Adaptive Population based Simplex - User contributions [en]

Programs

2021-02-13T21:15:15Z

MClerc:

== Codes ==
{| class="wikitable"
|-
! Name and link !! Comments !! Date
|-
| [[File:APS standard m.zip|Standard APS]] || MatLab (zipped), by Mahamed G. H. Omran || 2013-09-05
|-
| [[Media:Standard APS C.zip|Standard APS]] || C (zipped), by Maurice Clerc. Includes just an additional "tryMore" option || 2013-07-05
|-
| [[Media:Research_APS_C.zip|Research APS]] || C (zipped), by Maurice Clerc. A lot of options|| 2013-06-10
|-

|-
| [[Media:APS9.zip|APS 9]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. A version that easily beats CMA-ES and GA-MPC on the CEC2005 and CEC2011 benchmarks|| 2016-01-08
|-
| [[Media:APS11.zip|APS 11]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. Slightly modified version. Should be often better. || 2017-06-10
|-

|-
| [[Media:APS12_part_1.zip|APS 12, part 1]] || Matlab (double compression), by Maurice Clerc and Mahamed G. H. Omran. Research version. || 2018-11-14
|-
|-
| [[Media:APS12_part_2.zip|APS 12, part 2]] || Matlab (double compression) ||
|-
|-
| [[Media:MAMSO_3.zip|MAMSO]] || Multi-Agents Multi-Strategies Optimiser (Matlab/Octave) ||2021-02-13
|-

| || ||
|}

Or you may simply want to play with the "[[APS online]]" version.

File:MAMSO 3.zip

2021-02-13T21:13:45Z

MClerc:

File:MAMSO.zip

2021-01-25T21:06:03Z

MClerc:

== Licensing ==
{{GPL}}

Programs

2021-01-24T20:18:18Z

MClerc: MAMSO

== Codes ==
{| class="wikitable"
|-
! Name and link !! Comments !! Date
|-
| [[File:APS standard m.zip|Standard APS]] || MatLab (zipped), by Mahamed G. H. Omran || 2013-09-05
|-
| [[Media:Standard APS C.zip|Standard APS]] || C (zipped), by Maurice Clerc. Includes just an additional "tryMore" option || 2013-07-05
|-
| [[Media:Research_APS_C.zip|Research APS]] || C (zipped), by Maurice Clerc. A lot of options|| 2013-06-10
|-

|-
| [[Media:APS9.zip|APS 9]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. A version that easily beats CMA-ES and GA-MPC on the CEC2005 and CEC2011 benchmarks|| 2016-01-08
|-
| [[Media:APS11.zip|APS 11]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. Slightly modified version. Should be often better. || 2017-06-10
|-

|-
| [[Media:APS12_part_1.zip|APS 12, part 1]] || Matlab (double compression), by Maurice Clerc and Mahamed G. H. Omran. Research version. || 2018-11-14
|-
|-
| [[Media:APS12_part_2.zip|APS 12, part 2]] || Matlab (double compression) ||
|-
|-
| [[Media:MAMSO.zip|MAMSO]] || Multi-Agents Multi-Strategies Optimiser (Matlab/Octave) ||2021-01-24
|-

| || ||
|}

Or you may simply want to play with the "[[APS online]]" version.

Programs

2020-06-07T07:32:10Z

MClerc:

== Codes ==
{| class="wikitable"
|-
! Name and link !! Comments !! Date
|-
| [[File:APS standard m.zip|Standard APS]] || MatLab (zipped), by Mahamed G. H. Omran || 2013-09-05
|-
| [[Media:Standard APS C.zip|Standard APS]] || C (zipped), by Maurice Clerc. Includes just an additional "tryMore" option || 2013-07-05
|-
| [[Media:Research_APS_C.zip|Research APS]] || C (zipped), by Maurice Clerc. A lot of options|| 2013-06-10
|-

|-
| [[Media:APS9.zip|APS 9]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. A version that easily beats CMA-ES and GA-MPC on the CEC2005 and CEC2011 benchmarks|| 2016-01-08
|-
| [[Media:APS11.zip|APS 11]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. Slightly modified version. Should be often better. || 2017-06-10
|-

|-
| [[Media:APS12_part_1.zip|APS 12, part 1]] || Matlab (double compression), by Maurice Clerc and Mahamed G. H. Omran. Research version. || 2018-11-14
|-
|-
| [[Media:APS12_part_2.zip|APS 12, part 2]] || Matlab (double compression) ||
|-

| || ||
|}

Or you may simply want to play with the "[[APS online]]" version.

