model data for liu instance (12cde804) · Commits · miplib2017 / revised-submissions-final

miplib2010_liu/models/liu8_9.mai

0 → 100644

+210 −0

Original line number	Diff line number	Diff line
		From xiaowenl@twolf13.ee.washington.edu Mon Aug 7 11:55 PDT 1995
		Received: from dizzy.cplex.com (dizzy) by sierra with ESMTP
		(1.37.109.16/16.2) id AA057161731; Mon, 7 Aug 1995 11:55:31 -0700
		Return-Path: <xiaowenl@twolf13.ee.washington.edu>
		Received: from twolf13.ee.washington.edu by dizzy.cplex.com via SMTP (950511.SGI.8.6.12.PATCH526/cplex.950313)
		for <ed@cplex.com> id NAA29552; Mon, 7 Aug 1995 13:35:14 -0400
		Received: by twolf13.ee.washington.edu
		(5.65/UW-NDC Revision: 2.30 ) id AA04565; Mon, 7 Aug 1995 10:33:52 -0700
		From: Xiaowen Liu <xiaowenl@twolf13.ee.washington.edu>
		Message-Id: <9508071733.AA04565@twolf13.ee.washington.edu>
		Subject: questions about MIP
		To: ed@sierra
		Date: Mon, 7 Aug 1995 10:33:52 -0700 (PDT)
		X-Mailer: ELM [version 2.4 PL23]
		Mime-Version: 1.0
		Content-Type: text/plain; charset=US-ASCII
		Content-Transfer-Encoding: 7bit
		Content-Length: 911
		Status: RO

		Hi Ed,

		I presented my problem using CPLEX two months ago. It never
		gives me an optimal result when the integer variables are large.

		I think CPLEX ran too fast and didn't try enough branches.
		Is there any parameter I can set to let CPLEX run slower?
		Right now, I don't care the running time so much, but I
		do care about the final result.

		The parameters I set in my running experiment is:
		1. set mip strategy backtrack 1.0
		2. set mip strategy nodeselect 2
		3. set mip strategy variableselect 1
		The above settings gives me the best result I have got so far.
		Unfortunately, they are still not optimal.

		I need your help to figure it out. Any suggestions and comments
		will be highly appreciated. Thank you.

		Xiaowen
		-------------
		Xiaowen Liu
		Electrial Engineering Bldg, Rm #329
		University of Washington
		Box 352500
		Seattle, WA 98195-2500
		Email: xiaowenl@twolf13.ee.washington.edu
		Tel: (206)685-8678 (O)


		From xiaowenl@twolf13.ee.washington.edu Wed Aug 9 11:30 PDT 1995
		Received: from twolf13.ee.washington.edu by sierra with SMTP
		(1.37.109.16/16.2) id AA105933003; Wed, 9 Aug 1995 11:30:03 -0700
		Return-Path: <xiaowenl@twolf13.ee.washington.edu>
		Received: by twolf13.ee.washington.edu
		(5.65/UW-NDC Revision: 2.30 ) id AA10877; Wed, 9 Aug 1995 11:26:46 -0700
		From: Xiaowen Liu <xiaowenl@twolf13.ee.washington.edu>
		Message-Id: <9508091826.AA10877@twolf13.ee.washington.edu>
		Subject: Re: questions about MIP
		To: ed@sierra (Ed Klotz)
		Date: Wed, 9 Aug 1995 11:26:45 -0700 (PDT)
		Cc: Xiaowenl@twolf13.ee.washington.edu
		In-Reply-To: <199508091650.AA102567032@sierra> from "Ed Klotz" at Aug 9, 95 09:50:32 am
		X-Mailer: ELM [version 2.4 PL23]
		Mime-Version: 1.0
		Content-Type: text/plain; charset=US-ASCII
		Content-Transfer-Encoding: 7bit
		Content-Length: 599
		Status: RO

		Hi Ed,

		Thank you very much for your mail.

		I slightly changed my formulation. I can get 1360 by setting
		backtracking 1
		nodeselect 2
		variableselect 1
		But this is not optimal yet.

		I am going to mail you a brief description of my problem formulation
		in my next mail. If you have any questions about that, please let me
		know. Also, I will send you a new LP format file I have current.

