The progressive party problem: Integer linear programming and constraint programming compared

Abstract

Many discrete optimization problems can be formulated as either integer linear programming problems or constraint satisfaction problems. Although ILP methods appear to be more powerful, sometimes constraint programming can solve these problems more quickly. This paper describes a problem in which the difference in performance between the two approaches was particularly marked, since a solution could not be found using ILP.The problem arose in the context of organizing a "progressive party" at a yachting rally. Some yachts were to be designated hosts; the crews of the remaining yachts would then visit the hosts for six successive half-hour periods. A guest crew could not revisit the same host, and two guest crews could not meet more than once. Additional constraints were imposed by the capacities of the host yachts and the crew sizes of the guests.Integer linear programming formulations which included all the constraints resulted in very large models, and despite trying several different strategies, all attempts to find a solution failed. Constraint programming was tried instead and solved the problem very quickly, with a little manual assistance. Reasons for the success of constraint programming in this problem are identified and discussed.

Searching for Memories, Sudoku, Implicit Check Bits, and the Iterative Use of Not-Always-Correct Rapid Neural Computation

“…Such a neural network solves the problem through its state evolving (over time) from an initial condition describing the problem to a final stable state in which the answer can be read out from the activity level of the neurons. Inspired by the fact that some integer programming problems can be solved in a space of continuous variables [Smith 1996], we construct a linear programming network to solve the following problem Maximize E = Σ i,j,k V(i,j,k) (14) on continuous variables 0 ≤ V(i,j,k) with 324 linear constraints obtained by replacing the '=' in the integer programming version by '≤ '. The network contains 729 'V' neurons, with a semi-linear response, and 324 inhibitory constraint neurons, one for each inequality constraint.…”

Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems

“…However, since MILP requires solving an LP subproblem at each node of the search tree, all the constraints must be linear equalities or inequalities. This imposes a severe restriction on the expressiveness of MILP as a modeling language because for some problems, for example the progressive party problem (Smith et al 1997), modeling may require a very large number of variables and constraints. Since CP uses constraint propagation instead, it imposes no such restriction.…”

“…Recently, a number of papers have compared the performance of CP-and MILP-based approaches for solving a number of different problems, for example the modified generalized assignment problem (DarbyDowman et al 1997), the template design problem (Proll and Smith 1998), the progressive party problem (Smith et al 1997), and the change problem (Heipcke 1999a). Properties of a number of different problems were considered by Darby-Dowman and Little (1998), and their effect on the performance of CP and MILP approaches were presented.…”

Software engineering aspects of constraint-based timetabling—a case study

“…Then, instead of scheduling time slots for studentcourses, we can schedule sections to the student choice (assign one of the five sections to this choice), and time slots for sections (assign a time to each section, taking into consideration their assignments to student choices). It is widely believed that problem modeling may have a significant impact on search efficiency [8,46].…”