Programs

2020-06-07T07:31:13Z

MClerc: APS12

== Codes ==
{| class="wikitable"
|-
! Name and link !! Comments !! Date
|-
| [[File:APS standard m.zip|Standard APS]] || MatLab (zipped), by Mahamed G. H. Omran || 2013-09-05
|-
| [[Media:Standard APS C.zip|Standard APS]] || C (zipped), by Maurice Clerc. Includes just an additional "tryMore" option || 2013-07-05
|-
| [[Media:Research_APS_C.zip|Research APS]] || C (zipped), by Maurice Clerc. A lot of options|| 2013-06-10
|-

|-
| [[Media:APS9.zip|APS 9]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. A version that easily beats CMA-ES and GA-MPC on the CEC2005 and CEC2011 benchmarks|| 2016-01-08
|-
| [[Media:APS11.zip|APS 11]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. Slightly modified version. Should be often better. || 2017-06-10
|-

|-
| [[Media:APS12_part_1.zip|APS 12]] || Matlab (double compression), by Maurice Clerc and Mahamed G. H. Omran. Research version. || 2018-11-14
|-
|-
| [[Media:APS12_part_2.zip|APS 12]] || Matlab (double compression) ||
|-

| || ||
|}

Or you may simply want to play with the "[[APS online]]" version.

File:APS12 part 2.zip

2020-06-07T07:28:52Z

MClerc:

File:APS12 part 1.zip

2020-06-07T07:27:45Z

MClerc:

Programs

2020-06-07T07:01:08Z

MClerc: APS12

== Codes ==
{| class="wikitable"
|-
! Name and link !! Comments !! Date
|-
| [[File:APS standard m.zip|Standard APS]] || MatLab (zipped), by Mahamed G. H. Omran || 2013-09-05
|-
| [[Media:Standard APS C.zip|Standard APS]] || C (zipped), by Maurice Clerc. Includes just an additional "tryMore" option || 2013-07-05
|-
| [[Media:Research_APS_C.zip|Research APS]] || C (zipped), by Maurice Clerc. A lot of options|| 2013-06-10
|-

|-
| [[Media:APS9.zip|APS 9]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. A version that easily beats CMA-ES and GA-MPC on the CEC2005 and CEC2011 benchmarks|| 2016-01-08
|-
| [[Media:APS11.zip|APS 11]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. Slightly modified version. Should be often better. || 2017-06-10
|-

|-
| [[Media:APS12.zip|APS 12]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. Research version. || 2018-11-14
|-

| || ||
|}

Or you may simply want to play with the "[[APS online]]" version.

Papers

2018-01-26T19:27:05Z

MClerc:

Omran, Mahamed G. H., and Maurice Clerc. “[https://www.igi-global.com/article/an-adaptive-population-based-simplex-method-for-continuous-optimization/163061 An Adaptive Population-Based Simplex Method for Continuous Optimization.]” International Journal of Swarm Intelligence Research 7, no. 4 (2016): 22–49.

Omran, Mahamed G. H., and Maurice Clerc. “[https://link.springer.com/article/10.1007/s10489-017-1015-z APS 9: An Improved Adaptive Population-Based Simplex Method for Real-World Engineering Optimization Problems.]” Applied Intelligence, August 30, 2017, 1–13. doi:10.1007/s10489-017-1015-z.

Papers

2018-01-26T19:23:30Z

MClerc:

Omran, Mahamed G. H., and Maurice Clerc. “[https://www.igi-global.com/article/an-adaptive-population-based-simplex-method-for-continuous-optimization/163061 An Adaptive Population-Based Simplex Method for Continuous Optimization.]” International Journal of Swarm Intelligence Research 7, no. 4 (2016): 22–49.

Omran, Mahamed G. H., and Maurice Clerc. “[http://APS%209:%20An%20Improved%20Adaptive%20Population-Based%20Simplex%20Method%20for%20Real-World%20Engineering%20Optimization%20Problems. APS 9: An Improved Adaptive Population-Based Simplex Method for Real-World Engineering Optimization Problems.]” Applied Intelligence, August 30, 2017, 1–13. doi:10.1007/s10489-017-1015-z.

File:APS11.zip

2017-11-11T20:05:22Z

MClerc: MClerc uploaded a new version of File:APS11.zip

== Licensing ==
{{GPL}}

Papers

2017-09-18T08:23:40Z

MClerc:

Omran, Mahamed G. H., and Maurice Clerc. “[http://An%20Adaptive%20Population-Based%20Simplex%20Method%20for%20Continuous%20Optimization An Adaptive Population-Based Simplex Method for Continuous Optimization.]” International Journal of Swarm Intelligence Research 7, no. 4 (2016): 22–49.

Omran, Mahamed G. H., and Maurice Clerc. “[http://APS%209:%20An%20Improved%20Adaptive%20Population-Based%20Simplex%20Method%20for%20Real-World%20Engineering%20Optimization%20Problems. APS 9: An Improved Adaptive Population-Based Simplex Method for Real-World Engineering Optimization Problems.]” Applied Intelligence, August 30, 2017, 1–13. doi:10.1007/s10489-017-1015-z.

