Science topic

# Optimization (Mathematical Programming) - Science topic

Explore the latest questions and answers in Optimization (Mathematical Programming), and find Optimization (Mathematical Programming) experts.

Questions related to Optimization (Mathematical Programming)

In robust optimization, random variables are modeled as uncertain parameters belonging to a convex uncertainty set and the decision-maker protects the system against the worst case within that set.

In the context of nonlinear multi-stage max-min robust optimization problems:

What are the best robustness models such as Strict robustness, Cardinality constrained robustness, Adjustable robustness, Light robustness, Regret robustness, and Recoverable robustness?

How to solve max-min robust optimization problems without linearization/approximations efficiently? Algorithms?

How to approach nested robust optimization problems?

For example, the problem can be security-constrained AC optimal power flow.

I am solving Bi-objective integer programming problem using this scalarization function ( F1+ epslon F2). I have gotten all my result correct but it says Cplex can not give an accurate result with this objective function. It says cplex may give approximate non-dominated solution not exact. As I said before, I am very sure that my result is right because I already checked them. Do I need to prove that cplex give right result in my algorithm even sometimes it did mistake in large instance?

Thanks in advance.

Hi all, I'm using CPLEX for solving VRPTW (vehicle routing problem with time window) and observe there is a huge computing time difference even when I change the problem size by just 1. By "problem size", I mean number of nodes inside problem.

For example, for 20 nodes, it took only 20 secs to solve. However, it took more than 1 hour to solve 19 nodes instance. I understand VRPTW is NP-hard and so such phenomenon is expected to happen.

The gap is still too big, I wonder if there is any technique to make computing time more consistent with problem size?

I am using MATLAB's 'fmincon' to solve some nonlinear constrained optimisation problem. But it is very slow. What are the possible ways to speed up the simulation?

What is the best alternative to 'fmincon' to speed up the optimisation process so that I can use it with MATLAB?

Are there any (commercial) optimization solvers that make use of dynamic programming techniques when useful?

I made it but it gives different values from the literature.

Bat-inspired algorithm is a metaheuristic optimization algorithm developed by Xin-She Yang in 2010. This bat algorithm is based on the echolocation behaviour of microbats with varying pulse rates of emission and loudness.

The idealization of the echolocation of microbats can be summarized as follows: Each virtual bat flies randomly with a velocity v

_{i}at position (solution) x_{i}with a varying frequency or wavelength and loudness A_{i}. As it searches and finds its prey, it changes frequency, loudness and pulse emission rate r. Search is intensified by a local random walk. Selection of the best continues until certain stop criteria are met. This essentially uses a frequency-tuning technique to control the dynamic behaviour of a swarm of bats, and the balance between exploration and exploitation can be controlled by tuning algorithm-dependent parameters in bat algorithm. (Wikipedia)What are the applications of bat algorithm? Any good optimization papers using bat algorithm? Your views are welcome! - Sundar

Hello everyone,

We have the following integer programming problem with two integer decision variables, namely x and y:

Min F(f(x), g(y))

subject to the constraints

x <= x

_{b},y <= y

_{b},x, y non-negative integers.

Here, the objective function F is a function of f(x) and g(y). Both the functions f and g can be computed in linear time. Moreover, the function F can be calculated in linear time. Here, x

_{b}and y_{b}are the upper bounds of the decision variables x and y, respectively.How do we solve this kind of problem efficiently? We are not looking for any metaheuristic approaches.

I appreciate any help you can provide. Particularly, it would be helpful for us if you can provide any materials related to this type of problem.

Regards,

Soumen Atta

Hi All,

Are there any opinions and experiences of the LocalSolver solver?

Comparing for example accuracy, speed, etc. to other solvers, etc.

Interesting to hear about them ...

/Lars

Assume, we found an approximate solution A(D),

where A is a metaheuristic algorithm, D is concrete data of your problem.

How close the approximate solution A(D) to an optimal solution OPT(D)?

I am preparing a comparison between a couple of metaheuristics, but I would like to hear some points of view on how to measure an algorithm's efficiency. I have thought of using some standard test functions and comparing the convergence time and the value of the evaluated objective function. However, any comments are welcome, and appreciated.

