE alone will not result in a healthy or nutritionally adequate diet, indicating the importance of taking nutrition into consideration when deriving low-GHGE diets. In general, mathematical optimization models are sensitive to the local conditions food culture, nutrient intake, environmental footprints etc.
and assumptions made in different methodological choices discussed further in section 4. This makes comparisons across studies difficult but also highlights the importance of studying nation-specific settings to create relevant dietary models and recommendations.
estimated for the Danish plant-rich diet, which lays the foundation for the healthy and sustainable FBDGs in Denmark A transition from the current Danish diet to the plant-rich diet requires substantial changes in some foods i. Therefore, in this study, we optimized the diet to minimize the deviation from the current diet, in an attempt to improve diet acceptability and provide an alternative healthy and sustainable diet.
In comparison to the Danish plant-rich diet, the mathematically optimized NutriHealthGHGE contains more meat especially pork and animal-based foods overall including eggs and milk.
To attain the same GHGE reduction, the NutriHealthGHGE diet requires relatively larger decreases in certain high-GHGE foods cheese, ruminant meat, and high-GHGE fish and discretionary beverages alcoholic beverages and soft drinks compared to the plant-rich diet.
While the mathematically optimized diet outperforms the plant-rich diet in terms of similarity with the observed diet as indicated by a lower diet departure score , the aforementioned differences between the two low-GHGE diets may have different acceptability among different individuals. In accordance with the constraints applied in the optimization, the contents of all nutrients in the NutriHealthGHGE diet were consistent with recommendations and planning goals from NNR, except for sodium and vitamin D.
A large part of this reduction could be achieved through decreased use of discretionary salt, but focus on food reformulation strategies to, e.
Due to our decision to use the AR for premenopausal women as the constraint limit for iron, rather than the RI, there is a proportion of women whose iron requirements are not met with the NutriHealthGHGE diet. This high-iron diet requires larger changes from the observed diet and may therefore have poorer acceptability as a recommended diet.
These kinds of trade-offs between acceptability, nutritional adequacy, and environmental sustainability are important to consider in the planning of diets for the formulation of generalized FBDGs for a population. For example, to what extent the nutritional needs of a specific part of the population should determine the recommendations for the entire population, possibly at the expense of wider diet acceptability, and furthermore, to what extent the absolute healthiness and maximal acceptability of the diet should be ensured at the expense of potential further improvements to environmental sustainability.
For individuals with higher requirements of iron and other nutrients , other strategies to increase the intake and absorption may be considered instead, e. Difficulties in fulfilling iron recommendations are common in diet optimization studies. To address the problem, some have similarly to us used the AR instead of RI 48 , accepted a below-recommended amount of iron in the optimized diet 43 , 49 , or allowed the increase of single high-iron foods e.
Other critical micronutrients that determined the outcome of the optimization were calcium and selenium, indicating that these nutrients require special attention when deriving lower-GHGE diets.
In previous studies in high income-countries, critical nutrients in diets with lower environmental impact include in addition to the aforementioned nutrients for example α-linoleic acid, retinol, fiber, saturated fatty acids, thiamin, and zinc 40 , As the health dimension of diets encompasses more than just nutrient adequacy, a strength of the present study is our comprehensive approach to the healthiness of the diet by inclusion of both nutritional adequacy and epidemiology-based targets for food groups.
In addition, through the stepwise addition of constraints in the four optimization models, we can observe the impact of different constraints on the resulting diet and observe trade-offs and synergies between different diet dimensions.
An additional strength is that we consider diet acceptability by minimizing the departure from the observed diet while fulfilling criteria for health and lowered GHGE. This type of approach tends to produce more realistic results than approaches that directly minimize the environmental impact of a diet Despite this, acceptability is not guaranteed.
A major challenge of diet optimization is the choice of relevant criteria for diet acceptability, as highlighted by Perignon and Darmon in a recent review article The choice of model relies on assumptions of what is thought to be the most acceptable diet and the most acceptable dietary changes.
In the present study, the average observed diet of the Danish population is assumed to be the most acceptable diet, from which departure should be minimized. However, this population-based approach fails to account for individual variability in the underlying dietary patterns of the population and differences in the needs and preferences of various consumer groups.
Individual-level optimization is one option to better capture these perspectives and several such studies exist in previous literature 41 , 53 — These optimizations preserve the interdependencies between food groups or items as they are consumed by the individuals in the population and therefore have the potential to create more realistic diets.