Papers

2017-09-18T08:18:26Z

MClerc:

Omran, Mahamed G. H., and Maurice Clerc. “[http://An%20Adaptive%20Population-Based%20Simplex%20Method%20for%20Continuous%20Optimization An Adaptive Population-Based Simplex Method for Continuous Optimization.]” International Journal of Swarm Intelligence Research 7, no. 4 (2016): 22–49.

Omran, Mahamed G. H., and Maurice Clerc. “APS 9: An Improved Adaptive Population-Based Simplex Method for Real-World Engineering Optimization Problems.” Applied Intelligence, August 30, 2017, 1–13. doi:10.1007/s10489-017-1015-z.

Programs

2017-06-10T07:12:54Z

MClerc:

== Codes ==
{| class="wikitable"
|-
! Name and link !! Comments !! Date
|-
| [[File:APS standard m.zip|Standard APS]] || MatLab (zipped), by Mahamed G. H. Omran || 2013-09-05
|-
| [[Media:Standard APS C.zip|Standard APS]] || C (zipped), by Maurice Clerc. Includes just an additional "tryMore" option || 2013-07-05
|-
| [[Media:Research_APS_C.zip|Research APS]] || C (zipped), by Maurice Clerc. A lot of options|| 2013-06-10
|-

|-
| [[Media:APS9.zip|APS 9]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. A version that easily beats CMA-ES and GA-MPC on the CEC2005 and CEC2011 benchmarks|| 2016-01-08
|-
| [[Media:APS11.zip|APS 11]] || Matlab (zipped), by Maurice Clerc and Mahamed G. H. Omran. Slightly modified version. Should be often better. || 2017-06-10
|-

| || ||
|}

Or you may simply want to play with the "[[APS online]]" version.

File:APS11.zip

2017-06-10T07:07:57Z

MClerc:

== Licensing ==
{{GPL}}

Programs

2016-09-18T12:59:10Z

MClerc:

Programs

2013-06-26T06:35:26Z

MClerc: /* Codes */

== Codes ==
{| class="wikitable"
|-
! Name and link !! Comments !! Date
|-
| Standard APS || MatLab, by Mahamed G. H. Omran || 2013-06-10
|-
| [[Media:Standard APS C.zip|Standard APS]] || C (zipped), by Maurice Clerc. Include just an additional "tryMore" option || 2013-06-25
|-
| [[Media:Research_APS_C.zip|Research APS]] || C (zipped), by Maurice Clerc. A lot of options|| 2013-06-10
|-
| || ||
|}

File:Standard APS C.zip

2013-06-25T11:54:47Z

MClerc: MClerc uploaded a new version of "File:Standard APS C.zip": There was a small bug when tryMore>0 (x_c may be not evaluated)

== Licensing ==
{{GPL}}

Talk:Presentation

2013-06-18T19:05:19Z

MClerc: /* Contraction */

== Combinatorial APS? ==
For some problems that are at least partly discrete, the basic APS applies a ''quantisation'' operator. If the quantum is $q_{d}$ for
the dimension $d$, the operator is defined by 

$$
x_{i,d}\leftarrow q_{d}\left\lfloor \left(0.5+x_{i,d}/q_{d}\right)\right.\label{eq:quantis}
$$ 

where $\left\lfloor \right.$ is the floor operator.

Now, for combinatorial problems, it is certainly better to define specific operators for Expansion, Contraction, and Local search, similarly to what has been done, for example, [http://clerc.maurice.free.fr/pso/pso_tsp/Discrete_PSO_TSP.htm for PSO].

Let us consider the canonical case in which the search space is the set of permutations of $D$ different elements. We know how to "substract" two permutations, how to "add" two permutations, how to "multiply" a permutation by a real coefficient. At first glance, it is all we need to define a combinatorial APS.

=== Local search ===
The easiest one: we just have to apply a "small" number of transpositions.

=== Expansion (reflection) ===
We have three "positions" (i.e. permutations), $X_{best}$, $X_{worst}$, and $X_{worst2}$ (the second worst), we have to combine them.
In standard this combination is
$$
Y=X_{worst2}+(X_{worst}-X_{best})\label{eq:expansion}
$$

It is formally equivalent to the PSO operator "new_position = position + velocity", for the "velocity" is anyway the difference of two positions.

=== Contraction ===
$$
Y=(1/3)*(X_{best}+X_{worst2}+X_{worst})\label{eq:contraction}
$$

--------
However, in APS, the formulae for Expansion/Reflection and Contraction are applied in fact only for some dimensions, not for all, according to an adaptive probability threshold. In order to "simulate" the same method, we should apply the combinatorial equivalent formula only on a subset of the dimensions. The difficulty is that we are then not sure that the global result is still a permutation (we may generate two times the same element). How to cope with it?