Hi,

I have heard - but cannot find any documents about it, that some solvers are better at utilizing the "SOS1" variable type, whereas other solvers just converts the problem into one with binaries and a few more constraints. Is that true or not?

If true - which are the solvers that are more efficient by using SOS1 instead of binaries when applicable?

/Lars

I need implement the epsilon constraint method for solve multi objective optimization problems, but I don´t know how to choose each epsilon interval and neither when to terminate the algorithm, that is to say the stopping criteria.

I have rewritten an MPC problem to a QP formulation.

The QP solvers quadprog and Gurobi, which uses the interior-point algorithm, give me the same objective function value and optimized values x, but GPAD, a first-order solver, gives me the same optimized values x, but an objective function value, which is a factor 10 bigger compared to quadprog and Gurobi. Do you anyone know a possible explanation?

I need help on Lingo programming. I have a mixed integer programming to solve it using sets in Lingo. One of the constraints is :

S(i,k,w)>=m(i,j)*X(i,t) , for i=1,...,I ; j=1,...,J; t=1,..,T;

k=t+K(j,w)-1,..,t+K(j,w)+S(j)-2 ; w=1,..,W.

Here m(i,j), K(j,w) and S(j) are parameters.

The problem is i do not know how to enter index k using sets in Lingo.

Any help would be highly appreciated.

I'm currently working on an optimization problem (please see attached file).

Any tipps to linearize the objective function? Please note that a,b and c are real constants.

Thanks!

Dear Pierre Le Bot Thank you for introducting resources Please could i ask you If it's possible to answer these 2 questions : 1. What's the practical implication of CICA? and please mention some CICA for worker's hand cut off senario due to conveyor belt stiking in 2. After multiplying the results of 3 parameters (No reconfiguration probability -sf -cica) and obtaining a probability number , how the obtained probability number is interpreted? regards

I want to calculate distance distribution a point with distance d from the center of the circle to some random points uniformlly distributed in same circle so that the distribution function is dependent on distance d from the center of the circle, How can I calculate it?

...I read geometrical probability book but in this book two random points in circle investigated.

If there are at least 4-5 factors to consider, there will be too many samples. I have read something about 2k factorial level design, and some researchers used to screen out the important factors.

Consider the following elementary maximization problem:

\begin{align}

f{=}\mathrm{argmax}_{y_{l,c}, p_{l,c}}~\sum_{l=1}^{L}\sum_{c=1}^{C} y_{l,c}\text{log}_2\left(1+\frac{p_{l,c}}{I_{l,c}}\right)

\end{align}

s.t.,

\begin{align}

\sum_{l=1}^{L}y_{l,c}\leq 1

\end{align}

\begin{align}

\sum_{c=1}^{C}p_{l,c}\leq P_{max} \qquad \forall l

\end{align}

\begin{align}

\sum_{l=1}^{L}\sum_{c=1}^{C} \text{log}_2\left(1+\frac{I_{l,c}}{p_{l,c}}\right) \geq R_c

\end{align}

where, $l=1,2, \ldots L$, and $c=1, 2, \ldots C$

My questions are as follows:

1. Can I solve this problem as non-linear optimization?

2. I want to use generalized reduced gradient (GRG) method. Is it the correct approach? Can I transform this problem to minimization objective function?

3. Can any other optimization method be followed? Some suggestion.

What is the best method to solve Multiobjective Optimization , weight, bounded, goal....etc ?

I'm using optimization tool box in Matlab to solve multi-objective optimization, I have linear and nonlinear constraint, after running the optimization, I got Pareto front (see the file attached in this message), increasing the population size give me the same result.

what do you think ?

I have seen many scholars use CPLEX solver in GAMS as they can solve the problem with ILOG CPLEX software. So in this case,they should possesses same results?

Hi,

I am working with a

**VERY**large scale LP -- so large that simplex method takes forever to run. I've developed an efficient numerical algorithm to exploit the problem structure to significantly reduce the running time.The problem is, my application requires basic solutions. For now, I am using crossover, that is, take the optimal primal and dual solutions (numerical) from my algorithm, give them to a simplex solver, and use good old simplex to solve it to get basic solutions. This works well, but it's still a bit too slow, as most of the running time are used in the crossover phase.

So my question is, is there any other algorithm in the literature that can produce basic solution given a numerical solution with high accuracy?

