Alternative Integer linear and Quadratic Programming Formulations for HA-Assignment Problems

Abstract

Abstract. Home-Away Assignment problems are naturally cast as quadratic programming models in binary variables. In this work we compare alternative formulations. First, we propose another formulation by manipulating their special structure to obtain versions with 1/4 of the original size. By linearizing the quadratic objective function, we get two more alternative models to be compared with the quadratic ones. Numerical experiments exhibit the characteristics of each model. Palavras-chave.Sport scheduling, HA-assignment, Integer linear programming, Integer quadratic programming.

A Reduced Semidefinite Programming Formulation for HA Assignment Problems in Sport Scheduling

“…In this section we offer some computational experiments to compare the different studied models. At first, we deal with integer quadratic models, comparing the full sized and reduced versions, in a preliminary experiment, in part published at [10]. A more robust experiment is reported at the second part, comparing SDP relaxations for the HA-Assignment problem.…”

Solving large break minimization problems in a mirrored double round-robin tournament using quantum annealing

“…The break minimization problem in an RRT has been studied by many researchers [16,18,20]. In particular, De Werra and Dominique [28] proved that the number of breaks in an RRT is more than 2n − 2, and the number of breaks in an MDRRT is more than 6n − 6.…”

“…RRT, a DRRT, and an MDRRT. To solve this problem, constraint programming [17], integer programming [16,18], and an approximation algorithm [20] have been studied in the past. In recent years, Urdaneta et al [18] demonstrated, through numerical experiments that formulating the problem as an unconstrained quadratic integer programming problem and solving it using the mathematical optimization solver is superior to other formulations with constraints.…”

“…It has several practical constraints and splits into various combinatorial optimization problems [14,15]. Among them, in a round-robin tournament (RRT), where each team plays against every other team once, in a double round-robin tournament (DRRT), where each team plays against the others twice, and in a mirrored double round-robin tournament (MDRRT), which is a DRRT with the same combination of games in the first and second halves, much research has been conducted on the break minimization problem, which determines whether the game is held in the venue of the team, or its opponent [15][16][17][18][19][20][21]. RRTs, DRRTs, and MDRRTs are adopted in many professional sports, such as soccer and basketball [15,[22][23][24][25].…”

“…The break minimization problem is derived from practical requirements, and is known to be very difficult to solve. To address this problem, methods such as integer programming [16,18] and constraint programming [17] have been developed in the past.…”