Talk:Presentation

2013-06-18T19:04:31Z

MClerc: /* Combinatorial APS? */

== Combinatorial APS? ==
For some problems that are at least partly discrete, the basic APS applies a ''quantisation'' operator. If the quantum is $q_{d}$ for
the dimension $d$, the operator is defined by 

$$
x_{i,d}\leftarrow q_{d}\left\lfloor \left(0.5+x_{i,d}/q_{d}\right)\right.\label{eq:quantis}
$$ 

where $\left\lfloor \right.$ is the floor operator.

Now, for combinatorial problems, it is certainly better to define specific operators for Expansion, Contraction, and Local search, similarly to what has been done, for example, [http://clerc.maurice.free.fr/pso/pso_tsp/Discrete_PSO_TSP.htm for PSO].

Let us consider the canonical case in which the search space is the set of permutations of $D$ different elements. We know how to "substract" two permutations, how to "add" two permutations, how to "multiply" a permutation by a real coefficient. At first glance, it is all we need to define a combinatorial APS.

=== Local search ===
The easiest one: we just have to apply a "small" number of transpositions.

=== Expansion (reflection) ===
We have three "positions" (i.e. permutations), $X_{best}$, $X_{worst}$, and $X_{worst2}$ (the second worst), we have to combine them.
In standard this combination is
$$
Y=X_{worst2}+(X_{worst}-X_{best})\label{eq:expansion}
$$

It is formally equivalent to the PSO operator "new_position = position + velocity", for the "velocity" is anyway the difference of two positions.

=== Contraction ===
$$
Y=(1/3)*(X_{best}+X_{worst2}+X_{worst})\label{eq:contraction}
$$

--------
However, in APS, the formulae for Expansion/Reflection and Contraction are applied in fact only for some dimensions, not for all, according to an adaptive probability threshold. In order to "simulate" the same method, we should apply the combinatorial equivalent formula only on a subset of the dimensions. Th difficulty is that we are then not sure that the global result is still a permutation (we may generate two times the same element). How to cope with it?

Talk:Presentation

2013-06-14T16:31:38Z

MClerc: /* Contraction */

== Combinatorial APS? ==
For some problems that are at least partly discrete, the basic APS applies a ''quantisation'' operator. If the quantum is $q_{d}$ for
the dimension $d$, the operator is defined by 

$$
x_{i,d}\leftarrow q_{d}\left\lfloor \left(0.5+x_{i,d}/q_{d}\right)\right.\label{eq:quantis}
$$ 

where $\left\lfloor \right.$ is the floor operator.

Now, for combinatorial problems, it is certainly better to define specific operators for Expansion, Contraction, and Local search, similarly to what has been done, for example, [http://clerc.maurice.free.fr/pso/pso_tsp/Discrete_PSO_TSP.htm for PSO]. It means that we have to define a distance. Let us consider the canonical case in which the search space is the set of permutations of $D$ different elements. As we know, to transform a given permutation $X$ into another one $Y$, there exists a minimum number of transpositions. So we define the quasi-distance between $X$ and $Y$ as this minimum number. Here are a few ideas of how the specific operators could be defined. In what follows, we keep the same adaptive probability $p$ threshold than in standard APS. It means that we have to modify only

=== Expansion (reflection) ===
We have three "positions" (i.e. permutations), $X_{best}$, $X_{worst}$, and $X_{worst2}$ (the second worst), we have to combine them.
In standard this combination is
$$
Y=X_{worst2}+(X_{worst}-X_{best})\label{eq:expansion}
$$

It is formally equivalent to the PSO operator "new_position = position + velocity", for the "velocity" is anyway the difference of two positions. We already know how to compute the difference of two permutations, and how to add two permutations. We could apply here these two operators. However, in APS, the above formula is applied in fact only for some dimensions, not for all, according to the probability threshold. In order to "simulate" the same method, we have to apply the combinatorial equivalent formula only on a subset of the dimensions.

=== Contraction ===
We "add" the three permutations $X_{best}$, $X_{worst}$, and $X_{worst2}$, and we "multiply" the result by 1/3.

=== Local search ===
The easiest one: we just have to apply a "small" number of transpositions.

Talk:Presentation

2013-06-14T16:31:15Z

MClerc: /* Expansion (reflection) */

== Combinatorial APS? ==
For some problems that are at least partly discrete, the basic APS applies a ''quantisation'' operator. If the quantum is $q_{d}$ for
the dimension $d$, the operator is defined by 

$$
x_{i,d}\leftarrow q_{d}\left\lfloor \left(0.5+x_{i,d}/q_{d}\right)\right.\label{eq:quantis}
$$ 

where $\left\lfloor \right.$ is the floor operator.

