Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics

Hard graph problems are ubiquitous in Bioinformatics, inspiring the design of specialized Fixed-Parameter Tractable algorithms, many of which rely on a combination of tree-decomposition and dynamic programming. The time/space complexities of such approaches hinge critically on low values for the treewidth tw of the input graph. In order to extend their scope of applicability, we introduce the Tree-Diet problem, i.e. the removal of a minimal set of edges such that a given tree-decomposition can be slimmed down to a prescribed treewidth tw. Our rationale is that the time gained thanks to a smaller treewidth in a parameterized algorithm compensates the extra post-processing needed to take deleted edges into account. Our core result is an FPT dynamic programming algorithm for Tree-Diet, using 2^O(tw)n time and space. We complement this result with parameterized complexity lower-bounds for stronger variants (e.g., NP-hardness when tw or tw − tw is constant). We propose a prototype implementation for our approach which we apply on difficult instances of selected RNA-based problems: RNA design, sequence-structure alignment, and search of pseudoknotted RNAs in genomes, revealing very encouraging results. This work paves the way for a wider adoption of tree-decomposition-based algorithms in Bioinformatics.

LR-type fully pythagorean fuzzy linear programming problems with equality constraints

A Pythagorean fuzzy set is a powerful model for depicting fuzziness and uncertainty. This model is more flexible and practical as compared to an intuitionistic fuzzy model. This research article presents a new model called LR-type fully Pythagorean fuzzy linear programming problem. We consider the notions of LR-type Pythagorean fuzzy number, ranking for LR-type Pythagorean fuzzy numbers and arithmetic operations for unrestricted LR-type Pythagorean fuzzy numbers. We propose a method to solve LR-type fully Pythagorean fuzzy linear programming problems with equality constraints. We describe our proposed method with numerical examples including diet problem.

An Island-Based Hybrid Evolutionary Algorithm for Caloric-Restricted Diets

The most popular and successful way to maintain a healthy body is to have a rich and balanced diet, combined with physical exercise. Since it was proposed the diet dilemma, several works in the literature suggested calculating a diet that respects an individual's nutritional needs. In the Caloric-Restricted Diet Problem (CRDP), the goal is to find a reduced-calorie diet that meets an individual's dietary needs aiming for weight loss. This paper proposes a Hybrid Island-Based Evolutionary Algorithm (IBHEA) that combines a Genetic Algorithm (GA) with a Differential Evolution (DE) communicating through a migration policy to solve the CRDP. Computational experiments showed that IBHEA outperforms the non-distributed and non-hybrid implementations, generating a greater variety of diets with a small calorie count.

The Diet Problem on Minimizing Vitamin A: Linear Programming Problem

It is essential to practice a good diet in everyday life because human body needs a reasonable amount of nutrients. It is because excessive nutrient intake can lead to internal organs failure, such as kidney damage. This study focuses on minimizing vitamin A’s intake in daily diet because vitamin A can give good vision, maintain healthy skin, and improve body's immune system. This research involves a few nutrients, such as calcium, iron, cholesterol, and vitamin A. The diet problem of minimizing vitamin A will be solved by using the graphical method and excel solver. The results are compared to determine which ways is the best. The results obtained are optimal solution, which is the minimal amount of vitamin A from one of the methods.

Recommending healthy meal plans by optimising nature-inspired many-objective diet problem

Healthy eating is an important issue affecting a large part of the world population, so human diets are becoming increasingly popular, especially with the devastating consequences of Coronavirus Disease (Covid-19). A realistic and sustainable diet plan can help us to have a healthy eating habit since it considers most of the expectations from a diet without any restriction. In this study, the classical diet problem has been extended in terms of modelling, data sets and solution approach. Inspired by animals’ hunting strategies, it was re-modelled as a many-objective optimisation problem. In order to have realistic and applicable diet plans, cooked dishes are used. A well-known many-objective evolutionary algorithm is used to solve the diet problem. Results show that our approach can optimise specialised daily menus for different user types, depending on their preferences, age, gender and body index. Our approach can be easily adapted for users with health issues by adding new constraints and objectives. Our approach can be used individually or by dietitians as a decision support mechanism.

Testing the Robustness of Linear Programming* Using a Diet Problem on a Multi-Shop System

Time, raw materials and labour are some of the nite resources in the world. Due to this, Linear Programming* (LP) is adopted by key decision-markers as an innovative tool to wisely consume these resources. This paper test the strength of linear programming models and presents an optimal solution to a diet problem on a multi-shop system formulated as linear, integer linear and mixed-integer linear programming models. All three models gave different least optimal values, that is, in linear programming, the optimal cost was GHS15.26 with decision variables being continuous (R+) and discrete (Z+). The cost increased to GHS17.50 when the models were formulated as mixed-integer linear programming with decision variables also being continuous (R+) and discrete (Z+) and lastly GHS17.70 for integer linear programming with discrete (Z+) decision variables. The difference in optimal cost for the same problem under different search spaces sufficiently establish that, in programming, the search space undoubtedly affect the optimal value. Applications to most problems like the diet and scheduling problems periodically require both discrete and continuous decision variables. This makes integer and mixed-integer linear programming models also an effective way of solving most problems. Therefore, Linear Programming* is applicable to numerous problems due to its ability to provide different required solutions.

Mathematical Research on Optimization Technique for Diet Planning Problem: Case Research Autism Paralympic Athlete

This paper demonstrates distinctive methods used in operation research to experience with different diet issues. Every diet problem has its particular cost limitation and objective function. The designation of sufficient menus including the consideration of several types of constraints, for example, the ideal nutritional content, the amount of food to be consumed and others. The mathematical model is constructed to determine a diet plan as an optimal solution which fulfills every requirements and limitations. The application of different optimization techniques and weakness in each method has been reviewed. The use of integer programming and development that can be done also represents in this paper. An optimal and practical solution is acquired to solve the diet problem for autism Paralympic athlete