Thanks,

Alex

Hello Everyone,

I have been asked from a reviewer to apply our metaheuristic on an industrial or a real-world problem (in addiition to the CEC benchmarks).

We are working in the continuous space of variables, with unconstrained optimization, Hence, we need some benchmarks for any industrial or real-world problems.

Could any one please help in this matter?

Thank you in advance

When I read an article about supply chain design, three constraints which contains an uncertain operator "M". I think this "M" would be adaptive in optimization process, but I don't know how to find out the most suitable value to make these constraints tight.

**First Constraint:**inventory position <= reorder point + operator "M"*(1-binary decision variable).

**Explain:**If the inventory position <= reorder point, an procurement order need to be issued, so the binary decision variable = 1.

if the inventory position > reorder point, no procurement order is needed, so the binary decision variable = 0.

**Second Constraint:**logistics volume <= M*binary decision variable.

**Explain:**if the binary decision variable = 1, the logistics is allowed.

Therefore, the operator "M" is uncertain, how can I sure this value? Or how can I interpret this operator.

I attached this article, these equations are Eq. (20), Eq. (26), and Eq. (28).

Thanks! Longing for your reply.

I have formulated optimization problem for building, where cost concerns with energy consumption and constraints are related to hardware limits and model of building. To solve this formulation, I need to know if problem is convex or non-convex, to select appropriate tool to solve the same.

Thanks a million in advance.

Can anyone suggest me references about converting a constrained optimal control problem to an optimization problem?

I have seen problems being solved by this method, but I haven't been able to find an algorithm or set of instructions for the conversion process. I want to solve the problem using MATLAB fmincon function.

what is exactly the difficulty imposed by non-linear cosntraints relatively to linear ones for a multi-objective optimization genetic algorithm ?

Hello I am using MATLAB interfacing to read and write in Gams file. I am doing multi objective optimization. My first objective function i solved with MIP while second objective function required MINLP. Due to Limitation in license i cant optimize MINLP. Can someone tell me if possible to test my both files (.gms and .m ) online ??

Hi, I m developing to PSO algorithm in a set of integers numbers, but I cant apply the updating of speed

v(t)=v(t-1)+ (pBest -x(t)) + (gBest -x(t))

x(t)=v(t)+x(t-1)

Because each element of set is a number between 0-499. Then If you are adding 2 elements of diferent vector or particle, the result exceeds the high limit 500.

Then I might define to operators of add and rest , Do you help me with your experience in PSO.?

I am looking for Matlab code for Ant colony optmization or Simulated annealing which can handle mixed integer variables.

Thanks.

Suppose I am optimizing ZDT-1 2 objective test function. I want to stop the algorithm when there is no significant improvement in Pareto front. how can I achieve this?

The desired random vector is a series of number between [Xmin, Xmax] with N elements. For instance, [1 3 2 5 9 4] can be considered a random vector while N=6, Xmin=1 & Xmax=10.

Exploiting MATLAB,

**"randi([Xmin Xmax],1,N)"**can produces this vector**but**the vector probably includes similar elements randomly. For example:[1 3

**2 2**9 4], [1**3**2**3**9 4] , [1**9**2 5**9**4] or [**4**3 2 5 9**4**]**So, How I can generate a random vector without similar elements?**

Note that, I know by using

**if,for and loop programming syntax's, I**can revise the vector but I have to avoid loops in my MFILE!does Matlab R2014a support nonlinear constraint in multi objective optimization using optimization toolbox?

Thank you

How to write multiple nonlinear constraints?

I am trying to develop a long haul intermodal transportation route considering 4 countries for a research paper. Before processing with mixed integer linear programming (MILP) model, I need to calculate travel distance between cities and respective travel time. I prefer to work on R.

Unfortunately the OSRM package is not working on my R version.

Can anyone please suggest any alternative?

Given a minimization problem, i want to compute the lower bounds and upper bounds for the optimal solution to lie in. i have a scalar valued function f(x1,x2,... , xn). Then suppose i use GA, PSO etc. to minimize it. The algorithm outputs me some answer it thinks is good. i want to compute best possible lower and upper bounds but mostly lower bounds to make sanity check on the solution generated. What are the available methods to compute such bounds for the optimal solution on minimization problems? Assume both cases when f is differentiable and not. Second is of more importance to me. please suggest some seminal papers that do a good job at this.