However, the possibilities of change are limited within the realm of existing diets, i. While individual-level approaches in general can shed light on the inter-individual variability in food consumption, they are not only computationally heavier, but the results of such optimizations can be difficult to communicate in a simple way because of the multitude of optimization results.
In the formulation of population-targeted generalized FBDGs, where results need to be simplified for communicational purposes, population-based approaches suffice. The optimal choice of modeling approach therefore comes down to the specific purpose of the study.
To derive sustainable and healthy diets that minimize the departure from a reference diet, the majority of previously published studies have applied linear programming 14 , 15 , 40 , 41 , 43 , 44 , 50 , 59 — 62 , but in more recent years, many studies applying quadratic programming have been published 27 — 29 , 37 , 45 , There is no standard way of defining the minimal departure from a reference diet, and the choice of function to quantify the departure greatly impacts the type of behavior favored by the optimization model.
The quadratic objective function was our preferred option because it penalizes large deviations and thereby tends to generate relatively small changes to many foods, which was assumed to result in higher perceived diet acceptability.
Linear objective functions on the other hand or non-linear functions that are transformed and solved linearly , tend to generate changes to fewer foods, but those changes tend to be larger. In the present study, we standardized the objective function across food sub-groups, such that the departure from the observed diet was represented by the relative percentage difference from the observed to the optimized diet.
This is an advantage when different foods and beverages are consumed in widely different quantities as is often the case in whole diet optimization and absolute changes are not comparable across food sub-groups. The limitation of this approach in combination with the quadratic objective function is that foods that are consumed in very small amounts in the observed diet are highly unlikely to be modified markedly by the optimization model, potentially unnecessarily limiting the opportunities of change.
Finding relevant weighting factors to make such improvements remain perspectives for future research. Finally, standardization by division with the baseline amount causes problems for foods that have an intake of zero at the baseline division by zero , and therefore, adding new food items to the optimized diet requires a modified strategy.
As opposed to most previous optimization studies, we used 50 food sub-groups rather than the original food items as decision variables in the optimizations. The reduced number of decision variables reduces the flexibility of the model, i.
In addition, aggregating food items into food sub-groups guarantees a variety in the underlying food items, which is key to a healthy and acceptable diet. Allowing the optimization model enough flexibility without overcomplicating the results is a difficult balance to strike, and in the present study, there is a level of subjectivity in the grouping of foods which might be better handled with statistical methods of clustering foods into groups.
This notion is further enforced by the fact that the optimization is sensitive to the observed amounts of foods in the diet due to the relative term of the objective function; in essence, sensitive to the grouping of foods.
Further investigations into the best way of grouping foods and the sensitivity of the optimizations are warranted. Another important limitation worth mentioning is that only one environmental footprint, namely GHGE, was used to evaluate sustainability of the optimized diet, while the EAT Lancet global reference diet is constructed to respect six different planetary boundaries 3.
Previous research by Gephart et al. Nevertheless, for a more complete evaluation of environmental sustainability, and to avoid so-called burden shifting, other environmental footprints, such as land use, water use, and nitrogen footprints, should be evaluated. For example, Vellinga et al. demonstrated that healthier diets in the Netherlands were associated with lower GHGE but higher blue water footprint, stating that these environmental footprints need to be considered in unison In addition to the health and environmental dimension of sustainability, social, economic, and animal welfare concerns should be addressed to avoid unintended negative consequences of a wider food system transition.
Finally, the quality and uncertainties of both the dietary intake data and the environmental footprint data are limitations that might influence the validity of the results.
GHGE data are highly sensitive to the production systems they represent and quality of the input data both nutritional and environmental may have important implications for the optimization results. The robustness of the results in relation to data uncertainties and possible changes in future production systems need to be further investigated and taken into account in interpretation of the results and in the evaluation of absolute sustainability aspects of diets.
In addition, to suggest dietary changes that are compatible with a sustainable food system, consideration of coproduction of different foods belonging to the same production system e. For example, Kesse-Guyot et al. Lastly, this study is limited by the lack of diet cost as a subject of investigation, as this might be an important factor limiting acceptability, especially in lower income socio-economic groups By applying quadratic programming in four optimization models, this paper demonstrates how a nutritionally adequate, healthy, and low-GHGE diet can be composed for the adult Danish population, while having the least deviation possible from the average observed diet, in an attempt to improve acceptability.
The final optimized diet represents an alternative way of composing a nutritionally adequate and healthy diet that has the same GHGE as the Danish plant-rich diet, which lays the foundation for the FBDGs in Denmark. The presented diet deviated on average less from the observed diet than the Danish plant-rich and may be more acceptable to some individuals, therefore, having the potential to help facilitate, or act as a steppingstone in a transition toward more healthy and sustainable diets in Denmark.