Now, for combinatorial problems, it is certainly better to define specific operators for Expansion, Contraction, and Local search, similarly to what has been done, for example, [http://clerc.maurice.free.fr/pso/pso_tsp/Discrete_PSO_TSP.htm for PSO]. It means that we have to define a distance. Let us consider the canonical case in which the search space is the set of permutations of $D$ different elements. As we know, to transform a given permutation $X$ into another one $Y$, there exists a minimum number of transpositions. So we define the quasi-distance between $X$ and $Y$ as this minimum number. Here are a few ideas of how the specific operators could be defined. In what follows, we keep the same adaptive probability $p$ threshold than in standard APS. It means that we have to modify only

=== Expansion (reflection) ===
We have three "positions" (i.e. permutations), $X_{best}$, $X_{worst}$, and $X_{worst2}$ (the second worst), we have to combine them.
In standard this combination is
$$
Y=X_{worst2}+(X_{worst}-X_{best})\label{eq:expansion}
$$

It is formally equivalent to the PSO operator "new_position = position + velocity", for the "velocity" is anyway the difference of two positions. We already know how to compute the difference of two permutations, and how to add two permutations. We could apply here these two operators. However, in APS, the above formula is applied in fact only for some dimensions, not for all, according to the probability threshold. In order to "simulate" the same method, we have to apply the combinatorial equivalent formula only on a subset of the dimensions.

=== Contraction ===
We "add" the three permutations $X_{best}$, $X_{worst}, and $X_{worst2}$, and we "multiply" the result by 1/3.

=== Local search ===
The easiest one: we just have to apply a "small" number of transpositions.

Talk:Presentation

2013-06-14T16:30:56Z

MClerc: /* Expansion (reflection) */

== Combinatorial APS? ==
For some problems that are at least partly discrete, the basic APS applies a ''quantisation'' operator. If the quantum is $q_{d}$ for
the dimension $d$, the operator is defined by 

$$
x_{i,d}\leftarrow q_{d}\left\lfloor \left(0.5+x_{i,d}/q_{d}\right)\right.\label{eq:quantis}
$$ 

where $\left\lfloor \right.$ is the floor operator.

Now, for combinatorial problems, it is certainly better to define specific operators for Expansion, Contraction, and Local search, similarly to what has been done, for example, [http://clerc.maurice.free.fr/pso/pso_tsp/Discrete_PSO_TSP.htm for PSO]. It means that we have to define a distance. Let us consider the canonical case in which the search space is the set of permutations of $D$ different elements. As we know, to transform a given permutation $X$ into another one $Y$, there exists a minimum number of transpositions. So we define the quasi-distance between $X$ and $Y$ as this minimum number. Here are a few ideas of how the specific operators could be defined. In what follows, we keep the same adaptive probability $p$ threshold than in standard APS. It means that we have to modify only

=== Expansion (reflection) ===
We have three "positions" (i.e. permutations), $X_{best}$, $X_{worst}$, and $X_{worst2}$ (the second worst), we have to combine them.
In standard this combination is
$$
Y=X_{worst2}+(X_{worst}-X_{best}\label{eq:expansion}
$$

It is formally equivalent to the PSO operator "new_position = position + velocity", for the "velocity" is anyway the difference of two positions. We already know how to compute the difference of two permutations, and how to add two permutations. We could apply here these two operators. However, in APS, the above formula is applied in fact only for some dimensions, not for all, according to the probability threshold. In order to "simulate" the same method, we have to apply the combinatorial equivalent formula only on a subset of the dimensions.

=== Contraction ===
We "add" the three permutations $X_{best}$, $X_{worst}, and $X_{worst2}$, and we "multiply" the result by 1/3.

=== Local search ===
The easiest one: we just have to apply a "small" number of transpositions.

Talk:Presentation

2013-06-14T16:30:19Z

MClerc: /* Combinatorial APS? */

== Combinatorial APS? ==
For some problems that are at least partly discrete, the basic APS applies a ''quantisation'' operator. If the quantum is $q_{d}$ for
the dimension $d$, the operator is defined by 

$$
x_{i,d}\leftarrow q_{d}\left\lfloor \left(0.5+x_{i,d}/q_{d}\right)\right.\label{eq:quantis}
$$ 

where $\left\lfloor \right.$ is the floor operator.

