Flow Lines Research Articles

Electricity arbitrage for mobile energy storage in marginal pricing mechanism via bi-level programming

The rapid growth of renewable energy is integrated into the distribution system. The creation of both new market mechanisms and investment models has critical effects on the economics and security of the distribution market. Mobile energy storage has been used to increase the resilience of distribution grids due to their advantages in mobility and flexibility, which offer electricity arbitrage options for merchant investments. This paper presents a bi-level optimization framework based on location marginal pricing settlement of mobile energy storage financial rights revenue in active distribution systems. In the developed framework, the upper-level problem determines the optimal capacity, routing, and dispatching of mobile energy storage to maximize revenue in the liberalized electricity market. The lower-level problem performs the joint optimization of energy and reserve market clearing as well as renewable energy capacity optimization based on the alternating current optimal power flow model. The non-convexity of the line flow and location marginal pricing is linearized via second-order cone relaxation and Karush-Kuhn-Tucker. The bi-level programming is reformatted as mathematical programming with equilibrium constraints. Further, the revenue risk due to renewable energy uncertainty is measured via conditional value-at-risk. Finally, the effectiveness of the optimization framework and solution method is verified using the modified IEEE-33 test system. The results show that mobile energy storage promotes renewable energy and reduces distribution network costs by 2.3%.

Testing the functionality of OLGA software for determining optimal oil transport modes to prevent solid particle deposition

Background: During operation, all mechanical impurities entering the collector through the flow lines settle at the bottom due to a decrease in flow velocity. This leads to a reduction in the capacity of the pipeline network, increased pressure, and premature equipment wear. To address this issue it is essential to understand the dynamics and intensity of sludge formation at the bottom of the pipeline. Aim: Evaluate the functionality and efficiency of the dynamic multiphase flow simulator in addressing challenges related to the transport of borehole fluid containing solid particles. Materials and methods: To build a mathematical simulation of multiphase flow with solid particles using OLGA specialised software, we selected one of the oil gathering lines in field N, with a diameter of 159х10 mm and a length of 1600 m, as the study object. This oil gathering line collects production from 16 wells. The OLGA simulator was used to model the process and measure flow parameters with different particle diameters, predicting the dynamics of variables such as time-varying flow velocities, fluid composition, temperatures, and particulate deposition. For a flow with a particle diameter of 104 µm, active precipitation occurs at flow rates between 200 and 300 m³/day. At flow rates of 400 m³/day and above, the velocity is sufficient to carry the particles without significant accumulation in the pipeline. Results: The software enabled the calculation of the dynamic system for different solid particle diameters in multiphase flow, addressing the challenge of evaluating the dynamics of solid phase accumulation in the pipeline and determining the fluid flow velocity required to prevent sludge formation. The software is suitable for implementing simulation modelling to develop technical solutions that minimise the risks of solid particle deposition in oil gathering pipelines during the operation of on-shore infrastructure facilities. Conclusion: The software enabled the calculation of the dynamic system for different solid particle diameters in multiphase flow, addressing the challenge of evaluating the dynamics of solid phase accumulation in the pipeline and determining the fluid flow velocity required to prevent sludge formation. The software is suitable for implementing simulation modelling to develop technical solutions that minimise the risks of solid particle deposition in oil gathering pipelines during the operation of on-shore infrastructure facilities.

Analysis of Lofoten Vortex Merging Based on Altimeter Data

The Lofoten Vortex (LV), which is identified as a quasi-permanent anticyclonic eddy, strengthens through continuous merging with external anticyclonic eddies. Our investigation used the Lagrangian method to monitor the LV on a daily basis. Utilizing satellite altimeter data, we conducted multi-year tracking and statistical analysis of merging events involving the LV. The results indicate a characteristic radius of approximately 42.72 km and a mean vorticity at the eddy center of approximately −2.23 × 10−5 s−1. The eddy exhibits oscillatory motion within the sea basin depression, centered at 70°N, 3°E, characterized by counterclockwise trajectories between 0.5°E and 6°E and between 69°N and 70.5°N. There are two types of merging events: fusion events (55%), in which eddies of similar strengths interact within a closed flow line and then merge to form a new eddy; and absorption events (45%), in which the stronger LV absorbs the weaker anticyclonic eddies without destroying the structure of the LV itself. The nodes where strong vorticity advection occurs correspond to the nodes where merging occurs, suggesting that their effect on merging can be well characterized by the vorticity advection time series. We also observe occasional fluctuations and substitution events involving the LV and external anticyclonic eddies, suggesting a dynamic succession rather than a single vortex entity.