Solving large multi-stage stochastic problems may become intractable. There are some applications permit to solve such problems, among which "non-anticaptivity principle", "decomposition techniques", "lagrangian relaxation", and lately "optimal condition decomposition" are the most known ones. In this regard, what are the advantages and disadvantages of the "scenario reduction techniques" attribute to mentioned techniques to reduce computational burden as well as complexity with a good approximation to the original stochastic optimization problem? In advance, I'd appreciate your supportive message.

I am using multi-objectve GA toolbox in Matlab to optimize 3 objective function. I can plot pareto two objective each time, but I am unable to plot the pareto fronts of 3 objectives together.

Thanks in advance

My question goes from the explained in the attached document. It's about image denoising using regularization, with constraints. I used the Lagrange multipliers formulation, but, by obtaining the numerical solution, can't get the regularization parameter (Lagrange multiplier) as should be theoretically expected .

Any suggestion would be much appreciated.

Thanks in advance,

Miguel Tavares

Hi all, I would like some advice on efficiently resolving the QP problems that arise in Bundle methods at each iteration. As you may know, between iterations new affine constraints get added and the QP objective is also modified. It would be great if you can point me to an efficient implementation or suggest what best can be done with existing commercial software packages for optimization. Currently, I use CPLEX to solve each QP problem, however my guess is not much information is being re-used between iterations. Any suggestions to improve the performance?

I still confuse about how to determine the first population of fireflies in firefly algorithm for optimization to start the iteration

If anyone know about NSGA|| evolutionary algorithm then please let me know why crowded distance is not used in initial condition for the generation of the offspring.?

Global optimisation techniques

Let say you have obtained a Pareto front through a certain MOEA and you want to check every solution in that front against certain criterion. Will it be sound (correct) to use VIKOR in such a comparison if you consider each solution as a possible alternative?

Suppose we have to algorithm (A and B) to solve a multi-objective problem. Each algorithm provides a set of solutions. Which statistical test is appropriate to compare these algorithms? Is Wilcoxon test appropriate?

I am trying to maximize an efficiency function which is fractional in nature, through power allocation. It is already known that the function has an uni modal behavior with respect to power allocated. In this case, should I go for Dinkelbach's method of first converting it into a convex function and then optimize or can I go for other search methods(both direct and indirect ) to locate the peak value? Most papers (almost all) have tackled these types of problem by Dinkelbach's method. Some body please suggest a soution

I know that if we have a leader-follower game, and the follower's problem has inequality and equality constraints, it is considered a MPEC problem. What if the follower has an unconstrained problem, would it also be classified as MPEC? what if it has equality constraints only? wouldn't they be special cases of the problem with inequality constraints.

My understanding is that:

MPEC: problems with equality and inequality constraints

MPCC: problems with inequality constraints only (complementarity)

EPEC: problems with multiple leaders and equality and inequality constraints

Please correct me if i'm wrong. If so, please provide a source or chart that explains the difference with a complete list.

in my current work i employ the GA optimisation method in matlab to search for the best solution, hwoever i find that the GA method easily converges to local optimum but not global one, especially when this local optimum is very close to global optimum, could you help to explain how this happend, and how i can improve the GA method to avoid converging to the local optimum? thank you!!

Instead of converging to the max value the binary matrix is very random and the next random particle position (0,1) of the sigmoid function causes the objective to be be very low. Is this normal for BPSO. How does the solution converge for BPSO.

Hi dear all. Full description of my problem is in the attached pdf file.

I want to compare the SI techniques such as ACO, PSO, FA, TLBO,SA, DEM ABC,HS,ICA,IWO,CA,IFA,CS,SSO. For comparison I am using becnhmark functions as sphere,rosenbrock and ackley. Further I am taking constants as fixed no of iterations,max and min value.

While doing this even if I specigiy the range of [-10,10] I get optimized value as 784. Is it Correct?

I am current doing research on global optimization and test my algorithm on benchmark function on both unimodal and multimodal (eg: Sphere function, Rosenbrock function, Schaffer function and ect.).

I am thinking it could be best if I can implement my algorithm on real-life application other than benchmark functions. So, could somebody recommend me few recent hot global optimization problems (prefer continuous problem)?

Hello,

I am currently trying to create a compliant mechanism by topology optimization in Abaqus 6.14-1, but I am already stuck at the standard examples from literature.

Take the compliant gripper for example. I understand the theory of maximizing the geometrical advantage (GA = F

_{out}/F_{in}, or GA = u_{out}/u_{in}), while constraining the volume and input displacement.My problem is implementing the geometrical advantage into Abaqus. How can I add the geometrical advantage to the design responses? Under "single-term" I can (obviously) not find the GA.

Under "combined-term" I could (in theory) combine the two single-term displacements or forces, but a division or multiplication is not possible. Just "substract", "absoulte difference" and "weighted combination".

Any help how to implement the GA would be really appreciated! :-)

Best regards

Rene Moitroux

Hi to all ,

What is the interpretation of the pareto front graph when using a two-objective genetic algorithm (gamultiobj) in matlab . and how to choose one best individual from final points

Best regards

Last years for continuous multi-extremal optimization were developed a few random search oriented methods. There are Simulated Annealing and Genetic algorithms (implemented on the Matlab Global Optimization Toolbox), Ant Colony method, Cross-Entropy Method (see, e.g., https://www.researchgate.net/publication/225551595_The_Cross-Entropy_Method_for_Continuous_Multi-Extremal_Optimization ), etc. But a lot of researches yet often use traditional, gradient-based methods, as Newton-Raphson. The main drawback of these methods is that they, by their nature, do not cope well with optimization problems that have non-convex objective functions and/or many local optima. Optimization results essentially depend of the initial point selection. So, please, explain me, why researches don’t use random search oriented methods ?

Dears

I look for algorithms that resolve a sequencing problem (we need to minimize Cmax) with the following conditions:

1. m similar machines, when each one has a different capacity Ci

2. n job, when each one has a different process time Tj and a different priority Pj

Any contribution or suggestion is more than welcome.

Let's say the initial population in NSGA ii is i.i.d and uniformly distributed. Has anyone done research about what we can say about the distribution after k iterations in NSGA ii? The individuals are surely no longer i.i.d but are there asymptotic results for large populations sizes?

I am working on this project currently and I am not able to find any flowchart/algorithm for Dial a ride problem in order to code it in Matlab.Please do share any thesis papers/literature review if you have any.

I am using GAMS for solving a MILP problem which includes binary variables. However there is a problem in the solution. Surprisingly, I have seen that one of the binary variables in the solution has a found value of "-1" another one "2". That is not acceptable and logical. I do not know what happened. GAMS gives me the message primal infeasible."resolved with fixed discrete variables"

code has attached.

Hi,

I am working on optimization approaches on an intersection. And I have been getting some questionnable results on the simulator. I get some high troughputs of vehicle in the intersection but with big average delay of vehicles e.g :

In a scenario I get a throughput of 4544 with an average delay of 31.22 seconds and average queue length per phase of 41 meters

And in another scenario I get a 4551 throughput with an average delay of 31.26 seconds with an average queue length per phase of 39.68 meters

This compared to the average study of the same intersection we see different results, e.g in a scenario a throughput of 4343 with an average delay of 30.7 seconds and an average queue length per phase of 21.1 meters.

I am starting to question my results performance. Doesn't higher throughput mean minimum average delay and lesser queues on lanes ?

My problem is like, three objective equation

**\sum_{i=1,6;j=1,3} C**and six constraints like_{i,j}x^{-2}_{i}**\sum_{i=1,6; j=1,6} D**. Both the case_{i,j}x^{-2}_{i}==a_{i,j}**j**refers number of equations. How maximize the three objective equation simultaneously?I have used epsilon constraint method as well ass the sum weighted method to find Pareto point for bi-objective model;in this case I have found same results ,same number of Pareto points,

can we claim which our bi-objective model is not non-convex if the results raised from epsilon constraint method and the sum weight method are same?

I'm solving an optimization problem with two heterogeneous objective functions. The first one is a mixed-integer linear function and the second one is linear-fractional. How to combine these two functions and obtain a single objective function?

Would you say always the upper bound obtained in Dantzig Wolfe decomposition is better than upper bound in lagrangian relaxation method ( minimization) and lower bound conversely?

The solution of bi-level model is too hard. Generally, duality, decomposition and evolutionary algorithms are used for solving.

i have convex problem that start solved for first 50 iteration the after that its go to inaccurate solved .How to resolve the problem?

For both Bayesian and Frequentist expected loss, is the parameter an index of the data to which to make decisions on, or a state of nature?

Are there examples where a loss function is mapped using a vector of real observations to show what the parameter looks like?

I would like to write a multi objective function for optimizing several variables. However, I would like only certain objective functions effect certain optimization variables. For example, for a multi objective function of F = [f1 f2 f3] and optimization variables x = [x1 x2 x3], I would like x1 to be effected by f1 but not f2 or f3 etc. Optimization of all the variables should be performed together and I cannot assume that x2 and x3 for example are constant while I optimize for x1 . Is there an optimization algorithm that can handle this problem?

Thanks,

What is use of xmax in Quantum integrated Particle Swarm Optimization (QPSO)? How can I define xmax in QPSO? How it signifies QPSO?

In multi objective optimization, when I change the value of one constant in objective function I am getting pareto front for some xyz constants and for another set of constants, i am not getting any pareto front(pareto converges to point). So is this possible??

I have a symbolic integral with symbolic parameters (x(1), x(2),x(3),t). I am trying to fit this symbolic integral to experimental data and acquire those parameteres (x(1),x(2),x(3)). I tried to use fminsearch or fmincon; however, I couldn't use them and I faced different errors. for example: is not a valid MATLAB expression, has non-scalar coefficients, or cannot be evaluated: Error while trying to evaluate FITTYPE function. I attach my code. would you please help me to solve this error.

Thanks

clear all;

clc;

%%

beta=0.002;

alfa=0.004;

nu=0.49;

del=0.010;

t0=1.35;

syms eta G1 G2 A s t taw

x=sym('x',[1 3]);

p1=(eta)/(G1+G2);

q1=(2*G1*eta)/(G1+G2);

q0=(2*G1*G2)/(G1+G2);

B1=(2*G1*(1+nu))/(3*(1-2*nu));

B2=(2*G2*(1+nu))/(3*(1-2*nu));

B3=(2*eta*(1+nu))/(3*(1-2*nu));

q2=3*B1*B2/(B1+B2);

q3=B3/(B1+B2);

q4=3*B1*B3/(B1+B2);

Pc1=1+p1*A;

Qc1=q0+q1*A;

Pc2=1;

Qc2=q2;

f1=Pc1*Qc2*Pc1+2*Pc1*Pc2*Qc1;

c1 = coeffs(f1, A);

c1=simplify(c1);

f2=2*Pc1*Qc1*Qc2+Qc1*Pc2*Qc1;

c2=coeffs(f2,A);

c2=simplify(c2);

GG2=ilaplace((4*beta/(3*t0*sqrt(alfa)))*del*(c2(1,3)*s^2+c2(1,2)*s+c2(1,1))/((c1(1,3)*s^3+c1(1,2)*s^2+c1(1,1)*s)), t);

GGs2=subs(GG2, t, t-taw);

GGss2=subs(GGs2, {G1,G2,eta}, {x(1),x(2),x(3)});

assume(x(1) > 0)

assume(x(2) > 0)

assume(x(3) > 0)

assume(x(1),'real')

assume(x(2),'real')

assume(x(3),'real')

force2=int(GGss2*diff(taw^1.5,taw),taw,0,t0,'IgnoreAnalyticConstraints',true);

t0=[2 12 22 32 42 52 62 72 82 92 102 112];

F0=[0.77618 0.7259 0.70212 0.7011 0.69315 0.69324 0.67682 0.67658 0.67618 0.67669 0.67623 0.66831];

B2 = simplify(force2);

F2 = matlabFunction(B2,'vars', [{x(1),x(2),x(3)},t]);

%---------------------------------Error------------------------------------

funcfit1=fittype(F2,'indep','t','coefficients', {'x1','x2','x3'});

%--------------------------------------------------------------------------

F22=subs(numinteg, t, t0);

% fminsearch algorithm

fun = sum((F0-F22).^2);

%starting guess

pguess = [1000,1000,1000];

%optimise

[p,fminres] = fminsearch(fun,pguess)