Now, for combinatorial problems, it is certainly better to define specific operators for Expansion, Contraction, and Local search, similarly to what has been done, for example, [http://clerc.maurice.free.fr/pso/pso_tsp/Discrete_PSO_TSP.htm for PSO]. It means that we have to define a distance. Let us consider the canonical case in which the search space is the set of permutations of $D$ different elements. As we know, to transform a given permutation $X$ into another one $Y$, there exists a minimum number of transpositions. So we define the quasi-distance between $X$ and $Y$ as this minimum number. Here are a few ideas of how the specific operators could be defined. In what follows, we keep the same adaptive probability $p$ threshold than in standard APS. It means that we have to modify only

=== Expansion (reflection) ===
We have three "positions" (i.e. permutations), $X_{best}$, $X_{worst}$, and $X_{worst2}$ (the second worst), we have to combine them.
In standard this combination is
$$
Y=X_{worst2}+(X_{worst}-X_{best}\label{eq:expansion}$
$$

It is formally equivalent to the PSO operator "new_position = position + velocity", for the "velocity" is anyway the difference of two positions. We already know how to compute the difference of two permutations, and how to add two permutations. We could apply here these two operators. However, in APS, the above formula is applied in fact only for some dimensions, not for all, according to the probability threshold. In order to "simulate" the same method, we have to apply the combinatorial equivalent formula only on a subset of the dimensions.

=== Contraction ===
We "add" the three permutations $X_{best}$, $X_{worst}, and $X_{worst2}$, and we "multiply" the result by 1/3.

=== Local search ===
The easiest one: we just have to apply a "small" number of transpositions.

Talk:Initialisation

2013-06-14T12:14:11Z

MClerc: Created page with "== Specific initialisation? == For PSO and DE, it has been proved that, contrarily to the intuition, the pure random initialisation is as good as more "regular" ones: O..."

== Specific initialisation? ==
For PSO and DE, it has been proved that, contrarily to the intuition, the pure random initialisation is as good as more "regular" ones: 

Omran, M. G. H.; al Sharhan, S.; Salman, A. & Clerc, M. - [http://Studying%20the%20effect%20of%20using%20low-discrepancy%20sequences%20to%20initialize%20population-based%20optimization%20algorithms Studying the effect of using low-discrepancy sequences to initialize population-based optimization algorithms], Computational Optimization and Applications, 2013, 1-24

However, it may be not the same for APS. In particular, as the method is based on simplexes of $D+1$ points, it is perfectly possible that an initialisation method using such simplexes, as "different" as possible, would be better.

Talk:Presentation

2013-06-14T09:18:05Z

MClerc: /* Combinatorial APS? */

== Combinatorial APS? ==
For some problems that are at least partly discrete, the basic APS applies a ''quantisation'' operator. If the quantum is $q_{d}$ for
the dimension $d$, the operator is defined by 

$$
x_{i,d}\leftarrow q_{d}\left\lfloor \left(0.5+x_{i,d}/q_{d}\right)\right.\label{eq:quantis}
$$ 

where $\left\lfloor \right.$ is the floor operator.

Now, for combinatorial problems, it is certainly better to define specific operators for Expansion, Contraction, and Local search, similarly to what has been done, for example, for PSO. It means that we have to define a distance. Let us consider the canonical case in which the search space is the set of permutations of $D$ different elements. As we know, to transform a given permutation $X$ into another one $Y$, there exists a minimum number of transpositions. So we define the quasi-distance between $X$ and $Y$ as this minimum number.

The specific Local search operator is the easiest one to define: we have just to apply a "small" number of transpositions.

Expansion and Contraction are a bit more difficult. For Expansion, starting from three "positions" (i.e. permutations), $X_{best}$, $X_{worst}$, and $X_{worst2}$ (the second worst), we have to combine them in order to define $Y$ so that
$$
distance(Y,X_{best}) > distance(Y,X_{worst})
$$
and 
$$
distance(Y,X_{best}) > distance(Y,X_{worst2})
$$
and we should have
$$distance(X_{best},X_{worst})+distance(X_{worst},Y)$$
as similar as possible to
$$distance(X_{best},X_{worst2})+distance(X_{worst2},Y)$$

For Contraction, the three distances $distance(Y,X_{best})$, $distance(Y,X_{worst})$, and $distance(Y,X_{worst2})$, should be as similar as possible.

Moreover, in Standard APS only some components are modified (according to a probability threshold $p$). In order to "simulate" this, we should also randomly keep only some of the components of the $Y$ given by the above methods, the other ones being still the components of $X_{best}$.

Talk:Presentation

2013-06-14T09:17:28Z

MClerc: /* Combinatorial APS? */

== Combinatorial APS? ==
For some problems that are at least partly discrete, the basic APS applies a ''quantisation'' operator. If the quantum is $q_{d}$ for
the dimension $d$, the operator is defined by 

$$
x_{i,d}\leftarrow q_{d}\left\lfloor \left(0.5+x_{i,d}/q_{d}\right)\right.\label{eq:quantis}
$$ 

where $\left\lfloor \right.$ is the floor operator.

Now, for combinatorial problems, it is certainly better to define specific operators for Expansion, Contraction, and Local search, similarly to what has been done, for example, for PSO. It means that we have to define a distance. Let us consider the canonical case in which the search space is the set of permutations of $D$ different elements. As we know, to transform a given permutation $X$ into another one $Y$, there exists a minimum number of transpositions. So we define the quasi-distance between $X$ and $Y$ as this minimum number.

