Evolutionary models of quantitative traits often assume trade-offs between beneficial and detrimental traits, requiring modelers to specify a function linking costs to benefits. The choice of trade-off function is often consequential; functions that assume diminishing returns (accelerating costs) typically lead to single equilibrium genotypes, while decelerating costs often lead to evolutionary branching. Despite their importance, we still lack a strong theoretical foundation to base the choice of trade-off function. To address this gap, we explore how trade-off functions can emerge from the genetic architecture of a quantitative trait. We developed a multi-locus model of disease resistance, assuming each locus had random antagonistic pleiotropic effects on resistance and fecundity. We used this model to generate genotype landscapes and explored how additive versus epistatic genetic architectures influenced the shape of the trade-off function. Regardless of epistasis, our model consistently led to accelerating costs. We then used our genotype landscapes to build an evolutionary model of disease resistance. Unlike other models with accelerating costs, our approach often led to genetic polymorphisms at equilibrium. Our results suggest that accelerating costs are a strong null model for evolutionary trade-offs and that the eco-evolutionary conditions required for polymorphism may be more nuanced than previously believed.

In the area of Solid Waste Management, transportation of the collected waste is a critical aspect considering the substantial time spent by garbage trucks on public roads. Studies have reported that transporting garbage has challenges related to public exposure and aesthetics. This study presents a generalised bi-objective formulation for the optimal routing of garbage trucks from transfer stations to recycling sites/landfills considering the trade-off between public exposure and aesthetic loss and constraining the operating cost. The formulation uses the novel link capacity function to account for the delay at traffic signals and the mix of trucks and cars on link performance. The proposed formulation is solved using the weighted sum and ε-constraint methods and applied to a realistic case study of the City of Chicago, USA. The Pareto Front obtained for the bi-objective formulation offers diverse trade-off solutions catering to distinct performance metrics. The results highlight the disparity across the solutions; the solution (P0.95 on Pareto Front) for minimum operating cost (or travel time or distance travelled) is very different from the solution (P0.4 on Pareto Front) for aesthetic cost and public exposure. The parametric study indicated that a modest operating budget may suffice for achieving aesthetic benefits, but minimising public exposure requires a higher operating budget. Finally, the proposed framework is adaptable to address various challenges pertaining to waste transportation, thereby serving as a valuable tool for evaluating policies and practices geared towards sustainability objectives.

Groundwater contamination is a global concern that has detrimental effect on public health and the environment. Sustainable groundwater treatment technologies such as adsorption require attaining a high removal efficiency at a minimal cost. This study investigated the adsorption of arsenate from groundwater utilizing chitosan-coated bentonite (CCB) under a fixed-bed column setup. Fuzzy multi-objective optimization was applied to identify the most favorable conditions for process variables, including volumetric flow rate, initial arsenate concentration, and CCB dosage. Empirical models were employed to examine how initial concentration, flow rate, and adsorbent dosage affect adsorption capacity at breakthrough, energy consumption, and total operational cost during optimization. The ε-constraint process was used in identifying the Pareto frontier, effectively illustrating the trade-off between adsorption capacity at breakthrough and the cost of the fixed-bed system. The integration of fuzzy optimization for adsorption capacity and its total operating cost utilized the global solver function in LINGO 20 software. A crucial equation derived from the Box-Behnken design and a cost equation based on energy and material usage in the fixed-bed system was employed. The results from identifying the Pareto front determined boundary limits for adsorption capacity at breakthrough (ranging from 12.96 ± 0.19 to 12.34 ± 0.42 μg/g) and total operating cost (ranging from 955.83 to 1106.32 USD/kg). An overall satisfaction level of 35.46% was achieved in the fuzzy optimization process. This results in a compromise solution of 12.90 μg/g for adsorption capacity at breakthrough and 1052.96 USD/kg for total operating cost. Henceforth, this can allow a suitable strategic decision-making approach for key stakeholders in future applications of the adsorption fixed-bed system.