		Thank you very much.

		Xiaowen

		--
		Xiaowen Liu
		Electrial Engineering Bldg, Rm #329
		University of Washington
		Box 352500
		Seattle, WA 98195-2500
		Email: xiaowenl@twolf13.ee.washington.edu
		Tel: (206)685-8678 (O)


		From xiaowenl@twolf13.ee.washington.edu Wed Aug 9 11:31 PDT 1995
		Received: from twolf13.ee.washington.edu by sierra with SMTP
		(1.37.109.16/16.2) id AA106013090; Wed, 9 Aug 1995 11:31:30 -0700
		Return-Path: <xiaowenl@twolf13.ee.washington.edu>
		Received: by twolf13.ee.washington.edu
		(5.65/UW-NDC Revision: 2.30 ) id AA10887; Wed, 9 Aug 1995 11:28:13 -0700
		From: Xiaowen Liu <xiaowenl@twolf13.ee.washington.edu>
		Message-Id: <9508091828.AA10887@twolf13.ee.washington.edu>
		Subject: problem formulation
		To: eklotz@sierra
		Date: Wed, 9 Aug 1995 11:28:13 -0700 (PDT)
		Cc: xiaowenl@twolf13.ee.washington.edu (Xiaowen Liu)
		X-Mailer: ELM [version 2.4 PL23]
		Mime-Version: 1.0
		Content-Type: text/plain; charset=US-ASCII
		Content-Transfer-Encoding: 7bit
		Content-Length: 3598
		Status: RO


		Hi Ed,

		The following is a brief description of my problem formulation.

		I am working on the floorplan and placement problem in the
		physical design of VLSI circuits. The floorplan and placement
		is to place a set of rectangular modules(or blocks) on a chip.
		we know the initial topology of the modules, and want to locally
		swap the modules and/or orientate the modules such that the total
		area of the chip is minimized and there is no overlaps between
		between any two modules.

		We are trying to use Integer Programming to optimize the area.
		The problem formulation is described in the following.

		To prevent overlapping of modules i and j, it is required that
		at least one of the following linear inequalities holds:

		Xi + Wi <= Xj; /* i is to the left of j */
		Xi - Wj >= Xj; /* i is to the right of j */
		Yi + Hi <= Yj; /* i is below j */
		Yi - Hj >= Yj; /* i is abover j */ (1)
		where Xi, Yi, Xj, Yj is the continuous variables denote the position
		of the lower left corners of the modules i and j with respect to the
		center of coordinates. Wi, Hi is the width and height of module i,
		which is known values.

		In order to ensure that at least on of above inequalities always holds
		we introduce two 0-1 integer variables XXiXj and YYiYj, now we consider
		the following system of linear inequalities for any pair of modules i and j:

		Xi + Wi <= Xj + W * ( XXiXj + YYiYj);
		Xi - Wj >= Xj - W * (1 - XXiXj + YYiYj);
		Yi + Hi <= Yj + H * (1 + XXiXj - YYiYj);
		Yi - Hj >= Yj - H * (2 - XXiXj - YYiYj); (2)
		where W = Sum(Wi), H = Sum(Hi).

		Assume that X_STAR and Y_STAR are the final width and height of the chip,
		we need to optimize the area X_STAR * Y_STAR. If we know the range of the
		aspect ratio of X_STAR and Y_STAR to be 0.85 to 1.15, we can linearize the
		quadratic problem to a linear problem:

		Minimize: 0.495 * X_STAR + 0.5014 * Y_STAR

		The additional constraints are:
		Xi >= 0, Yi >= 0,
		X_STAR >= Xi + Wi,
		Y_STAR >= Yi + Hi, for all modules. (3)

		The above is the first formulation of our problem. In order to achieve
		better floorplan, we allow the rotation of the blocks by introduce another
		0-1 integer variable Zi, where Zi = 0 when i block is placed in its initial
		orientation and Zi = 1 when block i is rotated 90 degree. The constraints (1)
		is rewritten in the following form:

		Xi + ZiHi + (1-Zi)Wi <= Xj + M*(XXiXj + YYiYj);
		Xi - ZjHj - (1-Zj)Wj >= Xj - M*(1 - XXiYj + YYiYj);
		Yi + ZiWi + (1-Zi)Hi <= Yj + M(1 + XXiXj - YYiYj);
		Yi - ZjWj - (1-Zj)Hj >= Yj - M(2 - XXiYj - YYiYj); (4)

		and the constraints (3) is rewritten as:

		Xi >= 0, Yi >= 0,
		Xi + (1 - Zi)Wi + ZiHi <= X_STAR,
		Yi + ZiWi + (1 - Zi)Hi <= Y_STAR, for all modules (5)

		Because we have the initial topology of the modules, we only allow the
		local modules to swap. So to local module pairs they have constraints (4),
		where there are two integer variables to ensure nonoverlapping.
		To the modules are very far away, their topology is fixed, which means these
		pairs of modules need only one of inequalities of (1) to guarantee the non-
		overlapping.

		To this problem formulation, I tried to come up a priority order of the integer
		variables. Because the position of a module if more important than the orientation
		of a module, I set all the XXiXj and YYiYj variables priority 5 and all Zi variables
		to the default value. But from the experiments I have done, I can't see any
		improvement.


		Xiaowen
		--
		Xiaowen Liu
		Electrial Engineering Bldg, Rm #329
		University of Washington
		Box 352500
		Seattle, WA 98195-2500
		Email: xiaowenl@twolf13.ee.washington.edu
		Tel: (206)685-8678 (O)

miplib2010_liu/models/liumip.dat

0 → 100644

+11 −0

Original line number	Diff line number	Diff line
		nbRects = 33;

		bigM = 8398;
		//bigM = 1200; // based on easily obtained feasible solution
		// with objective 1200

		width = [118,356,132,560,132,314,182,132,84,182,182,370,118,118,118,118,
		160,294,196,140,140,174,118,182,160,378,336,126,210,182,132,132,174];

		height = [84,118,140,132,314,140,350,294,118,202,202,182,118,126,336,266,
		118,118,118,496,406,118,48,118,140,118,132,378,210,98,314,230,132];

miplib2010_liu/models/liumip.mod

0 → 100644

+53 −0

Original line number	Diff line number	Diff line
		// MIP formulation of liu.lp

		int nbRects = ...;

		int bigM = ...;

		range
		Rectangles = 1..nbRects;

		int width[Rectangles] = ...;
		int height[Rectangles] = ...;

		int totwidth = sum(i in 1..nbRects) width[i];
		int totheight = sum (i in 1..nbRects) height[i];
		//int maxlength = totwidth*(totwidth > totheight) +
		// totheight*(totheight >= totwidth);


		dvar int+ x[Rectangles]; //in 0..maxlength;
		dvar int+ y[Rectangles]; //in 0..maxlength;

		dvar int+ ystar; // in 0..maxlength; // max (width, height) of resulting rectangle
		dvar int rotate[Rectangles] in 0..1;
		dvar int XX[Rectangles,Rectangles] in 0..1;
		dvar int YY[Rectangles,Rectangles] in 0..1;



		minimize
		ystar;
		subject to {

		// Forbid overlap of rectangles while allowing 90 degree rotations.

		forall(ordered i, j in Rectangles) {
		x[i] + rotate[i]height[i] + (1 - rotate[i])width[i] <=
		x[j] + bigM * (XX[i,j] + YY[i,j]);
		x[j] + rotate[j]height[j] + (1 - rotate[j])width[j] <=
		x[i] + bigM * (1 + YY[i,j] - XX[i,j]);
		y[i] + (1 - rotate[i])height[i] + rotate[i]width[i] <=
		y[j] + bigM * (1 + XX[i,j] - YY[i,j]);
		y[j] + (1 - rotate[j])height[j] + rotate[j]width[j] <=
		y[i] + bigM * (2 - (XX[i,j] + YY[i,j]));

		};

		// ystar must satisfy its description (see above).

		forall(i in Rectangles) {
		ystar >= x[i] + rotate[i]height[i] + (1 - rotate[i])width[i];
		ystar >= y[i] + rotate[i]width[i] + (1 - rotate[i])height[i];
		};
		};
		No newline at end of file