The specific Local search operator is the easiest one to define: we have just to apply a "small" number of transpositions.

Expansion and Contraction are a bit more difficult. For Expansion, starting from three "positions" (i.e. permutations), $X_{best}$, $X_{worst}$, and $X_{worst2}$ (the second worst), we have to combine them in order to define $Y$ so that
$$
distance(Y,X_{best}) > distance(Y,X_{worst})
$$
and 
$$
distance(Y,X_{best}) > distance(Y,X_{worst2})
$$
and we should have
$$distance(X_{best},X_{worst})+distance(X_{worst},Y)$$
as similar as possible to
$$distance(X_{best},X_{worst2})+distance(X_{worst2},Y)$$

For Contraction, the three distances $distance(Y,X_{best})$, $distance(Y,X_{worst})$, and $distance(Y,X_{worst2})$, should be as similar as possible.

Moreover, in Standard APS only some components are modified (according to a probability threshold $p$. In order to "simulate" this, we should also randomly keep only some of the components of the $Y$ given by the above methods, the other ones being still the components of $X_{best}$.

Talk:Presentation

2013-06-14T09:08:37Z

MClerc: /* Combinatorial APS? */

Talk:Presentation

2013-06-14T09:06:30Z

MClerc: /* Combinatorial APS? */

Talk:Presentation

2013-06-14T09:04:47Z

MClerc:

Talk:Presentation

2013-06-14T09:03:12Z

MClerc: /* Combinatorial APS? */

Talk:Presentation

2013-06-13T20:55:09Z

MClerc: /* Combinatorial APS? */

Talk:Presentation

2013-06-13T20:46:07Z

MClerc: /* Combinatorial APS? */

== Combinatorial APS? ==
For some problems that are at least partly discrete, the basic APS applies a \emph{quantisation} operator. If the quantum is $q_{d}$ for
the dimension $d$, the operator is defined by 

$$
x_{i,d}\leftarrow q_{d}\left\lfloor \left(0.5+x_{i,d}/q_{d}\right)\right.\label{eq:quantis}
$$ 

where $\left\lfloor \right.$ is the floor operator.

Now, for combinatorial problems, it is certainly better to define specific operators for Expansion, Contraction, and Local search, similarly to what has been done, for example, for PSO.

Talk:Presentation

2013-06-13T20:45:14Z

MClerc: Created page with "== Combinatorial APS? == For some problems that are at least partly discrete, the basic APS applies a \emph{quantisation} operator. If the quantum is $q_{d}$ for the dimension..."

== Combinatorial APS? ==
For some problems that are at least partly discrete, the basic APS applies a \emph{quantisation} operator. If the quantum is $q_{d}$ for
the dimension $d$, the operator is defined by 

$$
x_{i,d}\leftarrow q_{d}\left\lfloor \left(0.5+x_{i,d}/q_{d}\right)\right.\label{eq:quantis}
$$ 

where $\left\lfloor \right.$ is the floor operator.

Now, for combinatorial, it is certainly better to define specific operators for Expansion, Contraction, and Local search, as it has been done, for example, for PSO.

Programs

2013-06-12T20:09:31Z

MClerc: /* Canonical flow chart */

== Canonical flow chart ==
<imagemap>
Image:Flow_chart.png|center|250px

rect 6 5 368 122 [[Initialisation|Initialisation]]
rect 198 234 563 346 [[Selection|Selection]]
rect 199 426 562 539 [[Expansion|Expansion]]
rect 198 617 563 732 [[Contraction|Contraction]]
rect 197 810 564 925 [[Local search|Local search]]
rect 134 547 268 565 [[Improvement|Improvement]]
rect 133 738 268 752 [[Improvement|Improvement]]

desc none
</imagemap>

Of course, the algorithm may stop after any phase, if a given stop criterion is met. This is not represented here, for simplicity.

== Codes ==
{| class="wikitable"
|-
! Name and link !! Comments !! Date
|-
| Basic APS || MatLab, by Mahamed G. H. Omran || 2013-06-10
|-
| [[Media:Research_APS_C.zip|Research APS]] || C (zipped file), by Maurice Clerc|| 2013-06-10
|-
| || ||
|}

Local search

2013-06-12T20:05:59Z

MClerc: Created page with "TO COMPLETE == Basic local search (l0) == Define a hypersphere around the best point of the three ones defined in the selection phase. Radius= maximum distance to the o..."