This research introduces the Multi-Objective Liver Cancer Algorithm (MOLCA), a novel approach inspired by the growth and proliferation patterns of liver tumors. MOLCA emulates the evolutionary tendencies of liver tumors, leveraging their expansion dynamics as a model for solving multi-objective optimization problems in engineering design. The algorithm uniquely combines genetic operators with the Random Opposition-Based Learning (ROBL) strategy, optimizing both local and global search capabilities. Further enhancement is achieved through the integration of elitist non-dominated sorting (NDS), information feedback mechanism (IFM) and Crowding Distance (CD) selection method, which collectively aim to efficiently identify the Pareto optimal front. The performance of MOLCA is rigorously assessed using a comprehensive set of standard multi-objective test benchmarks, including ZDT, DTLZ and various Constraint (CONSTR, TNK, SRN, BNH, OSY and KITA) and real-world engineering design problems like Brushless DC wheel motor, Safety isolating transformer, Helical spring, Two-bar truss and Welded beam. Its efficacy is benchmarked against prominent algorithms such as the non-dominated sorting grey wolf optimizer (NSGWO), multiobjective multi-verse optimization (MOMVO), non-dominated sorting genetic algorithm (NSGA-II), decomposition-based multiobjective evolutionary algorithm (MOEA/D) and multiobjective marine predator algorithm (MOMPA). Quantitative analysis is conducted using GD, IGD, SP, SD, HV and RT metrics to represent convergence and distribution, while qualitative aspects are presented through graphical representations of the Pareto fronts. The MOLCA source code is available at: https://github.com/kanak02/MOLCA.

Multi-criteria optimization (MCO) function has been available on commercial radiotherapy (RT) treatment planning systems to improve plan quality; however, no study has compared Eclipse and RayStation MCO functions for prostate RT planning. The purpose of this study was to compare prostate RT MCO plan qualities in terms of discrepancies between Pareto optimal and final deliverable plans, and dosimetric impact of final deliverable plans. In total, 25 computed tomography datasets of prostate cancer patients were used for Eclipse (version 16.1) and RayStation (version 12A) MCO-based plannings with doses received by 98% of planning target volume having 76 Gy prescription (PTV76D98%) and 50% of rectum (rectum D50%) selected as trade-off criteria. Pareto optimal and final deliverable plan discrepancies were determined based on PTV76D98% and rectum D50% percentage differences. Their final deliverable plans were compared in terms of doses received by PTV76 and other structures including rectum, and PTV76 homogeneity index (HI) and conformity index (CI), using a t-test. Both systems showed discrepancies between Pareto optimal and final deliverable plans (Eclipse: -0.89% (PTV76D98%) and -2.49% (Rectum D50%); RayStation: 3.56% (PTV76D98%) and -1.96% (Rectum D50%)). Statistically significantly different average values of PTV76D98%,HI and CI, and mean dose received by rectum (Eclipse: 76.07 Gy, 0.06, 1.05 and 39.36 Gy; RayStation: 70.43 Gy, 0.11, 0.87 and 51.65 Gy) are noted, respectively (p < 0.001). Eclipse MCO-based prostate RT plan quality appears better than that of RayStation.

This study predicts the parameters such as viscosity and thermal conductivity in silica-alumina-MWCN/water nanofluid using the artificial intelligence method and using design variables such as solid volume fraction and temperature. In this study, 6 optimization algorithms were used to predict and numerically model the μnf and TC of silica-alumina-MWCNT/water-NF. In this study, six measurement criteria were used to evaluate the estimates obtained from the coupling process of GMDH ANN with each of these 6 optimization algorithms. The results reveal that the influence of the φ is notably higher on both μnf and TC with values of 0.83 for μnf and 0.92 for TC, while Temp has a relatively weaker impact with -0.5 for μnf and 0.38 for TC. Among various algorithms, the coupling of the evolutionary algorithm NSGA II with ANN and GMDH performs best in predicting μnf and TC for the NF, with a maximum margin of deviation of -0.108 and an R2 evaluation criterion of 0.99996 for μnf and 1 for TC, indicating exceptional model accuracy. In the subsequent phase, a meta-heuristic Genetic Algorithm minimizes μnf and TC values. Four points (A, B, C, and D) along the Pareto front are selected, with point A representing the optimal state characterized by low values of φ and Temp (0.0002 and 50.8772, respectively) and corresponding target function values of 0.9988 for μnf and 0.6344 for TC. In contrast, point D represents the highest values of φ and Temp (0.49986 and 59.9775, respectively) and yields target function values of 2.382 for μnf and 0.8517 for TC. This analysis aids in identifying the optimal operating conditions for maximizing NF performance.

Shrimp waste is a valuable source for chitin extraction and consequently for chitosan preparation. In the process of obtaining chitosan, a determining step is the chitin deacetylation. The main characteristic of chitosan is the degree of deacetylation, which must be as high as possible. The molar mass is another important parameter that defines its utilizations, and according to these, high or low molar masses are required. The present study is an attempt to optimize the deacetylation step to obtain chitosan with a high degree of deacetylation and high or low molar mass. The study was carried out based on experimental data obtained in the frame of a central composite design where three working parameters were considered: NaOH concentration, liquid:solid ratio, and process duration. The regression models defined for the degree of deacetylation (DD) and for the mean molar mass (MM) of chitosan powders were used in the formulation of optimization problems. The objectives considered were simultaneous maximum DD and maximum/minimum MM for the final chitosan samples. For these purposes, multiobjective optimization problems were formulated and solved using genetic algorithms implemented in Matlab®. The multiple optimal solutions represented by trade-offs between the two objectives are presented for each case.

