Related papers: Finding One Local Optimum Is Easy -- but What Abou…
In this paper, we study the complexity of computing locally optimal solutions for weighted versions of standard set problems such as SetCover, SetPacking, and many more. For our investigation, we use the framework of PLS, as defined in…
How hard is it to find a local optimum? If we are given a graph and want to find a locally maximal cut--meaning that the number of edges in the cut can't be improved by moving a single vertex from one side to the other--then just iterating…
Local search is a fundamental optimization technique that is both widely used in practice and deeply studied in theory, yet its computational complexity remains poorly understood. The traditional frameworks, PLS and the standard algorithm…
Our research deals with the optimization version of the set partition problem, where the objective is to minimize the absolute difference between the sums of the two disjoint partitions. Although this problem is known to be NP-hard and…
The properties of local optimal solutions in multi-objective combinatorial optimization problems are crucial for the effectiveness of local search algorithms, particularly when these algorithms are based on Pareto dominance. Such local…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
Large Neighborhood Search (LNS) is a common heuristic in combinatorial optimization that iteratively searches over a large neighborhood of the current solution for a better one. Recently, neural network-based LNS solvers have achieved great…
We propose a unifying framework for smoothed analysis of combinatorial local optimization problems, and show how a diverse selection of problems within the complexity class PLS can be cast within this model. This abstraction allows us to…
We consider the problem of finding a local optimum for Max-Cut with FLIP-neighborhood, in which exactly one node changes the partition. Schaeffer and Yannakakis (SICOMP, 1991) showed PLS-completeness of this problem on graphs with unbounded…
One powerful technique to solve NP-hard optimization problems in practice is branch-and-reduce search---which is branch-and-bound that intermixes branching with reductions to decrease the input size. While this technique is known to be very…
Combinatorial optimization problems are encountered in many practical contexts such as logistics and production, but exact solutions are particularly difficult to find and usually NP-hard for considerable problem sizes. To compute…
Combinatorial optimization problems implicitly define fitness landscapes that combine the numeric structure of the 'fitness' function to be maximized with the combinatorial structure of which assignments are 'adjacent'. Local search starts…
In this thesis, we settle the computational complexity of some fundamental questions in polynomial optimization. These include the questions of (i) finding a local minimum, (ii) testing local minimality of a point, and (iii) deciding…
Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
We show that the simplest local search heuristics for two natural Euclidean clustering problems are PLS-complete. First, we show that the Hartigan--Wong method for $k$-Means clustering is PLS-complete, even when $k = 2$. Second, we show the…
Local search has recently been applied to SMT problems over various arithmetic theories. Among these, nonlinear real arithmetic poses special challenges due to its uncountable solution space and potential need to solve higher-degree…
In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible…
We propose an innovative Parallel Quantum Local Search (PQLS) methodology that leverages the capabilities of small-scale quantum computers to efficiently address complex combinatorial optimization problems. Traditional Quantum Local Search…
In 1988, Johnson, Papadimitriou and Yannakakis wrote that "Practically all the empirical evidence would lead us to conclude that finding locally optimal solutions is much easier than solving NP-hard problems". Since then the empirical…