Global optimization of mixed-integer nonlinear programming for engineering design problems

Wang, Pei-Chun; Tsai, Jung‐Fa

doi:10.1109/icsse.2011.5961909

“…Stepped Cantilever Beam Design The design variables of a stepped cantilever beam are the widths and depths of rectangular cross-sections. The objective of this problem is to minimize the volume of the beam under static loading [27]. This is a mixed-integer design problem having 10 variables and 11 constraints, where x 1 and x are integer, x 3 to x 6 are discrete and the remaining are continuous.…”

Section: Speed Reducer Designmentioning

confidence: 99%

“…We set G max = 1000. The comparative results from our mCDE with genetic algorithm, GA [9], and linearization techniques method [27] are shown in Table 7. From the Tables 4 -7, it is found that mCDE is competitive with other solution methods when solving engineering design problems.…”

Section: Speed Reducer Designmentioning

confidence: 99%

Modified Constrained Differential Evolution for Solving Nonlinear Global Optimization Problems

Azad

¹

,

Fernandes

²

2013

Studies in Computational Intelligence

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Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolution has shown to be very efficient when solving global optimization problems with simple bounds. In this paper, we propose a modified constrained differential evolution based on different constraints handling techniques, namely, feasibility and dominance rules, stochastic ranking and global competitive ranking and compare their performances on a benchmark set of problems. A comparison with other solution methods available in literature is also provided. The convergence behavior of the algorithm to handle discrete and integer variables is analyzed using four well-known mixed-integer engineering design problems. It is shown that our method is rather effective when solving nonlinear optimization problems.

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“…We use Optimization Interface Toolbox (OPTI toolbox) for solving this mixed integer non-linear programming (MINLP) problem. Lot of applications of MINLP are in engineering design problems, operations research and management [111,112]. OPTI toolbox is based on mesh adaptive direct search (MADS) [113][114][115][116][117] and we are using it for solving our optimization problem, which has not been used in M2M research for optimization of channel access and resource allocation.…”

Section: Introductionmentioning

confidence: 99%

Resource allocation in clustered M2M networks: a q-learning approach

Hussain¹

2021

Preprint

1

0

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Machine to machine (M2M) communication has received increasing attention in recent years. A M2M network exhibits salient features such as large number of machines/devices, low data rates, delay tolerant/sensitive, small sized packets, energy-constrained and low or no mobility. A large number of M2M terminals may exist in a small area with many trying to simultaneously and randomly access for channel resources - which will result in overload and access problem. This increased signaling overhead and diverse requirements of machine type communication devices (MTCDs) call for the development of flexible and efficient scheduling and random access techniques. In this thesis, we first review and compare various scheduling and random access techniques in LTE-based cellular networks for M2M communication. We also discuss how successful they are to fulfill the unique requirements of M2M communication and networking. Resource management in M2M networks with a large number devices is also reviewed from the access point of view. We propose a multi-objective optimization based solution to the problem of resource allocation in interference-limited M2M communication. We consider MTCDs in a clustered network structure, where they are divided into clusters and the devices belonging to a cluster communicate to cluster head (or controller). We maximize the number of admitted MTCD controllers and throughput with least interference caused to conventional primary users. We formulate the problem as a mixed-integer non-linear problem with multiple objectives and solve it using meshed adaptive direct search (MADS) algorithm. Simulation results show the effects of varying different parameters on cumulative throughput and the number of admitted iii MTCD controllers. We then formulate the slot selection problem in M2M networks with admitted MTCDs as an optimization problem. We present a solution using the Q-learning algorithm to select conflict-free slot assignment in a random access network with MTCD controllers. The performance of the solution is dependent on parameters such as learning rate and reward. We thoroughly analyze the performance of the proposed algorithm considering different parameters related to its operation. We also compare it with simple ALOHA and channel-based scheduled allocation and show that the proposed Q-learning based technique has a higher probability of assigning slots compared to these techniques. We then present a block based Q-learning algorithm for the scheduling of MTCDs in clustered M2M communication networks. At first centralized slot assignment is done and an algorithm is proposed for minimizing the inter-cluster interference. Then we propose to use an Q-learning algorithm to assign slots in a distributed manner and comparison is made between the two schemes. Afterwards, we show the effects of distributed slot-assignment with respect to varying signal-to-interference ratio on convergence rate and convergence probability. Cumulative distribution function is used to study the effect of various SIR threshold levels on the convergence probability. With the increase in SIR threshold levels, increase in convergence time and decrease in convergence probability are observed, as less block configuration fulfills the required threshold in the M2M network.

show abstract

“…We use Optimization Interface Toolbox (OPTI toolbox) for solving this mixed integer non-linear programming (MINLP) problem. Lot of applications of MINLP are in engineering design problems, operations research and management [111,112]. OPTI toolbox is based on mesh adaptive direct search (MADS) [113][114][115][116][117] and we are using it for solving our optimization problem, which has not been used in M2M research for optimization of channel access and resource allocation.…”

Section: Introductionmentioning

confidence: 99%

Resource allocation in clustered M2M networks: a q-learning approach

Hussain¹

2021

Preprint

0

View full text Add to dashboard Cite

Machine to machine (M2M) communication has received increasing attention in recent years. A M2M network exhibits salient features such as large number of machines/devices, low data rates, delay tolerant/sensitive, small sized packets, energy-constrained and low or no mobility. A large number of M2M terminals may exist in a small area with many trying to simultaneously and randomly access for channel resources - which will result in overload and access problem. This increased signaling overhead and diverse requirements of machine type communication devices (MTCDs) call for the development of flexible and efficient scheduling and random access techniques. In this thesis, we first review and compare various scheduling and random access techniques in LTE-based cellular networks for M2M communication. We also discuss how successful they are to fulfill the unique requirements of M2M communication and networking. Resource management in M2M networks with a large number devices is also reviewed from the access point of view. We propose a multi-objective optimization based solution to the problem of resource allocation in interference-limited M2M communication. We consider MTCDs in a clustered network structure, where they are divided into clusters and the devices belonging to a cluster communicate to cluster head (or controller). We maximize the number of admitted MTCD controllers and throughput with least interference caused to conventional primary users. We formulate the problem as a mixed-integer non-linear problem with multiple objectives and solve it using meshed adaptive direct search (MADS) algorithm. Simulation results show the effects of varying different parameters on cumulative throughput and the number of admitted iii MTCD controllers. We then formulate the slot selection problem in M2M networks with admitted MTCDs as an optimization problem. We present a solution using the Q-learning algorithm to select conflict-free slot assignment in a random access network with MTCD controllers. The performance of the solution is dependent on parameters such as learning rate and reward. We thoroughly analyze the performance of the proposed algorithm considering different parameters related to its operation. We also compare it with simple ALOHA and channel-based scheduled allocation and show that the proposed Q-learning based technique has a higher probability of assigning slots compared to these techniques. We then present a block based Q-learning algorithm for the scheduling of MTCDs in clustered M2M communication networks. At first centralized slot assignment is done and an algorithm is proposed for minimizing the inter-cluster interference. Then we propose to use an Q-learning algorithm to assign slots in a distributed manner and comparison is made between the two schemes. Afterwards, we show the effects of distributed slot-assignment with respect to varying signal-to-interference ratio on convergence rate and convergence probability. Cumulative distribution function is used to study the effect of various SIR threshold levels on the convergence probability. With the increase in SIR threshold levels, increase in convergence time and decrease in convergence probability are observed, as less block configuration fulfills the required threshold in the M2M network.

show abstract

Global optimization of mixed-integer nonlinear programming for engineering design problems

Cited by 4 publications

References 35 publications

Modified Constrained Differential Evolution for Solving Nonlinear Global Optimization Problems

Modified Constrained Differential Evolution for Solving Nonlinear Global Optimization Problems

Resource allocation in clustered M2M networks: a q-learning approach

Resource allocation in clustered M2M networks: a q-learning approach

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