These findings should be interpreted into relevant dietary guidelines and supplemented with targeted public health interventions and policies to guide consumers in shifting dietary habits.
Future research efforts should focus on expanding optimization modeling to include a more holistic perspective of the food system and more complete evaluation of different environmental footprints, and to better take into account the preferences and needs of different consumer groups to improve acceptability of the modeled diets.
Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent for participation was not required for this study in accordance with the national legislation and the institutional requirements.
MN, AL, ET, and AS contributed to conceptualization and design of the research. MN carried out data processing and calculations, performed diet optimizations with assistance from AS, and wrote the first draft of the manuscript. All authors contributed to the article and approved the submitted version.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher. Steffen, W, Richardson, K, Rockström, J, Cornell, SE, Fetzer, I, Bennett, EM, et al.
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Asmaa A, Zzaman W, Tajul A. Effect of superheated steam cooking on fat and fatty acid composition of chicken sausage. Int Food Res J. Download references. The authors would like to thank all of the subjects for their cooperation and support toward this research project.
The authors acknowledged the financial assistance for publication received from the Research University Grant awarded by the Ministry of Health to the National University of Malaysia specifically for the Consortium of B40 Research CB40R under the auspice of B40 Grand Challenges IDE — This article has been published as part of BMC Public Health Volume 19 Supplement 4, Health and Nutritional Issues Among Low Income Population in Malaysia.
Dietetics Programme, Faculty of Health Sciences, Universiti Kebangsaan Malaysia, , Kuala Lumpur, Malaysia. Financial Mathematics Programme, Faculty of Science and Technology, Universiti Sains Islam Malaysia, , Nilai, Negeri Sembilan, Malaysia. You can also search for this author in PubMed Google Scholar.
RR and SME conceived of the presented idea. RA did the data collection, performed the computations, analysed the data and drafted the manuscript. RA and SME verified the analytical methods and supervised the findings of this work. All authors provided critical feedback and helped shape the research, analysis and manuscript.
All authors have read and approved the manuscript. Correspondence to Roslee Rajikan. This study was approved by the Universiti Kebangsaan Malaysia National University of Malaysia Medical Research Ethics Committee UKMREC NN All participants provided written consent. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4. Reprints and permissions. Alaini, R. Diet optimization using linear programming to develop low cost cancer prevention food plan for selected adults in Kuala Lumpur, Malaysia.
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Skip to main content. Search all BMC articles Search. Download PDF. Volume 19 Supplement 4. Abstract Background Poor dietary habits have been identified as one of the cancer risks factors in various epidemiological studies.
Methods Therefore, using linear programming, this study is aimed to develop a healthy and balanced menu with minimal cost in accordance to individual needs that could in return help to prevent cancer.
In this section, we show how to solve a classic problem called the Stigler diet Optimiztion, named Diet optimization economics Nobel laureate George Stigler, who computed an optimiization way to fulfill Dieh nutritional needs Duet Speed up muscle recovery set of foods. Optimizatiob posed this as a mathematical exercisenot as eating recommendations, although the notion of computing optimal nutrition has of come into vogue recently. The set of foods Stigler evaluated was a reflection of the time The nutritional data below is per dollar, not per unit, so the objective is to determine how many dollars to spend on each foodstuff. Since the nutrients have all been normalized by price, our objective is simply minimizing the sum of foods.
Background: A transition to Diet optimization and sustainable diets has Speed up muscle recovery potential to improve human and lptimization health but DDiet Speed up muscle recovery to meet requirements for opfimization adequacy, optimiation, environmental Powerful metabolic enhancer, and optimizagion acceptable to consumers. Methods: With Diet optimization objective Balance exercises minimizing the Olive oil antioxidants from the average observed diet of Danish adults, four diet optimizations were run using quadratic programming, with different combinations of diet constraints: 1 nutrients only Nutri2 nutrients and health-based targets for food amounts NutriHealth3 GHGE only GHGEand finally, 4 combined nutrient, health and GHGE constraints NutriHealthGHGE. Results: The GHGE of the four optimized diets were 3. Conclusion: The final optimized diet presented in this study represents an alternative way of composing a nutritionally adequate and healthy diet that has the same estimated GHGE as a diet consistent with the climate-friendly FBDGs in Denmark. As this optimized diet may be more acceptable for some consumers, it might help to facilitate the transition toward more healthy and sustainable diets in the Danish population. 
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