Execution of revised BMIM similarity coefficient for part family formation in reconfigurable manufacturing system

The reconfigurable manufacturing system (RMS) is an advanced manufacturing strategy that enables precise adjustment of functionality and capacity to meet fluctuating demands economically. RMS focuses on part families, allowing configurations to be adapted for new part requirements. Optimizing flow line design to produce various parts involves minimizing reconfigurations and associated costs by enhancing operation sequence similarity. This article proposes a novel sequence optimization using the Longest Common Subsequence (LCS) method to reduce bypassing moves and machine idle times. The study introduces a similarity coefficient derived from LCS and employs average linkage hierarchical clustering to categorize parts in a case study. Unlike traditional methods, this approach considers material movements both before the initial machine and after the final processing station, addressing gaps in bypassing move calculations. The impact of different weighting scenarios for Type-II moves (ω) and machine idleness (β) on clustering was examined. For example, with Type-II move weights (ω) of {1.0, 0.6, 0.3, 0.0} and equal weightings for bypassing moves (α) and machine idleness (β) set at 0.5, a threshold value of 0.3 results in eight clusters, such as Cluster 1 {1, 11, 10, 12} and Cluster 3 {3, 5, 6, 4, 15, 9, 13, 14, 7, 8}. Lower threshold values lead to fewer clusters with larger sizes, indicating a more consolidated part family grouping. Various Type-II move weights and material handling scenarios demonstrate how different weighting configurations affect clustering and part family sizes. This approach enhances RMS efficiency by integrating comprehensive material handling considerations and optimizing clustering based on operational similarities.

Phase-space path integral approach to the kinetics of black hole phase transition in massive gravity

The dynamics of the state-switching process of black holes in dRGT massive gravity theory is presented using free energy landscape and stochastic Langevin equations. The free energy landscape is constructed using the Gibbons-Hawking path integral method. The black hole phases are characterized by taking its horizon radius as the order parameter. The free energy landscape provides three black hole phases: small, intermediate, and large. The small and large black holes are thermodynamically stable whereas the intermediate one is unstable. The Martin–Siggia–Rose–Janssen–de Dominicis (MSRJD) functional describes the stochastic dynamics of black hole phase transition. The Hamiltonian flow lines are obtained from the MSRJD functional and are used to analyze the stability and the phase transition properties. The dominant kinetic path between different phases is discussed for various configurations of the free energy landscape. We discuss the effect of black hole charge and the graviton mass on the critical behavior of black hole phase transition.

The impact of Microbially Induced Calcite Precipitation (MICP) on sand internal erosion resistance: A microfluidic study

Fine particle internal erosion involves the detachment, transport, and deposition of fine particles within soil, significantly impacting agriculture, engineering, and environmental protection. Microbially induced calcite precipitation (MICP) has proven to be an effective method for controlling internal erosion. To optimize MICP protocols for effective erosion control, understanding the microscopic mechanisms by which MICP reduces fine particle erosion is essential but remains unclear. In this study, microfluidic chip experiments were conducted to observe the characteristics of calcium carbonate crystals and fine particles before and after MICP reinforcement and erosion. Through quantitative analysis of the calcium carbonate produced by MICP and eroded fine particles, the effects of bacterial density, concentration of cementation solution, and flow rate on the efficiency of MICP in resisting soil internal erosion were investigated. In addition, three primary mechanisms by which MICP reduces fine particle erosion were identified. Firstly, in situ sand stabilization occurs when calcium carbonate generated by MICP bonds and encapsulates fine particles, forming larger particles that remain stable under erosive flow conditions. Secondly, regional sand stabilization is achieved as MICP-produced calcium carbonate crystals narrow or block the flow channels, preventing extensive migration of fine particles. Lastly, adjacent particle stabilization is facilitated by calcium carbonate crystals, which remain stable during water flow erosion and alter the erosion flow lines, creating zones adjacent to the crystals where fine particle movement is minimized. These findings provide a deeper understanding of the role of MICP in erosion control and can inform the development of more effective erosion mitigation strategies.

