Statistics of the number of equilibria in random social dilemma evolutionary games with mutation

In this paper, we study analytically the statistics of the number of equilibria in pairwise social dilemma evolutionary games with mutation where a game’s payoff entries are random variables. Using the replicator–mutator equations, we provide explicit formulas for the probability distributions of the number of equilibria as well as other statistical quantities. This analysis is highly relevant assuming that one might know the nature of a social dilemma game at hand (e.g., cooperation vs coordination vs anti-coordination), but measuring the exact values of its payoff entries is difficult. Our delicate analysis shows clearly the influence of the mutation probability on these probability distributions, providing insights into how varying this important factor impacts the overall behavioural or biological diversity of the underlying evolutionary systems. Graphic abstract

Statistics of the number of equilibria in random social dilemma evolutionary games with mutation

In this paper, we study analytically the statistics of the number of equilibria in pairwise social dilemma evolutionary games with mutation where a game's payoff entries are random variables. Using the replicator-mutator equations, we provide explicit formulas for the probability distributions of the number of equilibria as well as other statistical quantities. This analysis is highly relevant assuming that one might know the nature of a social dilemma game at hand (e.g., cooperation vs coordination vs anti-coordination), but measuring the exact values of its payoff entries is difficult. Our delicate analysis shows clearly the influence of the mutation probability on these probability distributions, providing insights into how varying this important factor impacts the overall behavioural or biological diversity of the underlying evolutionary systems.

Aplikasi Pertimbangan Wisata di Pulau Lombok dengan Metode Fuzzy Mamdani & Algoritma Genetika

<p class="Abstrak">Pulau Lombok memiliki pariwisata berupa keindahan alam dan kebudayaan yang menarik, sehingga juga mendapat tiga penghargaan pada <em>World Halal Tourism Awards</em> 2016 dengan faktor pertumbuhan kunjungan wisatawan sebesar 13% pada tahun tersebut. Adanya sebuah aplikasi yang dapat membantu wisatawan dalam menentukan keputusan perjalanan wisata mereka adalah wajib. Aplikasi ini dikembangkan dengan logika <em>Fuzzy</em> Mamdani dan Algoritma Genetika dengan tujuan memberikan rekomendasi pariwisata.Logika <em>Fuzzy</em> Mamdani memberikan pertimbangan wisata berdasarkan 5 parameter (anggaran, rencana perjalanan, akomodasi, makanan dan minuman, serta biaya transportasi) yang kemudian menjadi 5 fungsi keanggotaan untuk membangun kombinasi aturan pada fuzzy dan menghasilkan keluaran berupa pertimbangan wisata, yaitu: Tidak Memungkinkan, Cukup Memungkinkan, dan Memungkinkan. Kombinasi lima fungsi keanggotaan tersebut, menghasilkan 10.080 aturan, yang digunakan untuk mengetahui seseorang memungkinkan, atau tidak untuk berwisata ke pulau Lombok dengan <em>constrain</em> parameter yang dimiliki, yang dibangkitkan dengan menggunakan fungsi Defuzzifikasi <em>Mean of Max</em> (MOM). Algortima Genetika digunakan dalam memberikan alokasi penggunaan budget yang optimal dalam berwisata di Pulau Lombok.Hasil pengujian dengan perhitungan manual dan model defuzzifikasi yang berbeda memiliki akurasi 100%. Untuk implementasi Algoritma Genetika, aplikasi memperoleh alokasi anggaran optimal pada <em>probabilitas crossover</em> (pc) dan probabilitas mutasi (pm) dengan (pc) 0,7 dan (pm) 0,2.</p><p class="Abstrak"> </p><p class="Abstrak"><em><strong>Abstract</strong></em></p><p class="Abstract"><em>Tourism in Lombok has an interesting culture, it makes Lombok got three awards at the 2016 World Halal Tourism Awards and became a growth factor for tourist visits by 13% that year. An application that can help tourists in determining travel decision is mandatory.The application developed with Mamdani Fuzzy Logic and Genetic Algorithm to provide tourism recommendations. The Fuzzy Mamdani Logic Method provides tourism considerations based on 5 parameters (budget, travel plans, accommodation, food and drinks, and transportation costs) which then become 5 membership functions to build a combination of rules on fuzzy and produce output in the form of tourism's considerations: Not Enable, Enough Enable, and Enable. The combination of the 5 membership functions constructed 10.080 fuzzy rules, that's used to know wheater tourists enables them to go to Lombok with the limitation that they have. The defuzzification used is the Mean of Max (MOM). Genetic Algorithm (GA) is used in providing optimal budget allocation in traveling on Lombok IslandThe results of testing with manual calculations and different defuzzification models have 100% accurate, the application of GA obtained optimal budget allocation on crossover probability (pc) and mutation probability (pm) combination with (pc) 0.7 and (pm) 0.2.</em></p><p class="Abstrak"><em><strong><br /></strong></em></p>

Adapt or Perish: Evolutionary Rescue in a Gradually Deteriorating Environment

We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the absence of mutants, which can survive only if mutants sufficiently adapted to the new environment arise and fix. We show that mutants that appear later during the environment deterioration have a higher probability to fix. The rescue probability of the population increases with a sigmoidal shape when the product of the carrying capacity and of the mutation probability increases. Furthermore, we find that rescue becomes more likely for smaller population sizes and/or mutation probabilities if the environment degradation is slower, which illustrates the key impact of the rapidity of environment degradation on the fate of a population. We also show that our main conclusions are robust across various types of adaptive mutants, including specialist and generalist ones, as well as mutants modeling antimicrobial resistance evolution. We further express the average time of appearance of the mutants that do rescue the population and the average extinction time of those that do not. Our methods can be applied to other situations with continuously variable fitnesses and population sizes, and our analytical predictions are valid in the weak-to-moderate mutation regime.

In silico saturation mutagenesis of cancer genes

SummaryExtensive bioinformatics analysis of datasets of tumor somatic mutations data have revealed the presence of some 500-600 cancer driver genes. The identification of all potential driver mutations affecting cancer genes is essential to implement precision cancer medicine and to understand the interplay of mutation probability and selection in tumor development. Here, we present an in silico saturation mutagenesis approach to identify all driver mutations in 568 cancer genes across 66 tumor types. For most cancer genes the mutation probability across tissues --underpinned by active mutational processes-- influences which driver variants have been observed, although this differs significantly between tumor suppressor and oncogenes. The role of selection is apparent in some of the latter, the observed and unobserved driver mutations of which are equally likely to occur. The number of potential driver mutations in a cancer gene roughly determines how many mutations are available for detection across newly sequenced tumors.

Adapt or perish: Evolutionary rescue in a gradually deteriorating environment

We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the absence of mutants, which can only survive if mutants sufficiently adapted to the new environment arise and fix. We show that mutants that appear later during the environment deterioration have a higher probability to fix. The rescue probability of the population increases with a sigmoidal shape when the product of the carrying capacity and of the mutation probability increases. Furthermore, we find that rescue becomes more likely for smaller population sizes and/or mutation probabilities if the environment degradation is slower, which illustrates the key impact of the rapidity of environment degradation on the fate of a population. We also show that our main conclusions are robust across various types of adaptive mutants, including specialist and generalist ones, as well as mutants modeling antimicrobial resistance evolution. We further express the average time of appearance of the mutants that do rescue the population and the average extinction time of those that do not. Our methods can be applied to other situations with continuously variable fitnesses and population sizes, and our analytical predictions are valid in the weak-to-moderate mutation regime.

Fertilizer Production Planning Optimization Using Particle Swarm Optimization-Genetic Algorithm

Background: The applications of constrained optimization have been developed in many problems. One of them is production planning. Production planning is the important part for controlling the cost spent by the company.Objective: This research identifies about production planning optimization and algorithm to solve it in approaching. Production planning model is linear programming model with constraints : production, worker, and inventory.Methods: In this paper, we use heurisitic Particle Swarm Optimization-Genetic Algorithm (PSOGA) for solving production planning optimization. PSOGA is the algorithm combining Particle Swarm Optimization (PSO) and mutation operator of Genetic Algorithm (GA) to improve optimal solution resulted by PSO. Three simulations using three different mutation probabilies : 0, 0.01 and 0.7 are applied to PSOGA. Futhermore, some mutation probabilities in PSOGA will be simulated and percent of improvement will be computed.Results: From the simulations, PSOGA can improve optimal solution of PSO and the position of improvement is also determined by mutation probability. The small mutation probability gives smaller chance to the particle to explore and form new solution so that the position of improvement of small mutation probability is in middle of iteration. The large mutation probability gives larger chance to the particle to explore and form new solution so that the position of improvement of large mutation probability is in early of iteration.Conclusion: Overall, the simulations show that PSOGA can improve optimal solution resulted by PSO and therefore it can give optimal cost spent by the company for the planning.Keywords: Constrained Optimization, Genetic Algorithm, Linear Programming, Particle Swarm Optimization, Production Planning

Relevance Feedback using Genetic Algorithm on Information Retrieval for Indonesian Language Documents

Background: The Rapid growth of technological developments in Indonesia had resulted in a growing amount of information. Therefore, a new information retrieval environment is necessary for finding documents that are in accordance with the user’s information needs.Objective: The purpose of this study is to uncover the differences between using Relevance Feedback (RF) with genetic algorithm and standard information retrieval systems without relevance feedback for the Indonesian language documents.Methods: The standard Information Retrieval (IR) System uses Sastrawi stemmer and Vector Space Model, while Genetic Algorithm-based (GA-based) relevance feedback uses Roulette-wheel selection and crossover recombination. The evaluation metrics are Mean Average Precision (MAP) and average recall based on user judgments.Results: By using two Indonesian language document datasets, namely abstract thesis and news dataset, the results show 15.2% and 28.6% increase in the corresponding MAP values for both datasets as opposed to the standard Information Retrieval System. A respective 7.1% and 10.5% improvement on the recall value at 10th position was also observed for both datasets. The best obtained genetic algorithm parameters for abstract thesis datasets were a population size of 20 with 0.7 crossover probability and 0.2 mutation probability, while for news dataset, the best obtained genetic algorithm parameters were a population size of 10 with 0.5 crossover probability and 0.2 mutation probability.Conclusion: Genetic Algorithm-based relevance feedback increases both values of MAP and average recall at 10th position of retrieved document. Generally, the best genetic algorithm parameters are as follows, mutation probability is 0.2, whereas the size of population size and crossover probability depends on the size of dataset and length of the query.Keywords: Genetic Algorithm, Information Retrieval, Indonesian language document, Mean Average Precision, Relevance Feedback