We　present　a　local　search　framework　to　design　and　analyze　both　combinatorial　algorithms　and　rounding　algorithms　for　experimental　design　problems.　This　framework　provides　a　unifying　approach　to　match　and　improve　all　known　results　in　D/A/E-design　and　to　obtain　new　results　in　previously　unknown　settings.　For　combinatorial　algorithms,　we　provide　a　new　analysis　of　the　classical　Fedorov＇s　exchange　method.　We　prove　that　this　simple　local　search　algorithm　works　well　as　long　as　there　exists　an　almost　optimal　solution　with　good　condition　number.　Moreover,　we　design　a　new　combinatorial　local　search　algorithm　for　E-design　using　the　regret　minimization　framework.　For　rounding　algorithms,　we　provide　a　unified　randomized　exchange　algorithm　to　match　and　improve　previous　results　for　D/A/E-design.　Furthermore,　the　algorithm　works　in　the　more　general　setting　to　approximately　satisfy　multiple　knapsack　constraints,　which　can　be　used　for　weighted　experimental　design　and　for　incorporating　fairness　constraints　into　experimental　design.　©　2022　Society　for　Industrial　and　Applied　Mathematics.