The neural networking strategy results in the tri‐hybrid nanofluid flowing over a slippery flat plate to act as an antimicrobial agent through solar radiation

AbstractHybrid nanofluids are employed to enhance the antibacterial effect produced by solar radiation. Antimicrobial properties are present in metal nanoparticles (such as silver, copper, or zinc) or metal oxides (such as titanium dioxide or zinc oxide) when exposed to solar radiation. Nanomaterials that have antimicrobial properties are selected from the available literature. A solar sheet with an inclined plane has been chosen and filled with tri‐hybrid nanofluids (THNFs). Hybrid nanofluids including (CuO), Copper oxide, TiO2 (Titanium oxide), and SiO2 (Silicon dioxide), are selected from metal and metal oxide classes including water as a base fluid. The antimicrobial action caused by solar radiation is enhanced by the slip boundaries and variable porous space. The influence of flow and thermal fields on isotherms, velocities, flow lines, and Nusselt numbers are considered. The transformed system of differential equations is solved by the Control Volume Finite Element Method (CVFEM) and RK‐4 technique. The nanoparticulate volume fraction of CuO, TiO2, and SiO2 is largely responsible for the enhancement in the heat transfer rate (HT), as observed. Improved thermal performance is achieved through the flow of THNFs, which in turn acts as an antimicrobial agent. Increasing values of parameters lead to an improvement in the heat transfer rate, which in turn decreases microbial activity.

Study on the influence mechanism of electromagnetic field on multifield coupling during the laser cladding Fe60 process

During laser cladding, microdefects such as pores, cracks, and segregation inevitably occur. Practical experience has shown that applying an electromagnetic field is an effective method for eliminating these microdefects during the cladding process. In the study, a multifield coupling three-dimensional numerical model was established for the electromagnetic field-assisted laser cladding Fe60 process. The instantaneous evolution law in the temperature field, flow field, and stress field under the influence of a magnetic field and without magnetic influence was calculated and revealed. At the same time, the two were compared and analyzed, focusing on the influence of an external electromagnetic field on the flow of molten pool Marangoni and its action mechanism. The results show that under the electromagnetic conditions applied in the study, the maximum magnetic induction intensity and the maximum Lorentz force density in the molten pool reach 0.13 T and 6.84 × 103 N/m3. Under the influence of magnetic force, the “double vortex” flow of Marangoni convection is asymmetrically distributed in the center of the molten pool. The fluid flow line has irregular flow and the circulation area generated at the front of the molten pool is larger in the corresponding scanning direction. Under the magnetic field influence, the overall flow velocity of the molten pool obviously increases, and the maximum flow velocity of the molten pool reaches 0.28 m/s. The study lays a significant theoretical foundation for revealing the mechanism of laser cladding assisted by a magnetic field.

Exploring the interplay of costs and flow time in server allocation for flow lines with parallel non-identical machines

ABSTRACT The Server Allocation Problem is a significant challenge in manufacturing systems involving deciding the number and version of machines for each stage. This optimization problem is of utmost importance when there is a trade-off between minimizing investment costs and flow time while achieving target performance, such as a minimum throughput. Manufacturing systems often employ hybrid flow lines, with non-identical machines at each stage. This paper analyzes the trade-off between minimizing costs and flow time when allocating servers in hybrid flow lines by proposing a bi-criteria approach that uses an efficient pattern-based problem representation and a Variable Neighborhood Search solution algorithm. The objectives are to minimize total cost and flow time while ensuring a target throughput. A metric for comparing obtained solutions is proposed, providing insights for practical implementation. A comprehensive numerical analysis is conducted, to validate the proposed approach and demonstrate its applicability in real-world manufacturing settings.

Acquiring the Lefschetz thimbles: efficient evaluation of the diffraction integral for lensing in wave optics

ABSTRACT Evaluating the Kirchhoff–Fresnel diffraction integral is essential in studying wave effects in astrophysical lensing, but is often intractable because of the highly oscillatory integrand. A recent breakthrough was made by exploiting the Picard–Lefschetz theory: the integral can be performed along the ‘Lefschetz thimbles’ in the complex domain where the integrand is not oscillatory but rapidly converging. The application of this method, however, has been limited by both the unfamiliar concepts involved and the low numerical efficiency of the method used to find the Lefschetz thimbles. In this paper, we give simple examples of the Lefschetz thimbles and define the ‘flow lines’ that facilitate the understanding of the concepts. Based on this, we propose new ways to obtain the Lefschetz thimbles with high numerical efficiency, which provide an effective tool for studying wave effects in astrophysical lensing.

Geodesic vector fields, induced contact structures and tightness in dimension three

In this paper, we provide new and simpler proofs of two theorems of Gluck and Harrison on contact structures induced by great circle or line fibrations. Furthermore, we prove that a geodesic vector field whose Jacobi tensor is parallel along flow lines (e.g. if the underlying manifold is locally symmetric) induces a contact structure if the ‘mixed’ sectional curvatures are nonnegative, and if a certain nondegeneracy condition holds. Additionally, we prove that in dimension three, contact structures admitting a Reeb flow which is either periodic, isometric, or free and proper, must be universally tight. In particular, we generalise an earlier result of Geiges and the author, by showing that every contact form on R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}^3$$\\end{document} whose Reeb vector field spans a line fibration is necessarily tight. Furthermore, we provide a characterisation of isometric Reeb vector fields. As an application, we recover a result of Kegel and Lange on Seifert fibrations spanned by Reeb vector fields, and we classify closed contact 3-manifolds with isometric Reeb flows (also known as R-contact manifolds) up to diffeomorphism.

The specifics оf тhe development оf soil flushing during spring snowmelt in the arable land of the northern zone of the Krasnoyarsk forest-steppe

The results of studies of soil flushing and accumulation in the period 2009–2017 in the northern part of the Krasnoyarsk forest-steppe in areas with high intensity of erosive and accumulative processes are presented. A wide range of erosion values from meltwater has been established – from 0.4 to 25 mm for the spring period. The results of the application of a refined Regional model for calculating potential flushing for the northern part of the Krasnoyarsk forest-steppe are presented. The analysis of meteorological factors and conditions of the underlying surface affecting the distribution of values of melt runoff, flushing and accumulation of soils on arable massifs located on inclined watershed surfaces is carried out: the specificity of the distribution of meltwater flows determines the formation of zones of extreme erosion along the perimeter of arable land in the lower parts of the slope – up to 15–20 mm of soil layer. In conditions of low slope steepness, the effect of relief on erosion is largely determined by the high slope lengths and melt water flow lines. The distribution of flushing values over the area of arable land shows a close correlation with the values of snow accumulation and soil moisture. The spatial and temporal patterns of the influence of the previous autumn soil moisture on the intensity of erosion have been established: the values of flushing increase with increasing soil moisture, the average values of erosion correlate with the values of autumn soil moisture in dynamics over the years of field observations. Special soil protection measures have been proposed for sites with the most intensive flushing in the research area.

Water Treatment: Evaluation of Maleic Acid-Acrylamide Copolymer Inhibitor Efficiency on Calcite Scale by Response Surface Methodology

Mineral scales of calcite are common in the oil field and pose a serious integrity problem in the wellbore, flow lines, and equipment. It is also a challenge faced by industries such as refineries and power plants. Scale deposition is a complex process depending on various factors such as concentration of scaling species, temperature, pH, and flow rates. Deterministic models are used to predict the scale formation from the level of supersaturation of the scaling species in the water at the operating conditions. However, due to the complexity of the interaction of variables affecting the scaling and inhibition by chemicals, it is suitable to be represented by statistical models. This work focused on applying statistical analysis techniques such as response surface methodology to understand the effect of different operating parameters on the inhibition efficiency of maleic acid-acrylamide copolymer on CaCO3 scales. The copolymer was synthesized, and its inhibition efficiency on the calcite scale was tested using static jar tests at different pH, temperature, and inhibitor concentrations. The effect of the critical parameters on the inhibition efficiency was analyzed using the statistical technique of Response Surface Methodology (RSM). The design of experiments (DoE) was created using a Box–Behnken design with three levels for each factor. The linear and the quadratic effects of the factors were studied and the interaction effects were analyzed using analyses of variance (ANOVA) and RSM. A desirability function was used to optimize the performance for the combination of the variables. The analysis showed that the linear effect of the parameters had the highest impact on the inhibition efficiency. Significant interaction effects were also identified between the operating variables. A transfer function was used to model the experimental data of inhibitor performance.

Artificial immune systems (GA-AIS) enabled power loss mitigation in distributed generation: X3PAIS optimization approaches

The distribution network is a crucial component of the power system, with industrialization driving increased energy demand. Traditional power-generating techniques, such as thermal and hydroelectric are not enough to meet this demand, leading to the development of Distributed Generation (DG). DG requires an extensive re-evaluation of the current power system, as it modifies energy losses and line flows. Inadequate integration of DG can cause power outages, disruption of protection coordination, and lead to islanding. AI can help overcome this issue by determining the best system architecture. Researchers have been interested in the Artificial Immune System (AIS) algorithm, which has room for development and lacks a fixed template. In order to improve AIS, X3PAIS, a hybridization strategy that combines clonal selection with a three-parent crossover has been developed within the scope of the study. X3PAIS was pre-tested using applications in a planetary gear train, a wastewater treatment facility, and mathematical calculations, showcasing its robustness and versatility. In the context of power distribution, X3PAIS is used in the multiple DG architecture of the power distribution system, reducing power losses by placing DG units in the best locations and sizing them to match load profiles. The four DGs' experiment results show that X3PAIS can minimize power losses by more than 89 %. To optimize power losses in the power distribution system, X3PAIS may be improved with a three-parent multiple-point crossover operation.

A hybrid SATS algorithm based security constrained optimal power flow using FACTS devices

In the realm of power systems, achieving optimal operation while ensuring security remains a paramount challenge. The security constrained optimal power flow (SCOPF) problem deals with optimizing power system operations while taking into account security limitations. Flexible alternating current transmission system (FACTS) is a system consisting of static equipment used for transmitting electrical energy in the form of AC. The static synchronous series compensator (SSSC) is a specific form of series FACTS device. The unified power flow controller (UPFC) is a FACTS device that is connected in parallel and series with a transmission line. In this research, hybrid simulated annealing and tabu search (hybrid SATS) algorithm is designed to solve SCOPF problems that involve use of FACTS devices. The combination of simulated annealing and tabu search is intended to improve algorithm's pace of convergence and the quality of its solutions. Hybrid SATS with FACTS devices are used to investigate line flow limit violations during single line failures and ensure power flows remain within their security limitations. The efficacy of proposed algorithm is demonstrated through case studies utilizing IEEE 30 bus system. These case studies demonstrate algorithm's capabilities to achieve optimal and secure power system functioning to demonstrate its effectiveness.

Quasi-one-dimensional non-equilibrium method for shock tube and stagnation line flows

Shock tube experiments are used to investigate non-equilibrium thermochemistry and radiative processes in reacting gas hypersonic flows. Boundary layer and shock structure are known to influence the spatial variation of the test slug state properties. This work derives and validates a novel method for viscous, quasi-one-dimensional, non-equilibrium flow in a shock tube assuming constant shock speed. The proposed method fully resolves the shock structure. Mirels' estimate for boundary layer growth around the test slug determines the dilation rate at the centerline. This, along with relevant boundary conditions, appropriately models core flow in a shock tube. The flow equations are discretized by finite differences on a staggered grid. The resulting highly non-linear set of algebraic equations is solved by Newton iterations. The Jacobian matrix is block tridiagonal with a Schur complement, allowing efficient inversion. This culminates in a unique and computationally efficient quasi-one-dimensional method offering improved modeling of the physical characteristics of shock tube experiments. Results of a 3 km/s, 66.6 Pa argon test case solved by a viscous, axisymmetric Navier–Stokes solution had agreement with the proposed method in temperature and pressure profiles to within 2% and post-shock velocity to within 15%. Reacting gas shock tube experiments in synthetic air and synthetic Titan atmospheres were analyzed. Radiance values in the non-equilibrium and equilibrium regions were compared under various assumptions for the shock structure and radial velocity distribution. These results highlight the necessity of a dedicated shock tube solver when analyzing shock tube thermochemistry, particularly when determining reaction rates and relaxation parameters.

Linear Scheduling Method-Based Multi-Objective Optimization for Off-Site Construction Manufacturing

Optimal production scheduling in off-site construction is hindered by the lack of comprehensive methods that simultaneously addresses workforce allocation, realistic labor productivity, workstation idle time (WIT), work-in-progress (WIP), and project completion time (PCT). To overcome these limitations, this paper introduces a hybrid planning and scheduling method that integrates the linear scheduling method reflecting workforce allocation, Monte Carlo simulation for estimating realistic labor productivity, and a multi-objective optimization model to minimize WIT, WIP, and PCT concurrently. The proposed method is validated using the Taillard instance benchmark dataset, and a panelized production line located in Edmonton, Canada. As a result, the proposed method is effective in generating realistic and optimal production schedules, achieving reductions of 5.2 % in PCT, 41.45 % in WIT, and 56.42 % in WIP. These findings are crucial for industry professionals aiming to improve efficiency in the production line and provide a foundation for further research in off-site construction scheduling.

Research on the division of heat dissipation spaces for multiple heat sources based on the adiabatic characteristic of heat flow lines

Due to the pressing need for compact layouts, the spacing between high-power devices is gradually decreasing, making the mutual influence between multiple heat sources unavoidable. Therefore, this paper proposes a method based on the adiabatic characteristics of heat flow lines and their convergence positions to evaluate the rationality of the thermal space design of each heat source. This method has been validated for applicability in one-dimensional, two-dimensional, and three-dimensional multi-heat-source conjugate convection heat transfer. Heat flow lines have significant advantages in describing energy flow, as they align with the direction of the temperature gradient. In thermal spaces with adiabatic boundaries or mutual influences between multiple heat sources, heat flow lines converge at certain positions. The relationship between adiabatic boundaries and heat flow line convergence positions has been studied, and a more interpretative decoupling scheme for multi-heat-source systems has been proposed. The main feature of this scheme is the separation of each heat source in the same steady-state thermal space and assigning adiabatic boundaries to the solid partition surfaces, allowing efficient observation of the thermal conditions of individual heat sources and targeted layout optimization. Results indicate that this method can utilize changes in heat flow line convergence positions to assess current thermal conditions and can be used to compare the thermal performance of different shaped heat sinks. Simulation results show that under the same mass conditions, thin-fin heat sinks perform 47 % better than thick-fin heat sinks, providing a more comprehensive and intuitive assessment compared to metrics such as thermal resistance and average temperature. The proposed method offers new ideas for multi-heat-source layout optimization, heat flow control, multi-heat-source partitioned simulation, and abnormal heating detection in multiple heat sources.

Vibration and Flow Characteristics of a 200 MW Kaplan Turbine Unit under Off-Cam Conditions

Kaplan turbine units can adjust their blades to achieve wider outputs without a significant loss of efficiency. The combination of guide vane angle (GVA) and blade angle (BA) is selected based on efficiency curves obtained from cam tests. However, the vibration characteristics are not considered in the test. The vibration and flow characteristics are complex with different combinations of guide vane and blade angles. Different cam relation selection principles lead to varying machine vibration and flow characteristics. In this research, the flow and vibration characteristics were obtained by means of field test and numerical simulation. Vibration, pressure pulsation, and other stability indicators have been extracted and investigated under off-cam conditions. The flow and variation rules of different indicators have been thoroughly researched. The findings suggest that the magnitude of vibration in the X direction surpassed that in the Y direction for the head cover, upper frame, and lower frame under 22 experimental conditions. The disparity between the head cover and upper frame in both directions was not significant, whereas a substantial contrast existed between the lower frame in the X and Y directions. The calculation results indicate that when the guide vane angle was small, vortices appeared near the high-pressure edge of the runner in the vaneless region and caused disorganized flow lines in the runner, and this complex vortex behavior led to multiple frequency components in the pressure pulsation frequency domain. The conclusions provide references for the designers of Kaplan turbine units and improves the operating safety of Kaplan turbine power stations.

Fitness landscapes of buffer allocation problem for production lines with unreliable machines

We study the structural properties of the buffer allocation problem from the fitness landscape perspective. We consider manufacturing flow lines with series–parallel network structure. The machines are supposed to be unreliable, their time to failure and repair time are exponentially distributed. Tentative solutions are evaluated by means of an approximate method based on the Markov models aggregation. We carry out computational experiments with local search and genetic algorithms in order to evaluate the fitness landscape properties of previously published instances and their modifications. It turns out that the so-called ‘massif central’ or ‘big valley’ structure of the fitness landscape is present but only partially: The fitness of local optima is negatively correlated with the distance to the best found solution, yet the set of local optima cannot be encompassed by a ball of relatively small size with respect to the size of solution space. Moreover, we show that in many problem instances, several clusters of local optima can be identified. The performance of genetic algorithms is discussed with respect to population clustering and the permanent usage of crossover is recommended.