Not unlike the climate or what holds the galaxies and planetary motions together, cancer biology has an intrinsic nonlinear dynamic. In this overview we will outline how to connect temporal measurements of a nonlinear dynamical and unstable complex system, such as cancer, with well-established engineering methods, old and new, that are applied in linear dynamical systems.This proof-of-concept is therapeutically relevant in the development of new means to treat or control human cancer by either adding an appropriate external \"damping\" or a \"forcing\" term, or by a \"control\" actuator such that its nonlinear dynamic is steered to a spiral stably into zero forever as a sink attractor.

BACKGROUND: Studies comparing different radiotherapy treatment techniques-such as volumetric modulated arc therapy (VMAT) and helical tomotherapy (HT)-typically compare one treatment plan per technique. Often, some dose metrics favor one plan and others favor the other, so the final plan decision involves subjective preferences. Pareto front comparisons provide a more objective framework for comparing different treatment techniques. A Pareto front is the set of all treatment plans where improvement in one criterion is possible only by worsening another criterion. However, different Pareto fronts can be obtained depending on the chosen machine settings.
OBJECTIVE: To compare VMAT and HT using Pareto fronts and blind expert evaluation, to explain the observed differences, and to illustrate limitations of using Pareto fronts.
METHODS: We generated Pareto fronts for twenty-four prostate cancer patients treated at our clinic for VMAT and HT techniques using an in-house script that controlled a commercial treatment planning system. We varied the PTV under-coverage (100% - V95%) and the rectum mean dose, and fixed the mean doses to the bladder and femoral heads. In order to ensure a fair comparison, those fixed mean doses were the same for the two treatment techniques and the sets of objective functions were chosen so that the conformity indexes of the two treatment techniques were also the same. We used the same machine settings as are used in our clinic. Then, we compared the VMAT and HT Pareto fronts using a specific metric (clinical distance measure) and validated the comparison using a blinded expert evaluation of treatment plans on these fronts for all patients in the cohort. Furthermore, we investigated the observed differences between VMAT and HT and pointed out limitations of using Pareto fronts.
RESULTS: Both clinical distance and blind treatment plan comparison showed that VMAT Pareto fronts were better than HT fronts. VMAT fronts for 10 and 6 MV beam energy were almost identical. HT fronts improved with different machine settings, but were still inferior to VMAT fronts.
CONCLUSIONS: That VMAT Pareto fronts are better than HT fronts may be explained by the fact that the linear accelerator can rapidly vary the dose rate. This is an advantage in simple geometries that might vanish in more complex geometries. Furthermore, one should be cautious when speaking about Pareto optimal plans as the best possible plans, as their calculation depends on many parameters.

Water pollution escalates with rising waste discharge in river systems, as the rivers\' limited pollution tolerance and constrained self-cleaning capacity compel the release of treated pollutants. Although several studies have shown that the non-dominated sorting genetic algorithm-II (NSGA-II) is an effective algorithm regarding the management of river water quality to reach water quality standards, to our knowledge, the literature lacks using a new optimization model, namely, the multi-objective cuckoo optimization algorithm (MOCOA). Therefore, this research introduces a new optimization framework, including non-dominated sorting and ranking selection using the comparison operator densely populated towards the best Pareto front and a trade-off estimation between the goals of discharges and environmental protection authorities. The suggested algorithm is implemented for a waste load allocation issue in Jajrood River, located in the North of Iran. The limitation of this research is that discharges are point sources. To analyze the performance of the new optimization algorithm, the simulation model is linked with a hybrid optimization model using a cuckoo optimization algorithm and non-dominated sorting genetic algorithms to convert a single-objective algorithm to a multi-objective algorithm. The findings indicate that, in terms of violation index and inequity values, MOCOA\'s Pareto front is superior to NSGA-II, which highlights the MOCOA\'s effectiveness in waste load allocation. For instance, with identical population sizes and violation indexes for both algorithms, the optimal Pareto front ranges from 1.31 to 2.36 for NSGA-II and 0.379 to 2.28 for MOCOA. This suggests that MOCOA achieves a superior Pareto front in a more efficient timeframe. Additionally, MOCOA can attain optimal equity in the smaller population size.