TO COMPLETE

== Basic local search (l0) ==
Define a hypersphere around the best point of the three ones defined in the selection phase. 
Radius= maximum distance to the other vertices of the simplex

The test position is chosen at random in the hypersphere. Random direction (uniform), random radius (uniform), which implies that the distribution is '''not''' random (more dense near to the centre)

Contraction

2013-06-12T20:00:57Z

MClerc: Created page with "TO COMPLETE == Basic contraction (c0) == The new test position is the gravity centre of the three points defined during the selection phase."

TO COMPLETE

== Basic contraction (c0) ==

The new test position is the gravity centre of the three points defined during the selection phase.

Reflection/Expansion

2013-06-12T19:55:31Z

MClerc: Created page with "TO COMPLETE == Basic selection (s0) == Select $D+1$ agents at random Be sure that the current one is in this list. If not, replace the last of the list by the current o..."

TO COMPLETE

== Basic selection (s0) ==
Select $D+1$ agents at random 
Be sure that the current one is in this list. If not, replace the last of the list by the current one. 

Compute the volume $V_s$ of the simplex defined by these points.

Take the three first ones, and sort them by increasing order of fitness.

Selection

2013-06-12T19:49:01Z

MClerc:

TO COMPLETE

== Basic selection (s0) ==
Select a few agents (positions), typically three 

Sort them.

Initialisation

2013-06-12T19:47:35Z

MClerc: /* Basic APS */

== Basic initialisation (i0) ==

Draw at random $N$ agents (positions) in the search space, according to an uniform distribution.

$N=\max\left(40+2\sqrt{D},\sqrt{40^{2}+\left(D+2\right)^{2}}\right)\label{eq:N_popsize}$

where $D$ is the dimension of the search space. Note that $N$ needs to be at least equal to $D+1$.

[[File:Basic APS N vs D.png|center]]

Programs

2013-06-12T19:29:44Z

MClerc: /* Basic flow chart */

== Canonical flow chart ==
<imagemap>
Image:Flow_chart.png|center|250px

rect 6 5 368 122 [[Initialisation|Initialisation]]
rect 198 234 563 346 [[Selection|Selection]]
rect 199 426 562 539 [[Expansion|Expansion]]
rect 198 617 563 732 [[Contraction|Contraction]]
rect 197 810 564 925 [[Local search|Local search]]
rect 134 547 268 565 [[Improvement|Improvement]]
rect 133 738 268 752 [[Improvement|Improvement]]

desc none
</imagemap>

== Codes ==
{| class="wikitable"
|-
! Name and link !! Comments !! Date
|-
| Basic APS || MatLab, by Mahamed G. H. Omran || 2013-06-10
|-
| [[Media:Research_APS_C.zip|Research APS]] || C (zipped file), by Maurice Clerc|| 2013-06-10
|-
| || ||
|}

Programs

2013-06-10T09:36:48Z

MClerc:

{| class="wikitable"
|-
! Name and link !! Comments !! Date
|-
| Basic APS || MatLab, by Mahamed G. H. Omran || 2013-06-10
|-
| [[Media:Research_APS_C.zip|Research APS]] || C (zipped file), by Maurice Clerc|| 2013-06-10
|-
| || ||
|}

Programmes

2013-06-10T09:36:16Z

MClerc:

Merci de consulter la [[Programs|page en anglais]].

Programmes

2013-06-10T09:34:28Z

MClerc: Created page with "Please, go to the English page."

Please, go to the [[Programs|English page]].

Programs

2013-06-10T09:32:43Z

MClerc:

:Indented line
{| class="wikitable"
|-
! Name and link !! Comments !! Date
|-
| Basic APS || MatLab, by Mahamed G. H. Omran || 2013-06-10
|-
| [[Media:Research_APS_C.zip|Research APS]] || C (zipped file), by Maurice Clerc|| 2013-06-10
|-
| || ||
|}

File:Research APS C.zip

2013-06-10T09:23:37Z

MClerc: A C version of the basic APS, but with some options for research purpose

== Summary ==
A C version of the basic APS, but with some options for research purpose
== Licensing ==
{{GPL}}

MediaWiki:Licenses

2013-06-10T09:22:36Z

MClerc: Created page with "* Unknown_copyright|I don't know exactly * Free licenses: ** MW-screenshot|MediaWiki screenshot ** PD|PD: public domain ** CC-by-sa-2.5|Creative Commons Attribution ShareAlike..."

* Unknown_copyright|I don't know exactly
* Free licenses:
** MW-screenshot|MediaWiki screenshot
** PD|PD: public domain
** CC-by-sa-2.5|Creative Commons Attribution ShareAlike 2.5
** GFDL|GFDL: GNU Free Documentation License
** GPL|GPL: GNU General Public License
** LGPL|LGPL: GNU Lesser General Public License
* Non-free license (exception):

MediaWiki:Welcome/ar

2013-06-10T07:49:45Z

MClerc: Created page with "نرحبa"

نرحبa

MediaWiki:Sidebar

2013-06-09T20:44:42Z

MClerc: